diff options
Diffstat (limited to 'doc/design')
| -rw-r--r-- | doc/design/README | 25 | ||||
| -rw-r--r-- | doc/design/all | 58 | ||||
| -rw-r--r-- | doc/design/mydefs | 591 | ||||
| -rw-r--r-- | doc/design/outfile.ps | 11727 | ||||
| -rw-r--r-- | doc/design/s1_0 | 45 | ||||
| -rw-r--r-- | doc/design/s2_0 | 14 | ||||
| -rw-r--r-- | doc/design/s2_1 | 87 | ||||
| -rw-r--r-- | doc/design/s2_2 | 79 | ||||
| -rw-r--r-- | doc/design/s2_3 | 326 | ||||
| -rw-r--r-- | doc/design/s2_4 | 345 | ||||
| -rw-r--r-- | doc/design/s2_5 | 90 | ||||
| -rw-r--r-- | doc/design/s2_9 | 2 | ||||
| -rw-r--r-- | doc/design/s3_0 | 10 | ||||
| -rw-r--r-- | doc/design/s3_1 | 76 | ||||
| -rw-r--r-- | doc/design/s3_2 | 113 | ||||
| -rw-r--r-- | doc/design/s3_3 | 143 | ||||
| -rw-r--r-- | doc/design/s3_4 | 51 | ||||
| -rw-r--r-- | doc/design/s3_9 | 2 | ||||
| -rw-r--r-- | doc/design/s4_0 | 88 | ||||
| -rw-r--r-- | doc/design/s5_0 | 11 | ||||
| -rw-r--r-- | doc/design/s5_1 | 123 | ||||
| -rw-r--r-- | doc/design/s5_2 | 372 | ||||
| -rw-r--r-- | doc/design/s5_3 | 125 | ||||
| -rw-r--r-- | doc/design/s5_4 | 97 | ||||
| -rw-r--r-- | doc/design/s5_5 | 109 | ||||
| -rw-r--r-- | doc/design/s5_9 | 2 | ||||
| -rw-r--r-- | doc/design/s6_0 | 18 | ||||
| -rw-r--r-- | doc/design/s6_1 | 85 | ||||
| -rw-r--r-- | doc/design/s6_2 | 79 | ||||
| -rw-r--r-- | doc/design/s6_9 | 2 | ||||
| -rw-r--r-- | doc/design/s7_0 | 84 |
31 files changed, 14979 insertions, 0 deletions
diff --git a/doc/design/README b/doc/design/README new file mode 100644 index 0000000..1e7a8af --- /dev/null +++ b/doc/design/README @@ -0,0 +1,25 @@ +Directory lout/doc/design + +This directory contains the Lout source files +for the report entitled `The design and +implementation of the Lout document formatting +language' which appeared in Software--Practice +and Experience, vol 23, pp1001-1041 (September +1993). To produce the report, type the command + + lout all > outfile.ps + +in this directory. This must be done three +times to completely resolve all cross references, +although the PostScript file outfile.ps is +printable after the first run. Auxiliary files +with .li and .ld suffixes will be created in +this directory. A copy of the final outfile.ps +is included. + +The second and third runs should produce no error +messages (although changing the paper size might +produce one or two benign ones). + +Jeffrey H. Kingston +17 September 1999 diff --git a/doc/design/all b/doc/design/all new file mode 100644 index 0000000..2755e5b --- /dev/null +++ b/doc/design/all @@ -0,0 +1,58 @@ +@SysInclude { eq } +@SysInclude { tab } +@SysInclude { fig } +@SysInclude { report } +@SysDatabase @Reference { oldrefs } +@Report + @Title { The Design and Implementation +of the +Lout Document Formatting Language } + @Author { Jeffrey H. Kingston } + @Institution { Basser Department of Computer Science, +The University of Sydney 2006, +Australia } + @DateLine { 27 January, 1993 } + @InitialLanguage { English } + @OptimizePages { Yes } + @AbstractTitle { SUMMARY } + @Abstract +{ +Lout is a high-level language for document formatting, whose ease of use +has permitted an unprecedented number of advanced features to be added +quickly and reliably. This paper charts the evolution of the design and +implementation of Lout from conception in mid-1984 to public release in +October 1991. It includes extensive discussions of remaining problems +and possible solutions. +@DP +{@B Keywords} document formatting typesetting +} + +// + +@Include { s1_0 } +@Include { s2_0 } +@Include { s2_1 } +@Include { s2_2 } +@Include { s2_3 } +@Include { s2_4 } +@Include { s2_5 } +@Include { s2_9 } +@Include { s3_0 } +@Include { s3_1 } +@Include { s3_2 } +@Include { s3_3 } +@Include { s3_4 } +@Include { s3_9 } +@Include { s4_0 } +@Include { s5_0 } +@Include { s5_1 } +@Include { s5_2 } +@Include { s5_3 } +@Include { s5_4 } +@Include { s5_5 } +@Include { s5_9 } +@Include { s6_0 } +@Include { s6_1 } +@Include { s6_2 } +@Include { s6_9 } +@Include { s7_0 } diff --git a/doc/design/mydefs b/doc/design/mydefs new file mode 100644 index 0000000..5473fbf --- /dev/null +++ b/doc/design/mydefs @@ -0,0 +1,591 @@ + +def @TeX { T{ /0.2fo E}X } + +def @Code + right x +{ { Helvetica Base -1p } @Font lines @Break x +} + +###################################################### +# # +# Nodes and trees. # +# # +###################################################### + +import @Fig +def @FBox + named width { 0.6c } + named height { 0.4c } + named margin { 0.1c } + right x +{ + @Box margin { margin } + { width @Wide height @High + { /0.5rt |0.5rt @OneCol @OneRow 0.8f @Font x + } + } +} + +import @Fig +def @FEllipse + named width { 0.6c } + named height { 0.4c } + named margin { 0.1c } + right x +{ + @Ellipse margin { margin } + { height @High + { /0.5rt |0.5rt @OneCol @OneRow 0.8f @Font x + } + } +} + +import @Fig +def @FCircle + named width { 0.4c } + named height { 0.4c } + named margin { 0.1c } + right x +{ + @Circle margin { margin } + { width @Wide height @High + { /0.5rt |0.5rt @OneCol @OneRow 0.8f @Font x + } + } +} + +import @Fig +def @JoinFigures + left A + named linestyle { solid } + named linewidth { 0.5 pt } + named linecap { round } + named dashlength { 0.15 cm } + named arrow { noarrow } + named headstyle { open } + named headwidth { 0.05 cm } + named headlength { 0.15 cm } + right B +{ + @Line + from { {A"@CTR"} ++ {{A"@CTR"} @Angle {B"@CTR"} A"@CIRCUM"} } + to { {B"@CTR"} ++ {{B"@CTR"} @Angle {A"@CTR"} B"@CIRCUM"} } + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + arrow { arrow } + headstyle { headstyle } + headwidth { headwidth } + headlength { headlength } + {} +} + +import @Fig +export @LeftSub @RightSub @FirstSub @NextSub @StubSub @Node +def @Tree + named hmargin { 0.2c } + named vmargin { 0.3c } + named linestyle { solid } + named linewidth { 0.5 pt } + named linecap { round } + named dashlength { 0.15 cm } + named arrow { noarrow } + named headstyle { open } + named headwidth { 0.05 cm } + named headlength { 0.15 cm } + body x +@Begin + + def @LeftSub + precedence 90 + associativity left + left root + named hmargin { hmargin } + named linestyle { linestyle } + named linewidth { linewidth } + named linecap { linecap } + named dashlength { dashlength } + named arrow { arrow } + named headstyle { headstyle } + named headwidth { headwidth } + named headlength { headlength } + right x + { + { /vmargin {L::x} } |hmargin root | + L@T @JoinFigures + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + arrow { arrow } + headstyle { headstyle } + headwidth { headwidth } + headlength { headlength } + T + } + + def fixroot + precedence 90 + left root + { + |0.5rt root + } + + def firstsub + precedence 90 + associativity left + named hmargin { hmargin } + named linestyle { linestyle } + named linewidth { linewidth } + named linecap { linecap } + named dashlength { dashlength } + named arrow { arrow } + named headstyle { headstyle } + named headwidth { headwidth } + named headlength { headlength } + right x + { + S::x & + S@T @JoinFigures + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + arrow { arrow } + headstyle { headstyle } + headwidth { headwidth } + headlength { headlength } + T + } + + macro @FirstSub { fixroot //vmargin |0.5rt firstsub } + + def @NextSub + precedence 90 + associativity left + left others + named hmargin { hmargin } + named linestyle { linestyle } + named linewidth { linewidth } + named linecap { linecap } + named dashlength { dashlength } + named arrow { arrow } + named headstyle { headstyle } + named headwidth { headwidth } + named headlength { headlength } + right x + { + others &hmargin S::x & + S@T @JoinFigures + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + arrow { arrow } + headstyle { headstyle } + headwidth { headwidth } + headlength { headlength } + T + } + + def @RightSub + precedence 90 + associativity left + left root + named hmargin { hmargin } + named linestyle { linestyle } + named linewidth { linewidth } + named linecap { linecap } + named dashlength { dashlength } + named arrow { arrow } + named headstyle { headstyle } + named headwidth { headwidth } + named headlength { headlength } + right x + { + root |hmargin { /vmargin {R::x} } | + R@T @JoinFigures + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + arrow { arrow } + headstyle { headstyle } + headwidth { headwidth } + headlength { headlength } + T + } + + def @StubSub + precedence 90 + associativity left + left root + named linestyle { linestyle } + named linewidth { linewidth } + named linecap { linecap } + named dashlength { dashlength } + { + root | + @Figure + shape { T@SW + T@W -- { 0.1 cm 0.7 cm } + T@E -- {-0.1 cm 0.7 cm } + T@SE + } + linestyle { linestyle } + linewidth { linewidth } + linecap { linecap } + dashlength { dashlength } + { @Null } + } + + def @Node + # named mark {} + right root + { + T:: root + # & T@W ++ { -0.2 cm 0.1 cm } @BaseOf mark + } + + @OneCol @OneRow x + +@End @Tree + + +def @ShowMarks + named linewidth { 0.015 cm } + named linestyle { dashed } + named dashlength { 0.15 cm } + named paint { lightgrey } + named marks { both } # none, horizontal, vertical, or both + right x +{ + @Fig + { @Box margin { 0c } linewidth { linewidth } paint { paint } + { @Figure + shape { + marks @Case { + { horizontal both } @Yield + { -0.3 cm ymark {xsize ymark} ++ {0.3 cm 0} } + else @Yield {} + } + marks @Case { + both @Yield [] + else @Yield {} + } + marks @Case { + { vertical both } @Yield + { xmark -0.3 cm {xmark ysize} ++ {0 0.3 cm} } + else @Yield {} + } + } + linewidth { linewidth } + linestyle { linestyle } + dashlength { dashlength } + x + } + } +} + + import @Fig + def @DagBox + named top {} + named mid {} + named base {} + { + @OneRow { + TOP:: @FBox top + // MID:: @FBox mid + // BASE:: @FBox base + } + } + + import @Fig + def @BlackDot + named diameter { 0.07c } + { + @Circle + margin { 0c } + paint { black } + { diameter @Wide diameter @High {} + } + } + + import @Fig + def @TVShape # television shape enclosing points ne, nw, se, sw + named nw {} + named ne {} + named sw {} + named se {} + named delta { 0.5 cm } + { + @Figure + shape { + { {nw @Min sw @Min ne @Min se} -- { delta 0 } } @Label BL + { {nw @Max sw @Max ne @Max se} ++ { delta 0 } } @Label TR + BL ++ { 0 BL @YDistance TR } @Label TL + BL ++ { BL @XDistance TR 0 } @Label BR + BL + BR [ BR ++ {0 delta} ] + BR ++ {delta delta} + TR ++ {delta -delta} [ TR -- {0 delta} ] + TR + TL [ TL -- {0 delta} ] + TL -- {delta delta} + BL ++ {-delta delta} [ BL ++ {0 delta} ] + BL + } + {} + } + + import @Fig + def @FunnyArrow + named from {} + named to {} + named arrow { forward } + { + @Figure + shape {from from ++ {0 from @YDistance to} to} + arrow { arrow } + {} + } + + def "->" { {Symbol Base} @Font "\256" } #174 decimal + def "=>" { {Symbol Base} @Font "\336" } #222 decimal + macro @JP { /0.5v } + + ################################################### + # # + # Lout keywords. # + # # + ################################################### + + def @@Begin { @Code "@Begin" } + def @@Break { @Code "@Break" } + def @@Case { @Code "@Case" } + def @@Database { @Code "@Database" } + def @@End { @Code "@End" } + def @@Font { @Code "@Font" } + def @@Galley { @Code "@Galley" } + def @@Graphic { @Code "@Graphic" } + def @@HExpand { @Code "@HExpand" } + def @@HScale { @Code "@HScale" } + def @@High { @Code "@High" } + def @@Include { @Code "@Include" } + def @@Key { @Code "@Key" } + def @@LClos { @Code "@LClos" } + def @@LEnv { @Code "@LEnv" } + def @@LInput { @Code "@LInput" } + def @@Moment { @Code "@Moment" } + def @@Next { @Code "@Next" } + def @@Null { @Code "@Null" } + def @@OneCol { @Code "@OneCol" } + def @@OneRow { @Code "@OneRow" } + def @@Open { @Code "@Open" } + def @@Prepend { @Code "@Prepend" } + def @@Rotate { @Code "@Rotate" } + def @@Space { @Code "@Space" } + def @@SysDatabase { @Code "@SysDatabase" } + def @@SysInclude { @Code "@SysInclude" } + def @@SysPrepend { @Code "@SysPrepend" } + def @@Tag { @Code "@Tag" } + def @@Tagged { @Code "@Tagged" } + def @@Use { @Code "@Use" } + def @@VExpand { @Code "@VExpand" } + def @@VScale { @Code "@VScale" } + def @@Yield { @Code "@Yield" } + def @@Wide { @Code "@Wide" } + + + ################################################### + # # + # Miscellaneous, mostly graphical definitions. # + # # + ################################################### + + def @Leaders + { .. @Leaders + } + + def @HLine { + @BackEnd @Case { + PostScript @Yield { + { 0 0 moveto xsize 0 lineto stroke } + @Graphic {} + } + PDF @Yield { + { 0 0 m __xsize 0 l S } + @Graphic {} + } + } + } + + def @VDashLine + right length + { + @BackEnd @Case { + PostScript @Yield { + length @High + { 0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke } + @Graphic {} + } + PDF @Yield { + length @High + { [ __mul(3, __pt) ] 0 d 0 0 m 0 __ysize l stroke } + @Graphic {} + } + } + } + + def @LBox + right offset + { + @BackEnd @Case { + PostScript @Yield { + @OneCol @OneRow + { + { //0.2c + 0.6c @High 1.2c @Wide + { 0 0 moveto xsize 0 lineto + xsize ysize lineto 0 ysize lineto closepath + gsave 0.9 setgray fill grestore stroke } + @Graphic {} + } + ||offset @VDashLine 1c + } + } + PDF @Yield { + @OneCol @OneRow + { + { //0.2c + 0.6c @High 1.2c @Wide + { 0 0 m __xsize 0 l + __xsize __ysize l 0 __ysize l h + q 0.9 g f Q S } + @Graphic {} + } + ||offset @VDashLine 1c + } + } + } + } + + def @Arrow + right length + { @OneCol @OneRow + { + 30d @Rotate {0.12c @Wide @HLine} + // + length @Wide @HLine + // + "-30d" @Rotate {0.12c @Wide @HLine} + } + } + + def @DoubleArrow + right length + { @OneCol @OneRow + { + & 180d @Rotate @Arrow length + |0io @Arrow length + } + } + + def @Put + left coord + right x + { @OneCol @OneRow + { coord / | @OneCol @OneRow x + } + } + + macro @At { //0io } + + + ################################################### + # # + # Interpolated example documents. # + # # + ################################################### + + def @LittleEndRunPlace { @Galley } + def @LittleEndRun + force into { @LittleEndRunPlace&&preceding } + {} + + def @LittleTextPlace { @Galley } + def @LittleText into { @LittleTextPlace&&preceding } + right x + { x + } + + def @LittleFootPlace { @Galley } + def @LittleFootNote into { @LittleFootPlace&&following } + right x + { x + } + + def @LittlePageColumn + right x + { + 9px @Break 8p @Font + 2.8c @Wide x + } + + def @LittlePage + right x + { + @BackEnd @Case { + PostScript @Yield { + @HContract @VContract + { 0 0 moveto xsize 0 lineto xsize ysize lineto + 0 ysize lineto closepath stroke } @Graphic + { //0.3c ||0.3c + 9px @Break 8p @Font + 2.8c @Wide 3.8c @High x + ||0.3c //0.3c + } + } + PDF @Yield { + @HContract @VContract + { 0 0 m __xsize 0 l __xsize __ysize l 0 __ysize l s } @Graphic + { //0.3c ||0.3c + 9px @Break 8p @Font + 2.8c @Wide 3.8c @High x + ||0.3c //0.3c + } + } + } + } + + def @LittleFootSect + { 1c @Wide @HLine + //0.3v @LittleFootPlace ||0.5c + } + + def @LittlePageList + right @PageNum + { + @LittlePage { # |0.5rt @PageNum //0.8v + //0.3v @LittleTextPlace + //1rt @LittleFootSect + } + // + @LittlePageList @Next @PageNum + } + + def @LittleDocument + { @LittlePage + { @LittleTextPlace + //1rt @LittleFootSect + } + // @LittlePageList 2 + // @LittleEndRunPlace + } + + def @Strange + named @Format right @Val { [@Val] } + right x + { @Format x + } diff --git a/doc/design/outfile.ps b/doc/design/outfile.ps new file mode 100644 index 0000000..3f7525a --- /dev/null +++ b/doc/design/outfile.ps @@ -0,0 +1,11727 @@ +%!PS-Adobe-3.0 +%%Creator: Basser Lout Version 3.17 (September 1999) +%%CreationDate: Fri Sep 17 11:56:58 1999 +%%DocumentData: Binary +%%DocumentNeededResources: (atend) +%%DocumentMedia: Plain 595 842 0 white () +%%DocumentSuppliedResources: (atend) +%%Pages: (atend) +%%BoundingBox: 0 0 595 842 +%%EndComments + +%%BeginProlog +%%BeginResource: procset LoutStartUp +/m { 3 1 roll moveto show } bind def +/s { exch currentpoint exch pop moveto show } bind def +/k { exch neg 0 rmoveto show } bind def +/ul { gsave setlinewidth dup 3 1 roll + moveto lineto stroke grestore } bind def +/in { 1440 mul } def +/cm { 567 mul } def +/pt { 20 mul } def +/em { 120 mul } def +/sp { louts mul } def +/vs { loutv mul } def +/ft { loutf mul } def +/dg { } def + +/LoutGraphic { + /louts exch def + /loutv exch def + /loutf exch def + /ymark exch def + /xmark exch def + /ysize exch def + /xsize exch def +} def + +/LoutGr2 { gsave translate LoutGraphic gsave } def + +/LoutFont +{ findfont exch scalefont setfont +} bind def + +/LoutRecode { + { findfont dup length dict begin + {1 index /FID ne {def} {pop pop} ifelse} forall + /Encoding exch def + currentdict end definefont pop + } + stopped pop +} bind def + +/BeginEPSF { + /LoutEPSFState save def + /dict_count countdictstack def + /op_count count 1 sub def + userdict begin + /showpage { } def + 0 setgray 0 setlinecap + 1 setlinewidth 0 setlinejoin + 10 setmiterlimit [] 0 setdash newpath + /languagelevel where + { pop languagelevel + 1 ne + { false setstrokeadjust false setoverprint + } if + } if +} bind def + +/EndEPSF { + count op_count sub { pop } repeat + countdictstack dict_count sub { end } repeat + LoutEPSFState restore +} bind def +%%EndResource + +%%BeginResource encoding vec2 +/vec2 [ +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright +/parenleft /parenright /asterisk /plus /comma /hyphen /period /slash +/zero /one /two /three /four /five /six /seven +/eight /nine /colon /semicolon /less /equal /greater /question +/at /A /B /C /D /E /F /G +/H /I /J /K /L /M /N /O +/P /Q /R /S /T /U /V /W +/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore +/quoteleft /a /b /c /d /e /f /g +/h /i /j /k /l /m /n /o +/p /q /r /s /t /u /v /w +/x /y /z /braceleft /bar /braceright /asciitilde /.notdef +/quotesinglbase /quotedblbase /ellipsis /OE /oe /quotedblleft /quotedblright /fi +/fl /endash /emdash /bullet /dagger /daggerdbl /florin /fraction +/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent +/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron +/space /exclamdown /cent /sterling /currency /yen /brokenbar /section +/dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron +/degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered +/cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown +/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla +/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis +/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply +/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls +/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla +/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis +/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide +/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis +] def +%%EndResource + +%%BeginResource: procset LoutTabPrependGraphic +% @PrependGraphic file /usr/staff/jeff/lout.lib/include/tabf.lpg +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% PostScript @SysPrependGraphic file for @Tab % +% % +% To assist in avoiding name clashes, the names % +% of all these symbols begin with "ltab". % +% % +% Jeffrey H. Kingston % +% 24 September 1991 % +% 22 December 1992 % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% linewidth ltabhs - +% horizontal single line +/ltabhs +{ 0 0 moveto xsize 0 lineto + setlinewidth 0 setlinecap stroke +} def + +% linewidth ltabhsp - +% horizontal single line with projecting ends +/ltabhsp +{ 0 0 moveto xsize 0 lineto + setlinewidth 2 setlinecap stroke +} def + +% linewidth ltabhd - +% horizontal double line +/ltabhd +{ dup dup + 0 0 moveto xsize 0 lineto + 0 exch 3 mul moveto xsize exch 3 mul lineto + setlinewidth 0 setlinecap stroke +} def + +% linewidth ltabhdb - +% horizontal double line below mark +/ltabhdb +{ dup dup + 0 0 moveto xsize 0 lineto + 0 exch -3 mul moveto xsize exch -3 mul lineto + setlinewidth 0 setlinecap stroke +} def + +% linewidth ltabhdnw - +% horizontal double line with northwest corner +/ltabhdnw +{ dup dup dup dup + 0 0 moveto xsize 0 lineto + xsize exch 3 mul moveto + -3 mul exch 3 mul lineto + -3 mul 0 lineto + setlinewidth 0 setlinejoin 2 setlinecap stroke +} def + +% linewidth ltabhdne - +% horizontal double line with northeast corner +/ltabhdne +{ dup dup dup dup + 0 0 moveto xsize 0 lineto + 0 exch 3 mul moveto + 3 mul xsize add exch 3 mul lineto + 3 mul xsize add 0 lineto + setlinewidth 0 setlinejoin 2 setlinecap stroke +} def + +% linewidth ltabhdsw - +% horizontal double line with southwest corner +/ltabhdsw +{ dup dup dup dup + 0 0 moveto xsize 0 lineto + xsize exch -3 mul moveto + -3 mul exch -3 mul lineto + -3 mul 0 lineto + setlinewidth 0 setlinejoin 2 setlinecap stroke +} def + +% linewidth ltabhdse - +% horizontal double line with southeast corner +/ltabhdse +{ dup dup dup dup + 0 0 moveto xsize 0 lineto + 0 exch -3 mul moveto + 3 mul xsize add exch -3 mul lineto + 3 mul xsize add 0 lineto + setlinewidth 0 setlinejoin 2 setlinecap stroke +} def + +% linewidth ltabvs - +% vertical single line +/ltabvs +{ 0 0 moveto 0 ysize lineto + setlinewidth 0 setlinecap stroke +} def + +% linewidth ltabvd - +% vertical double line +/ltabvd +{ dup dup + 0 0 moveto 0 ysize lineto + -3 mul 0 moveto -3 mul ysize lineto + setlinewidth 0 setlinecap stroke +} def + +% linewidth ltabvdr - +% vertical double line to right of mark +/ltabvdr +{ dup dup + 0 0 moveto 0 ysize lineto + 3 mul 0 moveto 3 mul ysize lineto + setlinewidth 0 setlinecap stroke +} def +%%EndResource + +%%BeginResource: procset LoutFigPrependGraphic +% @PrependGraphic file /usr/staff/jeff/lout.lib/include/figf.lpg +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% PostScript @SysPrependGraphic file for @Fig Jeffrey H. Kingston % +% Version 2.0 (includes CIRCUM label) January 1992 % +% % +% To assist in avoiding name clashes, the names of all symbols % +% defined here begin with "lfig". However, this is not feasible % +% with user-defined labels and some labels used by users. % +% % +% <point> is two numbers, a point. % +% <length> is one number, a length % +% <angle> is one number, an angle in degrees % +% <dashlength> is one number, the preferred length of a dash % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +errordict begin + /handleerror + { + { /Times-Roman findfont 8 pt scalefont setfont + 0 setgray 4 pt 4 pt moveto + $error /errorname get + dup lfigdict exch known + { lfigdict exch get } + { 30 string cvs } ifelse + show + ( Command: ) show + $error /command get 30 string cvs show + } stopped {} if + showpage stop + } def +end + +% concat strings: <string> <string> lfigconcat <string> +% must be defined outside lfigdict since used in lfigpromotelabels +/lfigconcat +{ 2 copy length exch length add string + dup 0 4 index putinterval + dup 3 index length 3 index putinterval + 3 1 roll pop pop +} def + +% <string> lfigdebugprint - +% must be defined outside lfigdict since used in arbitrary places +% /lfigdebugprint +% { print +% (; operand stack:\n) print +% count copy +% count 2 idiv +% { == +% (\n) print +% } repeat +% (\n) print +% } def + +/lfigdict 120 dict def +lfigdict begin + +% error messages +/dictfull (dictfull error: too many labels?) def +/dictstackoverflow (dictstackoverflow error: labels nested too deeply?) def +/execstackoverflow (execstackoverflow error: figure nested too deeply?) def +/limitcheck (limitcheck error: figure nested too deeply or too large?) def +/syntaxerror (syntaxerror error: syntax error in text of figure?) def +/typecheck (typecheck error: syntax error in text of figure?) def +/undefined (undefined error: unknown or misspelt label?) def +/VMError (VMError error: run out of memory?) def + +% push pi onto stack: - lfigpi <num> +/lfigpi 3.14159 def + +% arc directions +/clockwise false def +/anticlockwise true def + +% maximum of two numbers: <num> <num> lfigmax <num> +/lfigmax { 2 copy gt { pop } { exch pop } ifelse } def + +% minimum of two numbers: <num> <num> lfigmin <num> +/lfigmin { 2 copy lt { pop } { exch pop } ifelse } def + +% add two points: <point> <point> lfigpadd <point> +/lfigpadd { exch 3 1 roll add 3 1 roll add exch } def + +% subtract first point from second: <point> <point> lfigpsub <point> +/lfigpsub { 3 2 roll sub 3 1 roll exch sub exch } def + +% max two points: <point> <point> lfigpmax <point> +/lfigpmax { exch 3 1 roll lfigmax 3 1 roll lfigmax exch } def + +% min two points: <point> <point> lfigpmin <point> +/lfigpmin { exch 3 1 roll lfigmin 3 1 roll lfigmin exch } def + +% scalar multiplication: <point> <num> lfigpmul <point> +/lfigpmul { dup 3 1 roll mul 3 1 roll mul exch } def + +% point at angle and distance: <point> <length> <angle> lfigatangle <point> +/lfigatangle { 2 copy cos mul 3 1 roll sin mul lfigpadd } def + +% angle from one point to another: <point> <point> lfigangle <angle> +/lfigangle { lfigpsub 2 copy 0 eq exch 0 eq and {pop} {exch atan} ifelse } def + +% distance between two points: <point> <point> lfigdistance <length> +/lfigdistance { lfigpsub dup mul exch dup mul add sqrt } def + +% difference in x coords: <point> <point> lfigxdistance <length> +/lfigxdistance { pop 3 1 roll pop sub } def + +%difference in y coords: <point> <point> lfigydistance <length> +/lfigydistance { 3 1 roll pop sub exch pop } def + +% stroke a solid line: <length> <dashlength> lfigsolid - +/lfigsolid +{ pop pop [] 0 setdash stroke +} def + +% stroke a lfigdashed line: <length> <dashlength> lfigdashed - +/lfigdashed +{ 2 copy div 2 le 1 index 0 le or + { exch pop 1 pt lfigmax [ exch dup ] 0 setdash } + { dup [ exch 4 2 roll 2 copy div + 1 sub 2 div ceiling dup 4 1 roll + 1 add mul sub exch div ] 0 setdash + } ifelse stroke +} def + +% stroke a lfigcdashed line: <length> <dashlength> lfigcdashed - +/lfigcdashed +{ 2 copy le 1 index 0 le or + { exch pop 1 pt lfigmax [ exch dup ] dup 0 get 2 div setdash } + { dup [ 4 2 roll exch 2 copy exch div + 2 div ceiling div 1 index sub + ] exch 2 div setdash + } ifelse stroke +} def + +% stroke a dotted line: <length> <dashlength> lfigdotted - +/lfigdotted +{ 2 copy le 1 index 0 le or + { exch pop 1 pt lfigmax [ exch 0 exch ] 0 setdash } + { 1 index exch div ceiling div + [ 0 3 2 roll ] 0 setdash + } ifelse stroke +} def + +% stroke a noline line: <length> <dashlength> lfignoline - +/lfignoline +{ pop pop +} def + +% painting (i.e. filling): - lfigwhite - (etc.) +/lfignopaint { } def +/lfignochange { fill } def +/lfigdarkblue { 0.0 0.0 0.5 setrgbcolor fill } def +/lfigblue { 0.0 0.0 1.0 setrgbcolor fill } def +/lfiglightblue { 0.5 0.5 1.0 setrgbcolor fill } def +/lfigdarkgreen { 0.0 0.5 0.0 setrgbcolor fill } def +/lfiggreen { 0.0 1.0 0.0 setrgbcolor fill } def +/lfiglightgreen { 0.5 1.0 0.5 setrgbcolor fill } def +/lfigdarkred { 0.5 0.0 0.0 setrgbcolor fill } def +/lfigred { 1.0 0.0 0.0 setrgbcolor fill } def +/lfiglightred { 1.0 0.5 0.5 setrgbcolor fill } def +/lfigdarkcyan { 0.0 0.5 0.5 setrgbcolor fill } def +/lfigcyan { 0.0 1.0 1.0 setrgbcolor fill } def +/lfiglightcyan { 0.5 1.0 1.0 setrgbcolor fill } def +/lfigdarkmagenta { 0.5 0.0 0.5 setrgbcolor fill } def +/lfigmagenta { 1.0 0.0 1.0 setrgbcolor fill } def +/lfiglightmagenta { 1.0 0.5 1.0 setrgbcolor fill } def +/lfigdarkyellow { 0.5 0.5 0.0 setrgbcolor fill } def +/lfigyellow { 1.0 1.0 0.0 setrgbcolor fill } def +/lfiglightyellow { 1.0 1.0 0.5 setrgbcolor fill } def +/lfigdarkgray { 0.2 0.2 0.2 setrgbcolor fill } def +/lfiggray { 0.5 0.5 0.5 setrgbcolor fill } def +/lfiglightgray { 0.8 0.8 0.8 setrgbcolor fill } def +/lfigdarkgrey { 0.2 0.2 0.2 setrgbcolor fill } def +/lfiggrey { 0.5 0.5 0.5 setrgbcolor fill } def +/lfiglightgrey { 0.8 0.8 0.8 setrgbcolor fill } def +/lfigblack { 0.0 0.0 0.0 setrgbcolor fill } def +/lfigwhite { 1.0 1.0 1.0 setrgbcolor fill } def + +% line caps (and joins, not currently used) +/lfigbutt 0 def +/lfiground 1 def +/lfigprojecting 2 def +/lfigmiter 0 def +/lfigbevel 2 def + +% shape and labels of the @Box symbol +/lfigbox +{ + 0 0 /SW lfigpointdef + xsize 0 /SE lfigpointdef + xsize ysize /NE lfigpointdef + 0 ysize /NW lfigpointdef + SE 0.5 lfigpmul /S lfigpointdef + NW 0.5 lfigpmul /W lfigpointdef + W SE lfigpadd /E lfigpointdef + S NW lfigpadd /N lfigpointdef + NE 0.5 lfigpmul /CTR lfigpointdef + [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef + SW SE NE NW SW +} def + +% shape and labels of the @CurveBox symbol +/lfigcurvebox +{ + + xsize 0.5 mul ysize 0.5 mul /CTR lfigpointdef + xsize 0.5 mul 0 /S lfigpointdef + xsize ysize 0.5 mul /E lfigpointdef + xsize 0.5 mul ysize /N lfigpointdef + 0 ysize 0.5 mul /W lfigpointdef + + xmark 0.293 mul xmark 0.293 mul /SW lfigpointdef + xsize xmark 0.293 mul sub xmark 0.293 mul /SE lfigpointdef + xsize xmark 0.293 mul sub ysize xmark 0.293 mul sub /NE lfigpointdef + xmark 0.293 mul ysize xmark 0.293 mul sub /NW lfigpointdef + + [ xsize ysize 0.5 lfigpmul xmark /lfigcurveboxcircum cvx ] lfigcircumdef + + xmark 0 + xsize xmark sub 0 + [ xsize xmark sub xmark ] + xsize xmark + xsize ysize xmark sub + [ xsize xmark sub ysize xmark sub ] + xsize xmark sub ysize + xmark ysize + [ xmark ysize xmark sub ] + 0 ysize xmark sub + 0 xmark + [ xmark xmark ] + xmark 0 +} def + +% shadow of the @ShadowBox symbol +% its shape and labels are done, somewhat inaccurately, with lfigbox +/lfigshadow +{ xmark 2 mul 0 moveto xsize 0 lineto + xsize ysize xmark 2 mul sub lineto + xsize xmark sub ysize xmark 2 mul sub lineto + xsize xmark sub xmark lineto + xmark 2 mul xmark lineto closepath fill +} def + +% shape and labels of the @Square symbol +/lfigsquare +{ + xsize ysize 0.5 lfigpmul /CTR lfigpointdef + CTR xsize xsize ysize ysize lfigpmax 0.5 lfigpmul lfigpadd /NE lfigpointdef + CTR 0 0 CTR NE lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef + CTR 0 0 CTR NE lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef + CTR 0 0 CTR NE lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef + SW 0.5 lfigpmul SE 0.5 lfigpmul lfigpadd /S lfigpointdef + NW 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /N lfigpointdef + SW 0.5 lfigpmul NW 0.5 lfigpmul lfigpadd /W lfigpointdef + SE 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /E lfigpointdef + [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef + SW SE NE NW SW +} def + +% shape and labels of the @Diamond symbol +/lfigdiamond +{ + xsize 0 0.5 lfigpmul /S lfigpointdef + 0 ysize 0.5 lfigpmul /W lfigpointdef + S W lfigpadd /CTR lfigpointdef + CTR W lfigpadd /N lfigpointdef + CTR S lfigpadd /E lfigpointdef + [ xsize ysize 0.5 lfigpmul /lfigdiamondcircum cvx ] lfigcircumdef + S E N W S +} def + +% shape and labels of the @Ellipse symbol +/lfigellipse +{ + xsize 0 0.5 lfigpmul /S lfigpointdef + 0 ysize 0.5 lfigpmul /W lfigpointdef + S W lfigpadd /CTR lfigpointdef + CTR W lfigpadd /N lfigpointdef + CTR S lfigpadd /E lfigpointdef + CTR xsize 0 0.3536 lfigpmul lfigpadd 0 ysize 0.3536 lfigpmul lfigpadd /NE lfigpointdef + 0 ysize 0.3536 lfigpmul CTR xsize 0 0.3536 lfigpmul lfigpadd lfigpsub /SE lfigpointdef + xsize 0 0.3536 lfigpmul CTR lfigpsub 0 ysize 0.3536 lfigpmul lfigpadd /NW lfigpointdef + 0 ysize 0.3536 lfigpmul xsize 0 0.3536 lfigpmul CTR lfigpsub lfigpsub /SW lfigpointdef + [ xsize ysize 0.5 lfigpmul /lfigellipsecircum cvx ] lfigcircumdef + S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S +} def + +% shape and labels of the @Circle symbol +/lfigcircle +{ + xsize ysize 0.5 lfigpmul /CTR lfigpointdef + CTR xsize 0 ysize 0 lfigpmax 0.5 lfigpmul lfigpadd /E lfigpointdef + CTR 0 0 CTR E lfigdistance 45 lfigatangle lfigpadd /NE lfigpointdef + CTR 0 0 CTR E lfigdistance 90 lfigatangle lfigpadd /N lfigpointdef + CTR 0 0 CTR E lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef + CTR 0 0 CTR E lfigdistance 180 lfigatangle lfigpadd /W lfigpointdef + CTR 0 0 CTR E lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef + CTR 0 0 CTR E lfigdistance 270 lfigatangle lfigpadd /S lfigpointdef + CTR 0 0 CTR E lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef + [ S E lfigpsub /lfigellipsecircum cvx ] lfigcircumdef + S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S +} def + +% shape and labels of the @HLine and @HArrow symbols +/lfighline +{ + 0 ymark lfigprevious /FROM lfigpointdef + xsize ymark lfigprevious /TO lfigpointdef +} def + +% shape and labels of the @VLine and @VArrow symbols +/lfigvline +{ + xmark ysize lfigprevious /FROM lfigpointdef + xmark 0 lfigprevious /TO lfigpointdef +} def + +% points of a polygon around base with given no of sides, vert init angle: +% <sides> <angle> figpolygon <point> ... <point> +/lfigpolygon +{ xsize ysize 0.5 lfigpmul /CTR lfigpointdef + 90 sub CTR 2 copy lfigmax 5 3 roll + [ 4 copy pop /lfigpolycircum cvx ] lfigcircumdef + exch dup 360 exch div exch + 1 1 3 2 roll + { 4 string cvs (P) exch lfigconcat cvn + 6 copy pop pop lfigatangle 2 copy 10 2 roll + 3 2 roll lfigpointdef + dup 3 1 roll add exch + } for + pop lfigatangle +} def + +% next array element: <array> <index> lfiggetnext <array> <index> <any> true +% or <array> <index> false +/lfiggetnext +{ 2 copy exch length ge + { false } + { 2 copy get exch 1 add exch true } ifelse +} def + +% check whether thing is number: <any> lfigisnumbertype <any> <bool> +/lfigisnumbertype +{ dup type dup + /integertype eq exch /realtype eq or +} def + +% check whether thing is an array: <any> lfigisarraytype <any> <bool> +/lfigisarraytype { dup type /arraytype eq } def + +% get next item: <array> <index> lfiggetnextitem <array> <index> 0 +% or <array> <index> <array> 1 +% or <array> <index> <point> 2 +/lfiggetnextitem +{ lfiggetnext + { lfigisarraytype + { 1 + } + { lfigisnumbertype + { 3 1 roll + lfiggetnext + { lfigisnumbertype + { 4 3 roll exch 2 + } + { pop 3 2 roll pop 0 + } ifelse + } + { 3 2 roll pop 0 + } ifelse + } + { pop 0 + } ifelse + } ifelse + } + { 0 + } ifelse +} def + +% set arc path: bool x1 y1 x2 y2 x0 y0 lfigsetarc <angle> <angle> <dist> +% the path goes from x1 y1 to x2 y2 about centre x0 y0, +% anticlockwise if bool is true else clockwise. +% The orientations of backwards pointing and forwards pointing +% arrowheads are returned in the two angles, and +% the length of the arc is returned in <dist>. +/lfigsetarc +{ + 20 dict begin + matrix currentmatrix 8 1 roll + 2 copy translate 2 copy 8 2 roll + 4 2 roll lfigpsub 6 2 roll lfigpsub + dup /y1 exch def dup mul /y1s exch def + dup /x1 exch def dup mul /x1s exch def + dup /y2 exch def dup mul /y2s exch def + dup /x2 exch def dup mul /x2s exch def + + y1s y2s eq + { -1 + } + { y1s x2s mul y2s x1s mul sub y1s y2s sub div + } ifelse + /da exch def + + x1s x2s eq + { -1 + } + { x1s y2s mul x2s y1s mul sub x1s x2s sub div + } ifelse + /db exch def + + da 0 gt db 0 gt and + { /LMax da sqrt db sqrt lfigmax def + /scalex da sqrt LMax div def + /scaley db sqrt LMax div def + scalex scaley scale + 0 0 LMax + 0 0 x1 scalex mul y1 scaley mul lfigangle + 0 0 x2 scalex mul y2 scaley mul lfigangle + 2 copy eq { 360 add } if + 2 copy 8 2 roll + 5 index { arc } { arcn } ifelse + 2 index 1 index + { 90 sub } { 90 add } ifelse + dup sin scaley mul exch cos scalex mul atan + 2 index 2 index + { 90 add } { 90 sub } ifelse + dup sin scaley mul exch cos scalex mul atan + 5 2 roll % res1 res2 ang1 ang2 anticlockwise + { exch sub } { sub } ifelse + dup 0 le { 360 add } if lfigpi mul LMax mul 180 div + } + { 0 0 x1 y1 lfigdistance 0 0 x2 y2 lfigdistance eq + 0 0 x1 y1 lfigdistance 0 gt and + { 0 0 + 0 0 x1 y1 lfigdistance + 0 0 x1 y1 lfigangle + 0 0 x2 y2 lfigangle + 2 copy eq { 360 add } if + 2 copy 8 2 roll + 5 index { arc } { arcn } ifelse + 2 index 1 index + { 90 sub } { 90 add } ifelse + 2 index 2 index + { 90 add } { 90 sub } ifelse + 5 2 roll % res1 res2 ang1 ang2 clockwise + { exch sub } { sub } ifelse + dup 0 le { 360 add } if lfigpi mul 0 0 x1 y1 lfigdistance mul 180 div + } + { x2 y2 lineto pop + x2 y2 x1 y1 lfigangle + x1 y1 x2 y2 lfigangle + x1 y1 x2 y2 lfigdistance + } ifelse + } ifelse + 4 -1 roll setmatrix + end +} def + +% lfigsetcurve: set up a Bezier curve from x0 y0 to x3 y3 +% and return arrowhead angles and length of curve (actually 0) +% x0 y0 x1 y1 x2 y2 x3 y3 lfigsetcurve <angle> <angle> <length> +/lfigsetcurve +{ 8 copy curveto pop pop + lfigangle + 5 1 roll + 4 2 roll lfigangle + exch + 0 +} def + +% lfigpaintpath: paint a path of the given shape +% /paint [ shape ] lfigpaintpath - +/lfigpaintpath +{ + 10 dict begin + 0 newpath + /prevseen false def + /curveseen false def + { lfiggetnextitem + dup 0 eq { pop exit } + { 1 eq + { /curveseen true def + /curve exch def + curve length 0 eq { /curveseen false def } if + } + { /ycurr exch def + /xcurr exch def + prevseen + { curveseen + { curve length 4 eq + { xprev yprev + curve 0 get curve 1 get + curve 2 get curve 3 get + xcurr ycurr + lfigsetcurve pop pop pop + } + { xprev yprev xcurr ycurr + curve length 1 ge { curve 0 get } { 0 } ifelse + curve length 2 ge { curve 1 get } { 0 } ifelse + curve length 3 ge { curve 2 get } { true } ifelse + 7 1 roll + lfigsetarc pop pop pop + } ifelse + } + { xcurr ycurr lineto + } ifelse + } + { xcurr ycurr moveto + } ifelse + /xprev xcurr def + /yprev ycurr def + /prevseen true def + /curveseen false def + } ifelse + } ifelse + } loop pop pop cvx exec + end +} def + +% stroke a path of the given shape in the given linestyle and dash length. +% Return the origin and angle of the backward and forward arrow heads. +% dashlength /linestyle [shape] lfigdopath [<point> <angle>] [<point> <angle>] +/lfigdopath +{ + 10 dict begin + 0 + /prevseen false def + /curveseen false def + /backarrow [] def + /fwdarrow [] def + { + lfiggetnextitem + dup 0 eq { pop exit } + { + 1 eq + { /curveseen true def + /curve exch def + curve length 0 eq { /prevseen false def } if + } + { /ycurr exch def + /xcurr exch def + prevseen + { newpath xprev yprev moveto + curveseen + { curve length 4 eq + { xprev yprev + curve 0 get curve 1 get + curve 2 get curve 3 get + xcurr ycurr lfigsetcurve + } + { xprev yprev xcurr ycurr + curve length 1 ge { curve 0 get } { 0 } ifelse + curve length 2 ge { curve 1 get } { 0 } ifelse + curve length 3 ge { curve 2 get } { true } ifelse + 7 1 roll + lfigsetarc + } ifelse + } + { xcurr ycurr lineto + xcurr ycurr xprev yprev lfigangle dup 180 sub + xprev yprev xcurr ycurr lfigdistance + } ifelse + 6 index 6 index cvx exec + [ xprev yprev 5 -1 roll ] + backarrow length 0 eq + { /backarrow exch def } + { pop } ifelse + [ xcurr ycurr 4 -1 roll ] /fwdarrow exch def + } if + /xprev xcurr def + /yprev ycurr def + /prevseen true def + /curveseen false def + } ifelse + } ifelse + } loop + pop pop pop pop + backarrow length 0 eq { [ 0 0 0 ] } { backarrow } ifelse + fwdarrow length 0 eq { [ 0 0 0 ] } { fwdarrow } ifelse + end +} def + +% lfigdoarrow: draw an arrow head of given form +% dashlength /lstyle /pstyle hfrac height width [ <point> <angle> ] lfigdoarrow - +/lfigdoarrow +{ matrix currentmatrix 8 1 roll + dup 0 get 1 index 1 get translate + 2 get rotate + [ 2 index neg 2 index 0 0 + 3 index 3 index neg + 1 index 10 index mul 0 + 7 index 7 index ] + 4 1 roll pop pop pop + dup 3 1 roll + gsave lfigpaintpath grestore lfigdopath pop pop + setmatrix +} def + +% arrow head styles +/lfigopen 0.0 def +/lfighalfopen 0.5 def +/lfigclosed 1.0 def + +% stroke no arrows, forward, back, and both +/lfignoarrow { pop pop pop pop pop pop pop pop } def +/lfigforward { 7 -1 roll lfigdoarrow pop } def +/lfigback { 8 -2 roll pop lfigdoarrow } def +/lfigboth { 8 -1 roll 7 copy lfigdoarrow pop 7 -1 roll lfigdoarrow } def + +% lfigprevious: return previous point on path +/lfigprevious +{ lfigisnumbertype + { 2 copy } + { lfigisarraytype + { 2 index 2 index } + { 0 0 } + ifelse + } ifelse +} def + +% label a point in 2nd top dictionary: <point> /name lfigpointdef - +/lfigpointdef +{ + % (Entering lfigpointdef) lfigdebugprint + [ 4 2 roll transform + /itransform cvx ] cvx + currentdict end + 3 1 roll + % currentdict length currentdict maxlength lt + % { def } + % { exec moveto (too many labels) show stop } + % ifelse + def + begin + % (Leaving lfigpointdef) lfigdebugprint +} def + +% promote labels from second top to third top dictionary +% <string> lfigpromotelabels - +/lfigpromotelabels +{ + % (Entering lfigpromotelabels) lfigdebugprint + currentdict end exch currentdict end + { exch 20 string cvs 2 index + (@) lfigconcat exch lfigconcat cvn exch def + } forall pop begin + % (Leaving lfigpromotelabels) lfigdebugprint +} def + +% show labels (except CIRCUM): - lfigshowlabels - +/lfigshowlabels +{ + % (Entering lfigshowlabels) lfigdebugprint + currentdict end + currentdict + { 1 index 20 string cvs (CIRCUM) search % if CIRCUM in key + { pop pop pop pop pop } + { pop cvx exec 2 copy + newpath 1.5 pt 0 360 arc + 0 setgray fill + /Times-Roman findfont 8 pt scalefont setfont + moveto 0.2 cm 0.1 cm rmoveto 20 string cvs show + } + ifelse + } forall + begin + % (Leaving lfigshowlabels) lfigdebugprint +} def + +% fix an angle to 0 <= res < 360: <angle> lfigfixangle <angle> +/lfigfixangle +{ + % (Entering lfigfixangle) lfigdebugprint + { dup 0 ge { exit } if + 360 add + } loop + { dup 360 lt { exit } if + 360 sub + } loop + % (Leaving lfigfixangle) lfigdebugprint +} def + +% find point on circumference of box: alpha a b lfigboxcircum x y +/lfigboxcircum +{ + % (Entering lfigboxcircum) lfigdebugprint + 4 dict begin + /b exch def + /a exch def + lfigfixangle /alpha exch def + 0 0 a b lfigangle /theta exch def + + % if alpha <= theta, return (a, a*tan(alpha)) + alpha theta le + { a a alpha sin mul alpha cos div } + { + % else if alpha <= 180 - theta, return (b*cot(alpha), b) + alpha 180 theta sub le + { b alpha cos mul alpha sin div b } + { + % else if alpha <= 180 + theta, return (-a, -a*tan(alpha)) + alpha 180 theta add le + { a neg a neg alpha sin mul alpha cos div } + { + % else if alpha <= 360 - theta, return (-b*cot(alpha), -b) + alpha 360 theta sub le + { b neg alpha cos mul alpha sin div b neg } + { + % else 360 - theta <= alpha, return (a, a*tan(alpha)) + a a alpha sin mul alpha cos div + } ifelse + } ifelse + } ifelse + } ifelse + end + % (Leaving lfigboxcircum) lfigdebugprint +} def + +% find quadratic roots (assume a != 0): a b c lfigqroots x1 x2 2 +% or x2 1 +% or 0 +/lfigqroots +{ + 4 dict begin + /c exch def + /b exch def + /a exch def + /disc b b mul 4 a c mul mul sub def + disc 0 lt + { 0 + } + { disc 0 eq + { b neg 2 a mul div + 1 + } + { b neg disc sqrt add 2 a mul div + b neg disc sqrt sub 2 a mul div + 2 + } + ifelse + } + ifelse + end +} def + +% work our which quadrant: <angle> lfigquadrant <0-3> +/lfigquadrant +{ dup 90 lt + { pop 0 + } + { dup 180 lt + { pop 1 + } + { 270 lt + { 2 + } + { 3 + } ifelse + } ifelse + } ifelse +} def + +% find curvebox circum, assuming upper right quadrant: alpha a b xmk lfigcb x y +/lfigcb +{ + 6 dict begin + /xmk exch def + /b exch def + /a exch def + /alpha exch def + /theta1 0 0 a b xmk sub lfigangle def + /theta2 0 0 a xmk sub b lfigangle def + alpha theta1 le + { % if alpha <= theta1, return (a, a*tan(alpha)) + a a alpha sin mul alpha cos div + } + { alpha theta2 ge + { % else if alpha > theta2, return (b*cot(alpha), b) + b alpha cos mul alpha sin div b + } + { + % else, return the intersection of line and circle + a xmk sub b xmk sub xmk 0 0 alpha lfigcircleintersect + dup 0 eq + { % should never happen, just return any reasonable point + pop + a b 0.5 lfigpmul + } + { 1 eq + { % should never happen, just return the point on top of stack + } + { % the usual case, two points on stack, return the larger + lfigpmax + } ifelse + } ifelse + } ifelse + } ifelse + end +} def + +% find point on circumference of curvebox: alpha a b xmk lfigcurveboxcircum x y +/lfigcurveboxcircum +{ + % (Entering lfigcurveboxcircum) lfigdebugprint + 5 dict begin + /xmk exch def + /b exch def + /a exch def + lfigfixangle /alpha exch def + + % work out which quadrant we are in, and reflect accordingly + /quad alpha lfigquadrant def + quad 0 eq + { alpha a b xmk lfigcb + } + { quad 1 eq + { 180 alpha sub a b xmk lfigcb exch neg exch + } + { quad 2 eq + { alpha 180 sub a b xmk lfigcb neg exch neg exch + } + { 360 alpha sub a b xmk lfigcb neg + } ifelse + } ifelse + } ifelse + end + % (Leaving lfigcurveboxcircum) lfigdebugprint +} def + +% find point on circumference of diamond: alpha a b lfigdiamondcircum x y +/lfigdiamondcircum +{ + % (Entering lfigdiamondcircum) lfigdebugprint + 4 dict begin + /b exch def + /a exch def + lfigfixangle /alpha exch def + b alpha cos abs mul a alpha sin abs mul add /denom exch def + a b mul alpha cos mul denom div + a b mul alpha sin mul denom div + end + % (Leaving lfigdiamondcircum) lfigdebugprint +} def + +% find point on circumference of ellipse: alpha a b lfigellipsecircum x y +/lfigellipsecircum +{ + % (Entering lfigellipsecircum) lfigdebugprint + 4 dict begin + /b exch def + /a exch def + lfigfixangle /alpha exch def + b alpha cos mul dup mul a alpha sin mul dup mul add sqrt /denom exch def + a b mul alpha cos mul denom div + a b mul alpha sin mul denom div + end + % (Leaving lfigellipsecircum) lfigdebugprint +} def + +% find point of intersection of two lines each defined by two points +% x1 y1 x2 y2 x3 y3 x4 y4 lfiglineintersect x y +/lfiglineintersect +{ + % (Entering lfiglineintersect) lfigdebugprint + 13 dict begin + /y4 exch def + /x4 exch def + /y3 exch def + /x3 exch def + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x2 x1 sub /x21 exch def + x4 x3 sub /x43 exch def + y2 y1 sub /y21 exch def + y4 y3 sub /y43 exch def + y21 x43 mul y43 x21 mul sub /det exch def + + % calculate x + y21 x43 mul x1 mul + y43 x21 mul x3 mul sub + y3 y1 sub x21 mul x43 mul add + det div + + % calculate y + x21 y43 mul y1 mul + x43 y21 mul y3 mul sub + x3 x1 sub y21 mul y43 mul add + det neg div + + end + % (Leaving lfiglineintersect) lfigdebugprint +} def + +% find point on circumference of polygon +% alpha radius num theta lfigpolycircum x y +/lfigpolycircum +{ + % (Entering lfigpolycircum) lfigdebugprint + 13 dict begin + /theta exch def + /num exch def + /radius exch def + /alpha exch def + + % calculate delta, the angle from theta to alpha + alpha theta sub lfigfixangle + + % calculate the angle which is the multiple of 360/num closest to delta + 360 num div div truncate 360 num div mul theta add /anglea exch def + + % calculate the next multiple of 360/num after anglea + anglea 360 num div add /angleb exch def + + % intersect the line through these two points with the alpha line + anglea cos anglea sin angleb cos angleb sin + 0 0 alpha cos 2 mul alpha sin 2 mul + lfiglineintersect radius lfigpmul + + end + % (Leaving lfigpolycircum) lfigdebugprint +} def + +% find point of intersection of a point and a circle +% x0 y0 r x1 y1 theta lfigcircleintersect xa ya xb yb 2 +% or xb yb 1 +% or 0 +/lfigcircleintersect +{ + % (Entering lfigcircleintersect) lfigdebugprint + 15 dict begin + /theta exch def + /y1 exch def + /x1 exch def + /r exch def + /y0 exch def + /x0 exch def + + % if sin(theta) = 0 then line is horizontal and y must be y1 + theta sin abs 0.00001 lt + { + /a 1 def + /b -2 x0 mul def + /c x0 dup mul y1 y0 sub dup mul add r dup mul sub def + a b c lfigqroots dup + 0 eq + { pop + 0 + } + { 1 eq + { y1 1 + } + { y1 exch y1 2 + } ifelse + } ifelse + } + { + /ct theta cos theta sin div def + /a ct ct mul 1 add def + /b ct x1 x0 sub mul y1 add y0 sub 2 mul def + /c x1 x0 sub dup mul y1 y0 sub dup mul add r dup mul sub def + a b c lfigqroots dup + 0 eq + { pop + 0 + } + { 1 eq + { y1 add /yb exch def + yb y1 sub ct mul x1 add /xb exch def + xb yb 1 + } + { y1 add /ya exch def + ya y1 sub ct mul x1 add /xa exch def + y1 add /yb exch def + yb y1 sub ct mul x1 add /xb exch def + xa ya xb yb 2 + } ifelse + } ifelse + } ifelse + end + % (Leaving lfigcircleintersect) lfigdebugprint +} def + +% add CIRCUM operator with this body: <array> lfigcircumdef - +/lfigcircumdef +{ % (Entering lfigcircumdef) lfigdebugprint + /CIRCUM exch cvx + currentdict end + 3 1 roll + % currentdict length currentdict maxlength lt + % { def } + % { exec moveto (too many labels) show stop } + % ifelse + def + begin + % (Leaving lfigcircumdef) lfigdebugprint +} def + +end +%%EndResource + +%%BeginResource: procset LoutBasicSetup +% @PrependGraphic file /usr/staff/jeff/lout.lib/include/bsf.lpg + +% width height linethickness louteuro - +% draw a Euro symbol of this width and height with this line thickness +% Author: Jeff Kingston, based on code from Andrew Beardsley +/louteuro { + 20 dict begin + /eurothick exch def + /euroheight exch def + /eurowidth exch def + /eurostrokewidth euroheight 0.8 mul def + /eurostep eurothick 60 cos mul 60 sin div def + /eurotheta 40 def + + % llx lly width thickness louteurobox - + % draw angled box starting at (llx, lly) with given width and thickness + /louteurobox + { + /euroboxthick exch def + /euroboxwidth exch def + newpath moveto euroboxwidth 0 rlineto + eurostep euroboxthick rlineto + euroboxwidth neg 0 rlineto closepath fill + } def + + % lower cross stroke + 0 euroheight 2 div eurothick 1.5 mul sub + eurostrokewidth eurothick louteurobox + + % upper cross stroke + 0 euroheight 2 div eurothick 0.5 mul add + eurostrokewidth eurostep 2 mul add eurothick louteurobox + + % circular part + /eurohctr eurowidth euroheight 2 div eurotheta cos mul sub def + /eurovctr euroheight 2 div def + newpath + eurohctr eurovctr eurovctr eurotheta 350 eurotheta sub arc + eurohctr eurovctr eurovctr eurothick sub 365 eurotheta sub eurotheta arcn + closepath fill + end +} def + +% path for @FullWidthRule symbol +/LoutRule +{ 0 0 moveto xsize 0 lineto +} def + +% path for @Box symbol +/LoutBox +{ 0 0 moveto xsize 0 lineto + xsize ysize lineto 0 ysize lineto + closepath +} def + +% path for @CurveBox symbol +/LoutCurveBox +{ xmark 0 moveto + xsize xmark sub xmark xmark 270 360 arc + xsize xmark sub ysize xmark sub xmark 0 90 arc + xmark ysize xmark sub xmark 90 180 arc + xmark xmark xmark 180 270 arc + closepath +} def + +% path for @ShadowBox symbol +/LoutShadowBox +{ xmark 2 mul 0 moveto xsize 0 lineto + xsize ysize xmark 2 mul sub lineto + xsize xmark sub ysize xmark 2 mul sub lineto + xsize xmark sub xmark lineto + xmark 2 mul xmark lineto + closepath +} def + +% set up dictionary containing margin note data: parity LoutMargSet - +/LoutMargSet +{ /LoutMargDict 12 dict def + LoutMargDict begin + /parity exch def + /matr matrix currentmatrix def + /rightx xsize def + /lefty ysize def % highest allowable point for top of next left note + /righty ysize def % highest allowable point for top of next right note + /max { 2 copy gt { pop } { exch pop } ifelse } def + /min { 2 copy lt { pop } { exch pop } ifelse } def + end +} def + +%translate coordinate system for marginal notes: type LoutMargShift - +% where type 0 is left margin, 1 is right margin, 2 is outer, 3 is inner +/LoutMargShift +{ LoutMargDict begin + + % y coordinate of top of note, in margin coords, before vertical adjust + 0 ysize transform matr itransform exch pop + + % decide whether left or right margin based on type and parity + exch [ 0 1 parity 1 parity sub ] exch get 0 eq + { + % left margin: adjust top of note downwards if overlaps previous note + lefty min + + % bottom of note is new lefty position and also translate position + ysize sub dup /lefty exch def + + % want right edge of note at coordinate zero + xsize neg exch + } + { + % right margin: adjust top of note downwards if overlaps previous note + righty min + + % bottom of note is new righty position and also translate position + ysize sub dup /righty exch def + + % want left edge of note at coordinate rightx + rightx exch + } ifelse + + % stack now contains coord of bottom left corner in margin coordinates + matr setmatrix translate + end +} def + +% create LoutPageDict with left, right, foot, top for @Place symbol users +/LoutPageSet +{ + /LoutPageDict 5 dict def + LoutPageDict begin + /matr matrix currentmatrix def + /left 0 def + /right xsize def + /foot 0 def + /top ysize def + end + +} def + +%%EndResource + +%%EndProlog + +%%BeginSetup +%%IncludeResource: font Times-Roman +/Times-Romanfnt82 vec2 /Times-Roman LoutRecode +/fnt82 { /Times-Romanfnt82 LoutFont } def +%%IncludeResource: font Times-Bold +/Times-Boldfnt84 vec2 /Times-Bold LoutRecode +/fnt84 { /Times-Boldfnt84 LoutFont } def +%%IncludeResource: font Times-Italic +/Times-Italicfnt83 vec2 /Times-Italic LoutRecode +/fnt83 { /Times-Italicfnt83 LoutFont } def +%%EndSetup + +%%Page: i 1 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup + +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +240 fnt84 2897 12401(The)m 3352(Design)s 4099(and)s 4540(Implementation)s +4239 11998(of)m 4511(the)s 2589 11595(Lout)m 3141(Document)s 4250(F)s 6(ormatting)k +5468(Language)s 240 fnt83 3630 11097(J)m 6(ef)k 4(fr)k 8(e)k 7(y)k +4310(H.)s 4577(Kingston)s 240 fnt82 2551 10596(Basser)m 3248(Department)s +4436(of)s 4707(Computer)s 5724(Science,)s 3007 10308(The)m 3435(Uni)s 6(v)k 3(ersity)k +4489(of)s 4760(Sydne)s 3(y)k 5530(2006,)s 4095 10020(Australia)m +3739 9568(27)m 4027(January)s 15(,)k 4863(1993)s 240 fnt84 +3901 8775(SUMMAR)m 8(Y)k 240 fnt82 480 8320(Lout)m 992(is)s +1202(a)s 1367(high-)s 1861(le)s 6(v)k 3(el)k +2371(language)s 3291(for)s 3628(document)s 4632(formatting,)s 5746(whose)s +6414(ease)s 6881(of)s 7151(use)s 7526(has)s 7895(permit)s +8518(-)s 480 8032(ted)m 839(an)s 1131(unprecedented)s 2593(number)s +3394(of)s 3674(adv)s 6(anced)k 4639(features)s 5454(to)s +5703(be)s 5994(added)s 6633(quickly)s 7414(and)s 7828(reliably)s 15(.)k +480 7744(This)m 942(paper)s 1518(charts)s 2125(the)s 2458(e)s 6(v)k 4(olution)k +3395(of)s 3651(the)s 3985(design)s 4652(and)s 5042(implementation)s +6584(of)s 6841(Lout)s 7338(from)s 7847(concep)s 8518(-)s +480 7456(tion)m 913(in)s 1161(mid-)s 1601(1984)s 2139(to)s +2383(public)s 3038(release)s 3761(in)s 4008(October)s 4843(1991.)s +5491(It)s 5701(includes)s 6553(e)s 3(xtensi)k 6(v)k 3(e)k +7505(discussions)s 480 7168(of)m 751(remaining)s 1773(problems)s 2714(and)s +3118(possible)s 3958(solutions.)s 240 fnt84 480 6664(K)m 6(eyw)k 2(ords)k +240 fnt82 1623 6665(document)m 2627(formatting)s 3688(typesetting)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 1 2 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +240 fnt84 2897 12401(The)m 3352(Design)s 4099(and)s 4540(Implementation)s +4239 11998(of)m 4511(the)s 2589 11595(Lout)m 3141(Document)s 4250(F)s 6(ormatting)k +5468(Language)s 240 fnt83 3630 11097(J)m 6(ef)k 4(fr)k 8(e)k 7(y)k +4310(H.)s 4577(Kingston)s 240 fnt82 2551 10596(Basser)m 3248(Department)s +4436(of)s 4707(Computer)s 5724(Science,)s 3007 10308(The)m 3435(Uni)s 6(v)k 3(ersity)k +4489(of)s 4760(Sydne)s 3(y)k 5530(2006,)s 4095 10020(Australia)m +3739 9568(27)m 4027(January)s 15(,)k 4863(1993)s 240 fnt84 +0 8926(1.)m 291(Intr)s 4(oduction)k 240 fnt82 480 8495(Lout)m +985([1,)s 1284(2])s 1515(is)s 1718(a)s 1877(high-le)s 6(v)k 3(el)k +2885(language)s 3798(for)s 4129(document)s 5126(formatting,)s 6234(designed)s +7136(and)s 7533(implemented)s 8832(by)s 0 8207(the)m 341(author)s 13(.)k +1096(The)s 1517(implementation,)s 3117(kno)s 6(wn)k 3814(as)s +4057(Basser)s 4747(Lout,)s 5299(is)s 5502(a)s 5661(fully)s +6159(operational)s 7282(production)s 8368(v)s 3(ersion)k 0 7919(written)m +736(in)s 983(C)s 1198(for)s 1540(the)s 1891(Unix)s +2429(operating)s 3389(system,)s 153 fnt82 4100 8008(1)m 240 fnt82 +4223 7919(which)m 4869(translates)s 5824(Lout)s 6340(source)s 7023(code)s +7535(into)s 7964(PostScript,)s 153 fnt82 8993 8008(2)m 240 fnt82 +0 7631(a)m 201(de)s 6(vice-independent)k 2164(graphics)s 3061(rendering)s +4066(language)s 5021(accepted)s 5951(by)s 6281(man)s 3(y)k +6900(high-resolution)s 8454(output)s 0 7343(de)m 6(vices,)k 833(including)s +1805(most)s 2346(laser)s 2871(printers.)s 3779(Basser)s 4492(Lout)s +5019(is)s 5244(a)s 4(v)k 6(ailable)k 6168(free)s +6609(of)s 6895(char)s 4(ge)k 7600([3].)s 8057(It)s +8278(includes)s 0 7055(installation)m 1118(instructions,)s 2339(C)s 2550(source,)s +3281(se)s 6(v)k 3(en)k 3873(standard)s 4740(packages,)s +5723(and)s 6127(complete)s 7058(documentation)s 8536(in)s 8778(the)s +0 6767(form)m 524(of)s 795(six)s 1129(technical)s 2046(reports)s +2760(and)s 3164(a)s 3330(manual)s 4089(page.)s 480 6393(The)m +900(Lout)s 1404(project)s 2118(arose)s 2670(out)s 3027(of)s +3290(the)s 3629(author')s 13(s)k 4442(desire)s 5060(to)s +5290(bring)s 5840(to)s 6070(document)s 7066(formatting)s 8118(languages)s +0 6105(the)m 343(ele)s 3(g)k 1(ance)k 1225(of)s +1491(e)s 3(xpression)k 2562(found)s 3174(in)s 3411(programming)s +4761(languages)s 5763(lik)s 2(e)k 6170(Algol-)s 6783(60)s +7072(and)s 7471(P)s 3(ascal.)k 8236(This)s 8706(em)s +8998(-)s 0 5817(phasis)m 638(on)s 924(e)s 3(xpressi)k 6(v)k 3(eness)k +2373(has)s 2731(produced)s 3669(an)s 3941(order)s 4493(of)s +4753(magnitude)s 5808(reduction)s 6757(in)s 6988(the)s 7325(cost)s +7759(of)s 8018(de)s 6(v)k 3(eloping)k 0 5529(document)m +998(formatting)s 2053(applications.)s 3366(F)s 3(or)k 3748(e)s 3(xample,)k +4656(an)s 4933(equation)s 5807(formatting)s 6862(application,)s 8025(which)s +8660(may)s 0 5241(be)m 282(dif\207cult)s 1098(or)s 1357(impossible)s +2449(to)s 2688(add)s 3092(to)s 3331(other)s 3882(systems,)s +4746(can)s 5135(be)s 5417(written)s 6150(in)s 6393(Lout)s +6905(in)s 7148(a)s 7314(fe)s 6(w)k 7720(days.)s +480 4867(When)m 1099(e)s 3(xpert)k 1742(users)s 2274(can)s +2652(implement)s 3724(such)s 4209(applications)s 5405(quickly)s 15(,)k +6204(non-)s 6632(e)s 3(xperts)k 7360(bene\207t.)s 8164(Although)s +0 4579(Lout)m 509(itself)s 1053(pro)s 3(vides)k 1922(only)s +2398(a)s 2560(small)s 3129(k)s 2(ernel)k 3775(of)s +4042(carefully)s 4941(chosen)s 5659(primiti)s 6(v)k 3(es,)k +6721(packages)s 7646(written)s 8375(in)s 8614(Lout)s 0 4291(and)m +399(distrib)s 4(uted)k 1470(with)s 1946(Basser)s 2638(Lout)s +3145(pro)s 3(vide)k 3923(an)s 4201(unprecedented)s 5649(array)s +6187(of)s 6453(adv)s 6(anced)k 7404(features)s 8204(in)s +8442(a)s 8602(form)s 0 4003(accessible)m 1035(to)s 1286(non-)s +1714(e)s 3(xpert)k 2380(users.)s 3047(The)s 3487(features)s +4305(include)s 5076(rotation)s 5888(and)s 6304(scaling,)s 7100(fonts,)s +7697(paragraph)s 8722(and)s 0 3715(page)m 500(breaking,)s 1436(displays)s +2263(and)s 2659(lists,)s 3141(\210oating)s 3917(\207gures)s 4611(and)s +5007(tables,)s 5662(footnotes,)s 6651(chapters)s 7490(and)s 7886(sections)s +8698(\(au)s 8998(-)s 0 3427(tomatically)m 1128(numbered\),)s 2272(running)s +3070(page)s 3579(headers)s 4361(and)s 4765(footers,)s 5536(odd-)s +5964(e)s 6(v)k 3(en)k 6464(page)s 6973(layouts,)s +7772(automatically)s 0 3139(generated)m 975(tables)s 1570(of)s 1829(contents,)s +2720(sorted)s 3350(inde)s 3(x)k 3(es)k 4113(and)s +4505(reference)s 5435(lists,)s 5914(bibliographic)s 7229(and)s 7621(other)s +8159(databases)s 0 2851(\(including)m 1038(databases)s 2008(of)s 2281(formats)s +3064(for)s 3405(printing)s 4217(references\),)s 5386(equations,)s 6412(tables,)s +7079(diagrams,)s 8065(formatting)s 0 2563(of)m 271(P)s 3(ascal)k +933(programs,)s 1943(and)s 2347(automatically)s 3701(maintained)s 4821(cross)s +5363(references.)s 480 2189(This)m 1015(paper)s 1666(charts)s 2347(the)s +2755(e)s 6(v)k 4(olution)k 3766(of)s 4097(Lout)s +4669(from)s 5253(conception)s 6420(in)s 6723(mid-1984)s 7768(to)s +8067(the)s 8475(public)s 0 1901(release)m 722(of)s 997(Basser)s +1699(Lout)s 2215(in)s 2462(October)s 3297(1991.)s 3945(Lout)s +4461(is)s 4676(or)s 4(g)k 1(anized)k 5676(around)s +6403(four)s 6866(k)s 2(e)k 3(y)k 7265(concepts)s +8157(\211)s 8342(objects,)s 0 1613(de\207nitions,)m 1131(g)s 1(alle)k 3(ys,)k +1925(and)s 2343(cross)s 2899(references)s 3944(\211)s 4138(and)s +4556(the)s 3(y)k 5033(were)s 5567(de)s 6(v)k 3(eloped)k +6614(in)s 6871(the)s 7233(order)s 7811(listed,)s 8449(so)s +8730(this)s 0 1325(paper)m 593(will)s 1022(treat)s 1508(each)s +2006(in)s 2252(turn,)s 2747(discussing)s 3800(its)s 4079(design,)s +4814(implementation,)s 6424(problems,)s 7424(and)s 7831(prospects)s 8788(for)s +1134 0 0 0 240 288 60 0 574 LoutGr2 +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +122 fnt82 0 379(1)m 192 fnt82 58 309(Unix)m 485(is)s +653(a)s 786(trademark)s 1609(of)s 1825(A)s 21(T&T)k +2370(Bell)s 2733(Laboratories.)s 122 fnt82 0 112(2)m 192 fnt82 +67 42(PostScript)m 900(is)s 1068(a)s 1201(trademark)s 2024(of)s +2240(Adobe)s 2796(Systems,)s 3519(Incorporated.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 2 3 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Symbol +%%+ font Times-Italic +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4348 13844(-)m 4476(2)s 4650(-)s 0 13256(further)m 709(impro)s 3(v)k 3(ement.)k +240 fnt84 0 12463(2.)m 291(Objects)s 240 fnt82 480 11987(The)m +923(essence)s 1725(of)s 2011(an)s 3(y)k 2424(mo)s 3(v)k 3(e)k +3021(to)s 3276(a)s 3457(higher)s 4144(le)s 6(v)k 3(el)k +4669(is)s 4895(the)s 5258(introduction)s 6500(of)s 6786(some)s +7363(abstraction)s 8484(which)s 0 11699(serv)m 3(es)k 639(to)s +872(or)s 4(g)k 1(anize)k 1740(the)s 2082(lo)s 6(w-)k +2503(le)s 6(v)k 3(el)k 3006(operations,)s 4103(resulting)s +4986(in)s 5223(a)s 5383(more)s 5923(succinct)s 6760(e)s 3(xpression)k +7831(of)s 8096(their)s 8586(com)s 8998(-)s 0 11411(mon)m +475(combinations)s 1806(at)s 2030(the)s 2369(cost)s 2805(of)s +3068(some)s 3620(loss)s 4034(of)s 4297(detailed)s 5102(control.)s +5934(The)s 6354(early)s 6876(part)s 7298(of)s 7561(the)s +7900(Lout)s 8403(project)s 0 11123(w)m 2(as)k 426(spent)s +996(in)s 1245(the)s 1598(de)s 6(v)k 3(elopment)k +2891(of)s 3167(such)s 3668(an)s 3957(abstraction)s 5067(for)s +5411(the)s 5764(b)s 4(uilding)k 6616(blocks)s 7298(of)s +7574(documents,)s 8724(one)s 0 10835(which)m 635(could)s 1217(e)s 3(xplain,)k +2017(not)s 2375(just)s 2772(the)s 3113(simple)s 3798(phenomena)s +4954(of)s 5217(w)s 2(ords,)k 5899(lines,)s 6450(and)s +6846(paragraphs,)s 7994(b)s 4(ut)k 8348(also)s 8778(the)s +0 10547(alignment)m 1016(of)s 1287(columns)s 2149(in)s 2392(tables,)s +3056(and)s 3460(the)s 3808(comple)s 3(x)k 4684(nested)s +5353(structures)s 6332(of)s 6603(equations.)s 240 fnt84 0 9898(2.1.)m +471(The)s 926(genesis)s 1697(of)s 1969(the)s 2343(object)s +3026(abstraction)s 240 fnt82 480 9421(When)m 1163(one)s 1620(e)s 3(xamines)k +2626(pre)s 6(vious)k 3549(document)s 4608(formatting)s 5724(systems)s +6587([4])s 6958(looking)s 7798(for)s 8191(ideas)s 8788(for)s +0 9133(abstractions,)m 1245(as)s 1492(the)s 1837(author)s 2505(did)s +2866(in)s 3106(1984,)s 3690(the)s 4035(Eqn)s 4475(formatting)s +5533(language)s 6450([5])s 6764(stands)s 7410(out)s 7773(lik)s 2(e)k +8182(a)s 8344(beacon.)s 0 8845(In)m 256(Eqn,)s 749(a)s +915(mathematical)s 2256(formula)s 3072(such)s 3568(as)s 168 fnt78 +586 8390(2)m 240 fnt83 480 8330(x)m 240 fnt78 738 8322(+)m +939(1)s gsave +480 8274 translate +240 fnt83 553 0 0 0 240 288 12 LoutGraphic +gsave +0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke +grestore + +grestore +700 8046(4)m 240 fnt82 0 7535(is)m 210(produced)s +1159(by)s 1453(typing)s 220 fnt35 480 7037({ x sup 2 + 1 } o)m 3(v)k 5(er 4)k +240 fnt82 0 6541(in)m 261(the)s 627(input)s 1197(\207le;)s +220 fnt35 1632 6538(sup)m 240 fnt82 2056 6541(and)m 220 fnt35 +2478 6538(o)m 3(v)k 5(er)k 240 fnt82 2975 6541(are)m +3340(binary)s 4023(operators,)s 5037(and)s 5459(braces)s 6138(are)s +6503(used)s 7018(for)s 7374(grouping.)s 8421(This)s 8916(is)s +0 6253(document)m 1017(formatting)s 2091(at)s 2337(a)s 2516(v)s 3(ery)k +3006(high)s 3502(le)s 6(v)k 3(el,)k 4077(close)s +4638(to)s 4890(the)s 5252(language)s 6185(of)s 6469(mathematics)s +7741(itself,)s 8337(with)s 8833(all)s 0 5965(reference)m 943(to)s +1182(font)s 1627(changes)s 2449(and)s 2853(spacing)s 3637(suppressed.)s +480 5591(Eqn)m 916(pro)s 3(vides)k 1780(a)s 1938(single)s +2557(data)s 3008(type)s 3468(\(let)s 3837(us)s 4093(call)s +4485(it)s 4669(the)s 240 fnt83 5009 5593(e)m 4(xpr)k 8(ession)k +240 fnt82 6014 5591(\),)m 6192(b)s 4(uilt)k 6679(up)s +6964(recursi)s 6(v)k 3(ely)k 8062(in)s 8297(conte)s 3(xt-)k +0 5303(free)m 457(style:)s 1106(where)s 1778(one)s 2212(e)s 3(xpression)k +3321(may)s 3819(appear)s 9(,)k 4586(an)s 3(y)k +5015(e)s 3(xpression)k 6124(may)s 6622(appear)s 13(.)k +7442(This)s 7950(approach)s 8916(is)s 0 5015(common)m 905(in)s +1158(algebra)s 1931(and)s 2345(programming)s 3710(languages,)s 4785(where)s +5435(its)s 5721(simplicity)s 6740(and)s 7154(e)s 3(xpressi)k 6(v)k 3(eness)k +8625(ha)s 4(v)k 3(e)k 0 4727(long)m 478(been)s +986(appreciated;)s 2198(b)s 4(ut)k 2559(Eqn)s 3001(w)s 2(as)k +3421(the)s 3768(\207rst)s 4198(language)s 5117(to)s 5355(demonstrate)s +6578(its)s 6853(utility)s 7476(in)s 7718(document)s 8720(for)s +8998(-)s 0 4439(matting.)m 480 4065(Each)m 1015(e)s 3(xpression)k +2092(is)s 2302(treated)s 3009(by)s 3304(Eqn)s 3747(as)s +3997(a)s 4163(rectangle)s 5094(with)s 5577(a)s 240 fnt83 +5743 4067(horizontal)m 6787(axis)s 240 fnt82 7167 4065(,)m 7274(used)s +7771(for)s 8110(alignment)s 0 3777(with)m 482(adjacent)s 1338(e)s 3(xpressions:)k +553 519 0 288 240 288 60 480 2918 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +553 519 0 288 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +553 519 0 288 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd + + ] lfigdopath +pop pop +grestore +168 fnt78 106 404(2)m 240 fnt83 0 344(x)m 240 fnt78 +258 336(+)m 459(1)s gsave +0 288 translate +240 fnt83 553 0 0 0 240 288 12 LoutGraphic +gsave +0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke +grestore + +grestore +220 60(4)m +grestore + +grestore +end end restore +grestore +0 2467(The)m 425(size)s +848(and)s 1248(rendering)s 2213(of)s 2481(the)s 2825(e)s 3(xpression)k +3898(on)s 4191(the)s 4536(printed)s 5267(page)s 5771(are)s +6114(kno)s 6(wn)k 6815(only)s 7291(to)s 7526(the)s +7870(implementa)s 8998(-)s 0 2179(tion,)m 481(ne)s 6(v)k 3(er)k +1066(e)s 3(xplicitly)k 2022(calculated)s 3051(or)s 3313(accessed)s +4209(by)s 4506(the)s 4857(user)s 13(.)k 5409(This)s +5888(prohibition)s 7010(is)s 7223(crucial)s 7930(to)s 8172(the)s +8523(main)s 8998(-)s 0 1891(tenance)m 785(of)s 1055(the)s +1402(conte)s 3(xt-)k 2171(free)s 2596(property)s 3459(in)s +3701(practice.)s 4619(In)s 4874(Lout,)s 5432(for)s 5769(e)s 3(xample,)k +6682(equations,)s 7705(\207gures,)s 8462(tables,)s 0 1603(and)m 393(arbitrary)s +1256(objects)s 1972(may)s 2427(be)s 2697(mix)s 3(ed)k +3338(together)s 4169(freely)s 15(.)k 4863(This)s 5327(w)s 2(ould)k +5970(be)s 6241(impossible)s 7321(if)s 7526(size)s 7941(information)s +0 1315(w)m 2(as)k 421(hidden)s 1130(from)s 1654(the)s +2002(implementation)s 3559(in)s 3802(user)s 4260(calculations.)s 480 941(The)m +927(object)s 1591(abstraction)s 2715(of)s 3006(Lout)s 3537(is)s +3767(a)s 3952(direct)s 4575(descendant)s 5717(of)s 6008(the)s +6375(Eqn)s 6838(e)s 3(xpression.)k 8041(It)s 8266(emplo)s 2(ys)k + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 3 4 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Times-Bold +%%+ font Symbol +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4353 13844(-)m 4481(3)s 4645(-)s 0 13253(the)m 385(same)s +969(conte)s 3(xt-free)k 2212(recursi)s 6(v)k 3(e)k +3171(style)s 3715(of)s 4023(construction,)s 5350(and)s 5791(each)s +6323(object)s 7004(is)s 7251(treated)s 7995(by)s 8326(Lout)s +8876(as)s 0 12965(a)m 166(rectangle:)s 1701 453 567 198 240 288 60 480 12172 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +1701 453 567 198 240 288 60 0 0 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +1701 453 567 198 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1701 453 567 198 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore + +grestore + +grestore +end end restore +grestore +end end restore +grestore +0 11719(The)m 442(horizontal)s +1481(axis,)s 1987(called)s 2630(a)s 240 fnt83 2810 11721(r)m 10(ow)k +3244(mark)s 240 fnt82 3814 11719(in)m 4072(Lout,)s 4645(has)s +5030(a)s 5210(v)s 3(ertical)k 5992(analogue)s 6926(called)s +7569(a)s 240 fnt83 7749 11721(column)m 8523(mark)s 240 fnt82 +9019 11719(,)m 0 11431(creating)m 822(a)s 988(v)s 6(aluable)k +1848(symmetry)s 2857(between)s 3711(horizontal)s 4735(and)s 5139(v)s 3(ertical.)k +6014(Multiple)s 6893(column)s 7668(and)s 8072(ro)s 6(w)k +8491(marks)s 0 11143(are)m 347(permitted:)s 1984 1189 0 1189 240 288 60 480 9614 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +680 453 0 453 240 288 60 0 736 LoutGr2 +currentdict end 200 dict begin begin +grestore +680 453 0 453 240 288 60 0 0 LoutGr2 +/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(A) lfigpromotelabels +grestore +737 453 0 453 240 288 60 1247 736 LoutGr2 +currentdict end 200 dict begin begin +grestore +567 453 0 453 240 288 60 0 0 LoutGr2 +/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(B) lfigpromotelabels +grestore +680 453 0 453 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +396 453 0 453 240 288 60 0 0 LoutGr2 +/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(C) lfigpromotelabels +grestore +737 453 0 453 240 288 60 1247 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +737 453 0 453 240 288 60 0 0 LoutGr2 +/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(D) lfigpromotelabels +grestore +0 0 0 0 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ 0.3 cm 0 A@W lfigpsub lfigprevious /FROM lfigpointdef +B@W 1.6 cm 0 lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ 0.3 cm 0 C@W lfigpsub lfigprevious /FROM lfigpointdef +D@W 1.6 cm 0 lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ A@NW 0 0.3 cm lfigpadd lfigprevious /FROM lfigpointdef +0 0.3 cm C@SW lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ B@NW 0.3 cm 0.3 cm lfigpadd lfigprevious /FROM lfigpointdef +D@SW 0.3 cm -0.3 cm lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 9163(so)m 266(that)s +684(objects)s 1412(are)s 1759(able)s 2213(to)s 2452(represent)s +3387(tables.)s 480 8789(This)m 946(abstraction)s 2041(has)s 2401(some)s +2952(limitations,)s 4069(the)s 4407(most)s 4922(ob)s 3(vious)k +5719(being)s 6293(the)s 6631(restriction)s 7645(of)s 7906(size)s +8322(calcula)s 8998(-)s 0 8501(tions)m 507(to)s 736(rectangular)s +1860(bounding)s 2809(box)s 3(es.)k 3519(Non-)s 4000(rectangular)s +5124(and)s 5518(disconnected)s 6815(shapes)s 7494(arise)s 7990(naturally)s +8883(in)s 0 8213(\207gures)m 704(and)s 1111(in)s 1356(the)s +1707(characters)s 2727(of)s 3001(fonts;)s 3594(the)s 3944(e)s 3(xtension)k +4918(to)s 5159(them)s 5700(is)s 5912(conceptually)s 7191(straightforw)s 2(ard)k +8722(and)s 0 7925(might)m 615(help)s 1076(to)s 1311(e)s 3(xplain)k +2066(some)s 2623(\207ne)s 3034(points)s 3667(of)s 3934(layout)s +4588(such)s 5081(as)s 5327(k)s 2(erning.)k 6216(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k +7173(there)s 7702(are)s 8045(implemen)s 8998(-)s 0 7637(tation)m +599(and)s 1001(language)s 1918(design)s 2598(problems,)s 3592(particularly)s +4744(when)s 5317(\207lling)s 5939(non-)s 6367(rectangular)s 7498(shapes)s +8185(with)s 8664(te)s 3(xt,)k 0 7349(and)m 404(so)s +670(the)s 1018(author)s 1689(chose)s 2290(to)s 2529(k)s 2(eep)k +3032(to)s 3271(Eqn')s 13(s)k 3867(rectangles.)s 480 6975(A)m +766(more)s 1370(fundamental)s 2676(limitation)s 3718(of)s 4045(the)s +4450(object)s 5151(abstraction)s 6312(arises)s 6963(from)s 7543(the)s +7948(inability)s 8855(of)s 0 6687(recursi)m 6(v)k 3(e)k +936(data)s 1408(types)s 1978(to)s 2231(describe)s 3097(cross-link)s 2(ed)k +4335(structures,)s 5384(which)s 6040(seem)s 6605(to)s 6858(require)s +7604(some)s 8179(means)s 8855(of)s 0 6399(naming)m 756(the)s +1089(multiply)s 1938(referenced)s 2988(parts.)s 3601(Lout)s 4098(is)s +4293(obliged)s 5054(to)s 5278(introduce)s 6222(additional)s 7218(abstractions)s +8395(to)s 8618(cope)s 0 6111(with)m 490(cross)s 1040(linking:)s +1892(g)s 1(alle)k 3(ys)k 2624(for)s 2970(inserting)s +3867(te)s 3(xt)k 4291(into)s 4724(pages)s 5328(\(Section)s +6189(5.1\),)s 6683(cross)s 7233(references)s 8273(\(Section)s 0 5823(6.1\),)m +490(and)s 898(labelled)s 1716(points)s 2356(in)s 2603(\207gure)s +3221(dra)s 3(wing)k 4059([6].)s 4506(An)s 4860(abstraction)s +5969(closer)s 6603(to)s 6846(h)s 1(yperte)k 3(xt)k +7809(might)s 8431(form)s 8960(a)s 0 5535(more)m 547(uni\207ed)s +1270(basis)s 1799(for)s 2137(these)s 2684(features.)s 240 fnt84 +0 4936(2.2.)m 471(Grammatical)s 1893(and)s 2334(lexical)s 3039(structur)s 4(e)k +240 fnt82 480 4504(If)m 700(objects)s 1418(are)s 1755(to)s +1984(be)s 2256(constructed)s 3406(lik)s 2(e)k 3807(mathematical)s +5138(e)s 3(xpressions,)k 6348(the)s 6686(natural)s 7394(notation)s +8225(is)s 8425(a)s 8580(func)s 8998(-)s 0 4216(tional)m +599(language)s 1519(based)s 2122(on)s 2419(operators,)s 3415(as)s +3665(in)s 3908(Eqn.)s 4458(The)s 4886(grammar)s 5808(of)s +6079(Lout)s 6591(objects)s 7319(is)s 7529(accordingly)s 240 fnt78 +1332 3657(\256)m 1332 3324(\256)m 1332 2991(\256)m 1332 2707(\256)m 1332 2374(\256)m +1332 2080(\256)m 1332 1747(\256)m 1332 1463(\256)m 240 fnt83 480 3665(object)m +1826(object)s 2498(in\207xop)s 3227(object)s 1826 3332(pr)m 8(e\207xop)k +2680(object)s 1826 2999(object)m 2498(post\207xop)s 1826 2715(nopar)m 2(sop)k +1826 2382(liter)m 3(alwor)k 8(d)k 220 fnt35 1826 2083({)m +240 fnt83 1974 2088(object)m 220 fnt35 2646 2083(})m 240 fnt83 +1826 1755(object)m 2498(object)s 240 fnt82 0 960(where)m 240 fnt83 +640 962(in\207xop)m 240 fnt82 1285 960(,)m 240 fnt83 1391 962(pr)m 8(e\207xop)k +240 fnt82 2161 960(,)m 240 fnt83 2267 962(post\207xop)m 240 fnt82 +3125 960(,)m 3232(and)s 240 fnt83 3635 962(nopar)m 2(sop)k +240 fnt82 4591 960(are)m 4938(identi\207ers)s 5943(naming)s 6713(operators)s +7653(which)s 8294(tak)s 2(e)k 8745(0,)s 8971(1)s +0 672(or)m 255(2)s 424(parameters,)s 1573(as)s 1819(sho)s 6(wn,)k +2541(and)s 240 fnt83 2940 674(liter)m 3(alwor)k 8(d)k +240 fnt82 4067 672(is)m 4272(a)s 4433(sequence)s 5362(of)s +5628(non-space)s 6649(characters,)s 7719(or)s 7973(an)s 8251(arbitrary)s + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 4 5 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4348 13844(-)m 4476(4)s 4650(-)s 0 13256(sequence)m 969(of)s +1276(characters)s 2330(enclosed)s 3262(in)s 3541(double)s 4285(quotes.)s +5110(Ambiguities)s 6380(are)s 6763(resolv)s 3(ed)k 7664(by)s +7995(precedence)s 0 12968(and)m 404(associati)s 6(vity)k 15(.)k +480 12594(The)m 941(last)s 1366(production)s 2494(allo)s 6(ws)k +3197(a)s 3397(meaning)s 4307(for)s 4679(e)s 3(xpressions)k +5877(such)s 6407(as)s 220 fnt35 6691 12591({})m 240 fnt82 +6828 12594(,)m 6968(in)s 7245(which)s 7921(an)s 8238(object)s +8916(is)s 0 12306(missing.)m 907(The)s 1333(v)s 6(alue)k +1899(of)s 2168(this)s 240 fnt83 2562 12308(empty)m 3187(object)s +240 fnt82 3833 12306(is)m 4041(a)s 4205(rectangle)s 5135(of)s +5404(size)s 5829(0)s 6002(by)s 6294(0,)s 6519(with)s +6999(one)s 7399(column)s 8172(mark)s 8722(and)s 0 12018(one)m +402(ro)s 6(w)k 822(mark,)s 1420(that)s 1838(prints)s +2433(as)s 2683(nothing.)s 480 11644(The)m 938(second-last)s 2103(production)s +3227(generates)s 4210(sequences)s 5261(of)s 5562(arbitrary)s 6467(objects)s +7225(separated)s 8215(by)s 8539(white)s 0 11356(space,)m 671(called)s +240 fnt83 1333 11358(par)m 3(a)k 2(gr)k 3(aphs)k +240 fnt82 2439 11356(.)m 2636(Ignoring)s 3547(paragraph)s 4593(breaking)s +5517(for)s 5888(no)s 6(w)k 15(,)k 6421(the)s +6802(natural)s 7554(meaning)s 8464(is)s 8708(that)s 0 11068(the)m +361(tw)s 2(o)k 784(objects)s 1525(should)s 2235(appear)s +2946(side)s 3400(by)s 3707(side,)s 4212(and)s 4629(Lout')s 13(s)k +5305(parser)s 5961(accordingly)s 7157(interpolates)s 8335(an)s 8632(in\207x)s +0 10780(horizontal)m 1017(concatenation)s 2395(operator)s 3244(\(see)s 3677(belo)s 6(w\))k +4377(between)s 5224(them.)s 5859(This)s 6328(operator)s 7177(is)s +7380(associati)s 6(v)k 3(e,)k 8519(so)s 8778(the)s +0 10492(grammatical)m 1262(ambiguity)s 2301(does)s 2806(no)s 3113(harm.)s +3783(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k +4758(the)s 5120(Algol-60)s 6054(rule)s 6496(that)s 6928(white)s +7530(space)s 8132(should)s 8844(be)s 0 10204(signi\207cant)m 1056(only)s +1536(as)s 1786(a)s 1952(separator)s 2887(is)s 3097(necessarily)s +4212(brok)s 2(en)k 4932(by)s 5226(Lout)s 5738(in)s +5981(just)s 6386(this)s 6782(one)s 7184(place.)s 480 9830(Algol-lik)m 2(e)k +1506(languages)s 2504(distinguish)s 3601(literal)s 4201(strings)s 4879(from)s +5393(identi\207ers)s 6389(by)s 6673(enclosing)s 7633(them)s 8161(in)s +8394(quotes,)s 0 9542(b)m 4(ut)k 372(literals)s 1082(are)s +1440(f)s 2(ar)k 1773(too)s 2143(frequent)s 3010(in)s +3264(document)s 4278(formatting)s 5350(for)s 5699(this)s 6106(to)s +6356(be)s 6649(viable.)s 7408(The)s 7847(con)s 9(v)k 3(entional)k +0 9254(solution)m 829(is)s 1041(to)s 1282(be)s 3(gin)k +1870(identi\207ers)s 2878(with)s 3362(a)s 3530(special)s 4250(character)s 9(,)k +5224(and)s 5630(Lout)s 6144(follo)s 6(ws)k 6908(Scribe)s +7576([7])s 7895(in)s 8140(using)s 8714(`@')s 0 8966(rather)m +616(than)s 1085(the)s 1433(`\\')s 1690(of)s 1961(trof)s 6(f)k +2450([8])s 2767(and)s 3171(T)s 3313 8918(E)m 3456 8966(X)m +3685([9].)s 480 8592(Ho)m 6(we)k 6(v)k 3(er)k 9(,)k +1447(Lout)s 1966(tak)s 2(es)k 2513(the)s 2868(unusual)s +3675(step)s 4120(of)s 4398(making)s 5176(an)s 5466(initial)s +6084(`@')s 6503(optional.)s 7458(The)s 7893(designers)s 8855(of)s +0 8304(Eqn)m 449(apparently)s 1519(considered)s 2620(such)s 3122(characters)s +4147(dis\207guring)s 5244(in)s 5494(\207ne-grained)s 6713(input)s 7272(lik)s 2(e)k +7691(equations,)s 8722(and)s 0 8016(this)m 401(author)s 1077(agrees.)s +1856(The)s 2289(implementation)s 3851(is)s 4066(straightforw)s 2(ard:)k +5707(`@')s 6124(is)s 6339(classed)s 7092(as)s 7347(just)s +7757(another)s 8539(letter)s 9(,)k 0 7728(and)m 407(e)s 6(v)k 3(ery)k +986(w)s 2(ord)k 1537(is)s 1750(searched)s 2647(for)s +2988(in)s 3234(the)s 3585(symbol)s 4348(table.)s 4979(If)s +5212(it)s 5407(is)s 5620(found,)s 6289(it)s 6484(is)s +6697(an)s 6983(identi\207er)s 9(,)k 7946(otherwise)s 8934(it)s +0 7440(is)m 214(a)s 384(literal.)s 1107(A)s 1341(w)s 2(arning)k +2181(message)s 3051(is)s 3265(printed)s 4004(when)s 4585(a)s +4755(literal)s 5369(be)s 3(ginning)k 6381(with)s 6867(`@')s +7284(is)s 7498(found,)s 8168(since)s 8719(it)s 8916(is)s +0 7152(probably)m 905(a)s 1071(mis-spelt)s 2006(identi\207er)s 13(.)k +3019(No)s 3365(such)s 3861(safety)s 4485(net)s 4837(is)s +5047(possible)s 5887(for)s 6225(identi\207ers)s 7231(without)s 8022(`@'.)s +480 6778(Equation)m 1418(formatting)s 2496(also)s 2951(demands)s 3871(symbols)s +4737(made)s 5328(from)s 5869(punctuation)s 7074(characters,)s 8165(such)s +8678(as)s 220 fnt35 8946 6775(+)m 240 fnt82 0 6490(and)m +220 fnt35 404 6487(<=)m 240 fnt82 652 6490(.)m 816(It)s +1021(is)s 1231(traditional)s 2267(to)s 2506(allo)s 6(w)k +3085(such)s 3581(symbols)s 4430(to)s 4669(be)s 4951(juxtaposed,)s +6095(which)s 6737(means)s 7399(that)s 7817(the)s 8165(input)s +220 fnt35 480 6040(<=++)m 240 fnt82 0 5589(for)m 354(e)s 3(xample)k +1234(must)s 1776(be)s 2075(interpreted)s 3184(within)s 3869(the)s +4234(le)s 3(xical)k 4939(analyser)s 5812(by)s 6123(searching)s +7109(the)s 7474(symbol)s 8251(table)s 8788(for)s 0 5301(its)m +306(pre\207x)s 3(es)k 1142(in)s 1416(the)s 1795(order)s +220 fnt35 2390 5298(<=++)m 240 fnt82 2894 5301(,)m 220 fnt35 +3032 5298(<=+)m 240 fnt82 3408 5301(,)m 220 fnt35 3546 5298(<=)m +240 fnt82 3794 5301(.)m 3988(Although)s 4981(this)s 5408(tak)s 2(es)k +5979(quadratic)s 6952(time,)s 7514(in)s 7788(practice)s 8630(such)s +0 5013(sequences)m 1021(are)s 1368(too)s 1727(short)s 2265(to)s +2504(mak)s 2(e)k 3076(a)s 3242(more)s 3789(sophisticated)s +5095(linear)s 5698(method)s 6474(lik)s 2(e)k 6886(tries)s +7347(w)s 2(orthwhile.)k 240 fnt84 0 4364(2.3.)m 471(Basic)s +1073(structural)s 2149(operators)s 240 fnt82 480 3887(A)m 696(programming)s +2036(language)s 2941(may)s 3393(be)s 3660(considered)s 4739(complete)s +5656(when)s 6218(it)s 6395(attains)s 7054(the)s 7388(po)s 6(wer)k +8025(of)s 8281(a)s 8432(T)s 10(uring)k 0 3599(machine,)m +917(b)s 4(ut)k 1280(no)s 1574(such)s 2071(criterion)s +2937(seems)s 3573(rele)s 6(v)k 6(ant)k 4390(to)s +4630(document)s 5635(formatting.)s 6808(Instead,)s 7606(as)s 7857(the)s +8206(language)s 0 3311(de)m 6(v)k 3(elops)k 913(and)s +1338(ne)s 6(w)k 1806(applications)s 3033(are)s 3401(attempted,)s +4471(de\207ciencies)s 5670(are)s 6038(e)s 3(xposed)k 6899(and)s +7324(the)s 7693(operator)s 8570(set)s 8916(is)s 0 3023(re)m 6(vised)k +742(to)s 981(o)s 3(v)k 3(ercome)k 1974(them.)s +480 2649(Lout)m 1025(has)s 1429(a)s 1629(repertoire)s 2646(of)s +2950(23)s 3268(primiti)s 6(v)k 3(e)k 4224(operators)s +5198(\(Figure)s 5990(1\),)s 6390(which)s 7066(has)s 7470(pro)s 3(v)k 3(en)k +8220(adequate)s 0 2361(for)m 348(a)s 525(wide)s 1056(v)s 6(ariety)k +1778(of)s 2059(features,)s 2932(including)s 3899(equations,)s 4934(tables,)s +5609(and)s 6023(page)s 6542(layout,)s 7257(and)s 7672(so)s +7948(seems)s 8594(to)s 8844(be)s 0 2073(reasonably)m 1077(complete)s +1995(in)s 2225(this)s 2607(pragmatic)s 3602(sense.)s 4270(In)s +4513(this)s 4895(section)s 5616(we)s 5937(introduce)s 6883(the)s +7217(eight)s 7741(concatenation)s 0 1785(and)m 424(mark-hiding)s 1680(operators.)s +2754(T)s 19(o)k 3075(them)s 3634(f)s 2(alls)k +4114(the)s 4482(basic)s 5047(task)s 5514(of)s 5806(assembling)s +6956(comple)s 3(x)k 7853(objects)s 8602(from)s 0 1497(simple)m +693(ones,)s 1239(and)s 1643(the)s 3(y)k 2106(were)s +2626(the)s 2974(\207rst)s 3405(to)s 3644(be)s 3926(designed)s +4835(and)s 5239(implemented.)s 480 1123(Man)m 3(y)k 1094(of)s +1370(the)s 1723(operators)s 2668(of)s 2944(Eqn)s 3392(can)s +3786(be)s 4073(vie)s 6(wed)k 4821(as)s 5076(b)s 4(uilding)k +5928(small)s 6505(tables.)s 7231(A)s 7466(b)s 4(uilt-up)k +8277(fraction,)s 0 835(for)m 367(e)s 3(xample,)k 1310(has)s +1710(one)s 2141(column)s 2945(and)s 3379(three)s 3941(ro)s 6(ws)k +4480(\(numerator)s 9(,)k 5669(line,)s 6163(and)s 6596(denominator\).)s +8078(Numerous)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 5 6 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4352 13841(-)m 4480(5)s 4646(-)s 240 fnt83 266 13217(object)m +220 fnt35 974 13212(/)m 240 fnt83 1038 13217(gap)m 1511(object)s +240 fnt82 3816 13215(V)m 26(ertical)k 4613(concatenation)s 5998(with)s +6480(mark)s 7032(alignment)s 240 fnt83 266 12929(object)m 220 fnt35 +974 12924(//)m 240 fnt83 1099 12929(gap)m 1572(object)s 240 fnt82 +3816 12927(V)m 26(ertical)k 4613(concatenation)s 5998(with)s 6480(left)s +6857(justi\207cation)s 240 fnt83 266 12641(object)m 220 fnt35 974 12636(|)m +240 fnt83 1011 12641(gap)m 1484(object)s 240 fnt82 3816 12639(Horizontal)m +4893(concatenation)s 6278(with)s 6760(mark)s 7312(alignment)s 240 fnt83 +266 12353(object)m 220 fnt35 974 12348(||)m 240 fnt83 1068 12353(gap)m +1541(object)s 240 fnt82 3816 12351(Horizontal)m 4893(concatenation)s 6278(with)s +6760(top-justi\207cation)s 240 fnt83 266 12065(object)m 220 fnt35 974 12060(&)m +240 fnt83 1116 12065(gap)m 1589(object)s 240 fnt82 3816 12063(Horizontal)m +4893(concatenation)s 6278(within)s 6946(paragraphs)s 220 fnt35 266 11772(@OneCol)m +240 fnt83 1338 11777(object)m 240 fnt82 3816 11775(Hide)m 4337(all)s +4630(b)s 4(ut)k 4992(one)s 5394(column)s 6169(mark)s +6721(of)s 240 fnt83 6992 11777(object)m 220 fnt35 266 11484(@OneRo)m 3(w)k +240 fnt83 1457 11489(object)m 240 fnt82 3816 11487(Hide)m 4337(all)s +4630(b)s 4(ut)k 4992(one)s 5394(ro)s 6(w)k +5814(mark)s 6366(of)s 240 fnt83 6637 11489(object)m 266 11201(font)m +220 fnt35 762 11196(@F)m 6(ont)k 240 fnt83 1534 11201(object)m +240 fnt82 3816 11199(Render)m 240 fnt83 4567 11201(object)m 240 fnt82 +5215 11199(in)m 5458(nominated)s 6526(font)s 240 fnt83 266 10913(br)m 8(eakstyle)k +220 fnt35 1353 10908(@Break)m 240 fnt83 2269 10913(object)m 240 fnt82 +3816 10911(Break)m 4448(paragraphs)s 5548(of)s 240 fnt83 5819 10913(object)m +240 fnt82 6467 10911(in)m 6710(nominated)s 7778(style)s 240 fnt83 +266 10625(spacestyle)m 220 fnt35 1361 10620(@Space)m 240 fnt83 2318 10625(object)m +240 fnt82 3816 10623(Render)m 4567(spaces)s 5242(between)s 6096(w)s 2(ords)k +6730(in)s 6973(nominated)s 8041(style)s 240 fnt83 266 10337(length)m +220 fnt35 979 10332(@Wide)m 240 fnt83 1813 10337(object)m 240 fnt82 +3816 10335(Render)m 240 fnt83 4567 10337(object)m 240 fnt82 5215 10335(to)m +5454(width)s 240 fnt83 6056 10337(length)m 266 10049(length)m 220 fnt35 +979 10044(@High)m 240 fnt83 1758 10049(object)m 240 fnt82 3816 10047(Render)m +240 fnt83 4567 10049(object)m 240 fnt82 5215 10047(to)m 5454(height)s +240 fnt83 6112 10049(length)m 220 fnt35 266 9756(@HExpand)m 240 fnt83 +1499 9761(object)m 240 fnt82 3816 9759(Expand)m 4606(horizontal)s 5630(g)s 1(aps)k +6119(to)s 6358(\207ll)s 6678(a)s 4(v)k 6(ailable)k +7586(space)s 220 fnt35 266 9468(@VExpand)m 240 fnt83 1487 9473(object)m +240 fnt82 3816 9471(Expand)m 4606(v)s 3(ertical)k 5373(g)s 1(aps)k +5862(to)s 6101(\207ll)s 6421(a)s 4(v)k 6(ailable)k +7329(space)s 220 fnt35 266 9180(@HScale)m 240 fnt83 1307 9185(object)m +240 fnt82 3816 9183(Horizontal)m 4893(geometrical)s 6075(scaling)s 6805(to)s +7044(\207ll)s 7364(a)s 4(v)k 6(ailable)k 8272(space)s +220 fnt35 266 8892(@VScale)m 240 fnt83 1295 8897(object)m 240 fnt82 +3816 8895(V)m 26(ertical)k 4613(geometrical)s 5795(scaling)s 6525(to)s +6764(\207ll)s 7084(a)s 4(v)k 6(ailable)k 7992(space)s +240 fnt83 266 8609(angle)m 220 fnt35 911 8604(@Rotate)m 240 fnt83 +1892 8609(object)m 240 fnt82 3816 8607(Rotate)m 240 fnt83 4496 8609(object)m +240 fnt82 5144 8607(by)m 240 fnt83 5438 8609(angle)m 266 8321(P)m 19(ostScript)k +220 fnt35 1367 8316(@Gr)m 2(aphic)k 240 fnt83 2471 8321(object)m +240 fnt82 3816 8319(Escape)m 4549(to)s 4788(graphics)s 5649(language)s +220 fnt35 266 8028(@Ne)m 6(xt)k 240 fnt83 1050 8033(object)m +240 fnt82 3816 8031(Add)m 4287(1)s 4442(to)s 4681(an)s +4964(object)s 5608(denoting)s 6499(a)s 6665(number)s 240 fnt83 +266 7745(object)m 220 fnt35 974 7740(@Case)m 240 fnt83 1821 7745(alternatives)m +240 fnt82 3816 7743(Select)m 4459(from)s 4983(a)s 5149(set)s +5474(of)s 5745(alternati)s 6(v)k 3(e)k 6799(objects)s +240 fnt83 266 7457(identi\207er)m 220 fnt35 1254 7452(&&)m 240 fnt83 +1662 7457(object)m 240 fnt82 3816 7455(Cross)m 4412(reference)s 240 fnt83 +266 7169(cr)m 10(oss-r)k 8(efer)k 8(ence)k 220 fnt35 +1839 7164(@Open)m 240 fnt83 2705 7169(object)m 240 fnt82 3816 7167(Retrie)m 6(v)k 3(e)k +4672(v)s 6(alue)k 5240(from)s 5764(cross)s 6306(reference)s +240 fnt83 266 6881(cr)m 10(oss-r)k 8(efer)k 8(ence)k +220 fnt35 1839 6876(@T)m 26(agged)k 240 fnt83 2888 6881(object)m +240 fnt82 3816 6879(Attach)m 4510(cross)s 5052(referencing)s 6192(tag)s +6537(to)s 6776(object)s 240 fnt84 472 6199(Figur)m 4(e)k +1201(1.)s 1492(The)s 1947(23)s 2240(primiti)s 2(v)k 2(e)k +3233(operators)s 4270(of)s 4542(Lout,)s 5148(in)s 5403(order)s +6032(of)s 6304(incr)s 4(easing)k 7405(pr)s 4(ecedence.)k +240 fnt82 0 5562(in)m 9(v)k 3(estig)k 1(ations)k +1377(of)s 1660(this)s 2068(kind)s 2564(con)s 9(vinced)k +3609(the)s 3969(author)s 4652(that)s 5082(operators)s 6034(capable)s +6832(of)s 7115(assembling)s 8256(the)s 8616(ro)s 6(ws)k +0 5274(and)m 404(columns)s 1266(of)s 1537(tables)s 2145(w)s 2(ould)k +2800(suf\207ce)s 3493(for)s 3831(b)s 4(uilding)k 4678(all)s +4971(kinds)s 5541(of)s 5812(objects.)s 480 4900(The)m 906(simplest)s +1759(objects)s 2485(are)s 2829(empty)s 3479(objects)s 4204(and)s +4605(literal)s 5213(w)s 2(ords)k 5844(lik)s 2(e)k +220 fnt35 6254 4897(metempsychosis)m 240 fnt82 7882 4900(,)m 7986(which)s +8625(ha)s 4(v)k 3(e)k 0 4612(one)m 402(column)s +1177(mark)s 1729(and)s 2133(one)s 2535(ro)s 6(w)k +2955(mark:)s 1572 215 0 106 240 288 60 480 4106 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +1572 215 0 106 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1572 215 0 106 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 52(metempsychosis)m +grestore + +grestore +end end restore +grestore +0 3655(T)m 19(o)k 337(place)s +934(tw)s 2(o)k 1381(arbitrary)s 2294(objects)s 3059(side)s +3537(by)s 3868(side,)s 4398(we)s 4770(use)s 5182(the)s +5567(in\207x)s 6099(operator)s 220 fnt35 6992 3652(|)m 240 fnt82 +7029 3655(,)m 7173(denoting)s 8102(horizontal)s 0 3367(concatenation.)m 1492(F)s 3(or)k +1881(e)s 3(xample,)k 220 fnt35 480 2866(USA |0.2i A)m 6(ustr)k 2(alia)k +240 fnt82 0 2411(produces)m 915(the)s 1263(object)s 476 166 0 57 240 288 60 480 1905 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 3(USA)m + +grestore + +grestore +end end restore +grestore +875 166 0 57 240 288 60 1244 1905 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +875 165 0 56 240 288 60 0 1 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +875 165 0 56 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 2(Australia)m +grestore + +grestore +end end restore +grestore +0 1454(The)m 443(ro)s 6(w)k 879(marks)s +1529(are)s 1892(mer)s 4(ged)k 2678(into)s 3119(one,)s +3587(\207xing)s 4215(the)s 4579(v)s 3(ertical)k 5361(position)s +6205(of)s 6491(the)s 6855(objects)s 7598(relati)s 6(v)k 3(e)k +8376(to)s 8631(each)s 0 1166(other;)m 611(their)s 1116(horizontal)s +2148(separation)s 3196(is)s 3414(determined)s 4555(by)s 4857(the)s +240 fnt83 5214 1168(gap)m 240 fnt82 5635 1166(attached)m 6497(to)s +6744(the)s 7101(operator)s 9(,)k 8003(in)s 8254(this)s +8659(case)s 0 878(0.2)m 361(inches.)s 1143(W)s 19(e)k +1519(think)s 2080(of)s 2358(the)s 2713(g)s 1(ap)k +3118(as)s 3376(part)s 3814(of)s 4092(the)s 4448(operator)s 9(,)k +5349(although)s 6251(strictly)s 6974(it)s 7174(is)s 7391(a)s +7564(third)s 8081(parameter)s 13(.)k 0 590(It)m 205(may)s +671(be)s 953(omitted,)s 1790(def)s 2(aulting)k 2810(to)s +220 fnt35 3049 587(0i)m 240 fnt82 3205 590(.)m 240 fnt83 +480 218(V)m 26(ertical)k 1294(concatenation)s 240 fnt82 2644 216(,)m +2762(denoted)s 3590(by)s 3895(the)s 4254(in\207x)s 4760(operator)s +220 fnt35 5627 213(/)m 240 fnt82 5691 216(,)m 5809(is)s +6031(the)s 6390(same)s 6948(apart)s 7497(from)s 8032(the)s +8392(change)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 6 7 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4348 13842(-)m 4476(6)s 4649(-)s 0 13251(of)m 271(direction:)s +220 fnt35 480 12800(A)m 6(ustr)k 2(alia /0.1i USA)k 240 fnt82 +0 12345(produces)m 915(the)s 1263(object)s 875 165 0 56 240 288 60 480 11840 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +875 165 0 56 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +875 165 0 56 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 2(Australia)m +grestore + +grestore +end end restore +grestore +875 165 0 57 240 288 60 480 11531 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 3(USA)m + +grestore + +grestore +end end restore +grestore +0 11080(with)m 482(column)s 1257(marks)s 1892(mer)s 4(ged)k +2663(and)s 3067(a)s 3233(0.1)s 3568(inch)s 4037(g)s 1(ap.)k +480 10706(Consider)m 1404(no)s 6(w)k 1865(what)s 2390(happens)s +3226(when)s 3802(horizontal)s 4826(and)s 5230(v)s 3(ertical)k +5997(are)s 6344(combined:)s 220 fnt35 1000 10205({)m 1186(USA)s +2442(|0.2i)s 2958(A)s 6(ustr)k 2(alia)k 3919(})s +480 9917(/0.1i)m 1000({)s 1186(W)s 8(ashington)k 2442(|)s +2958(Canberr)s 2(a)k 3987(})s 240 fnt82 0 9418(The)m +445(tw)s 2(o)k 872(parameters)s 1987(of)s 220 fnt35 +2275 9415(/)m 240 fnt82 2416 9418(no)m 6(w)k 2895(ha)s 4(v)k 3(e)k +3413(tw)s 2(o)k 3840(column)s 4632(marks)s 5284(each,)s +5846(and)s 6268(the)s 3(y)k 6748(will)s 7191(be)s +7490(mer)s 4(ged)k 8278(with)s 8778(the)s 0 9130(corresponding)m +1422(marks)s 2057(in)s 2300(the)s 2648(other)s 3199(parameter)s 9(,)k +4251(yielding)s 5088(the)s 5436(object)s 476 166 0 57 240 288 60 480 8624 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +476 165 0 57 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 3(USA)m +grestore + +grestore +end end restore +grestore +659 166 0 57 240 288 60 956 8624 LoutGr2 +0 ymark moveto xsize 10 pt add ymark lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +876 166 0 57 240 288 60 1903 8624 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +875 165 0 56 240 288 60 0 1 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +875 165 0 56 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 2(Australia)m + +grestore + +grestore +end end restore +grestore +1135 215 0 106 240 288 60 480 8265 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +1135 215 0 106 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1135 215 0 106 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 52(W)m 19(ashington)k +grestore + +grestore +end end restore +grestore +876 215 0 106 240 288 60 1903 8265 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +876 166 0 57 240 288 60 0 49 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +876 166 0 57 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 3(Canberra)m +grestore + +grestore +end end restore +grestore +0 7814(The)m 220 fnt35 +425 7811(0.2i)m 240 fnt82 821 7814(g)m 1(ap)k 1216(separates)s +2139(columns,)s 3054(not)s 3416(indi)s 6(vidual)k 4432(items)s +4997(in)s 5237(columns,)s 6152(so)s 6414(a)s 6577(g)s 1(ap)k +6972(attached)s 7823(to)s 8059(the)s 8403(second)s 220 fnt35 +0 7523(|)m 240 fnt82 96 7526(w)m 2(ould)k 749(serv)s 3(e)k +1304(no)s 1595(purpose;)s 2464(an)s 3(y)k 2859(such)s +3353(g)s 1(ap)k 3749(is)s 3957(ignored.)s 4851(If)s +5079(the)s 5425(number)s 6214(of)s 6484(marks)s 7117(to)s +7354(be)s 7634(mer)s 4(ged)k 8403(dif)s 6(fers,)k +0 7238(empty)m 638(columns)s 1485(are)s 1818(added)s 2433(at)s +2651(the)s 2984(right)s 3481(to)s 3705(equalize)s 4542(the)s +4876(number)s 13(.)k 5743(The)s 6157(four)s 6600(marks)s +7221(protruding)s 8269(from)s 8778(the)s 0 6950(result)m 601(are)s +959(all)s 1263(a)s 4(v)k 6(ailable)k 2182(for)s +2531(mer)s 4(ging)k 3389(with)s 3882(neighbouring)s 5223(marks)s +5869(by)s 6174(other)s 6736(concatenation)s 8133(operators.)s 0 6662(The)m +428(precedence)s 1559(of)s 220 fnt35 1830 6659(|)m 240 fnt82 +1927 6662(is)m 2137(higher)s 2808(than)s 3277(the)s 3625(precedence)s +4756(of)s 220 fnt35 5027 6659(/)m 240 fnt82 5091 6662(,)m +5198(so)s 5464(the)s 5812(braces)s 6473(could)s 7063(be)s +7345(omitted.)s 480 6288(When)m 1131(lines)s 1656(of)s 1950(te)s 3(xt)k +2387(are)s 2757(concatenated,)s 4135(it)s 4349(is)s 4582(con)s 9(v)k 3(entional)k +5884(to)s 6145(measure)s 7020(their)s 7540(separation)s 8602(from)s +0 6000(baseline)m 832(to)s 1063(baseline)s 1894(\(mark)s 2517(to)s +2748(mark)s 3292(in)s 3527(Lout\),)s 4157(rather)s 4765(than)s +5226(from)s 5742(edge)s 6242(to)s 6473(edge)s 6973(as)s +7215(abo)s 3(v)k 3(e.)k 7937(This)s 8405(idea)s +8855(of)s 0 5712(dif)m 6(ferent)k 863(reference)s 1794(points)s +2417(for)s 2743(measurement)s 4065(e)s 6(v)k 4(olv)k 3(ed)k +4855(o)s 3(v)k 3(er)k 5322(the)s 5658(years)s +6200(into)s 6613(a)s 6767(system)s 7478(of)s 7737(six)s +240 fnt83 8059 5714(gap)m 8459(modes)s 240 fnt82 0 5424(\(Figure)m +769(2\),)s 1085(e)s 3(xpressed)k 2094(by)s 2398(appending)s +3460(a)s 3636(letter)s 4195(to)s 4445(the)s 4803(length.)s +5576(F)s 3(or)k 5975(e)s 3(xample,)k 220 fnt35 +6899 5421(|0.2i)m 240 fnt82 7366 5424(is)m 7586(an)s 7880(abbre)s 6(viation)k +0 5136(for)m 220 fnt35 377 5133(|0.2ie)m 240 fnt82 901 5136(,)m +1047(meaning)s 1963(0.2)s 2356(inches)s 3057(measured)s 4070(from)s +4633(edge)s 5180(to)s 5458(edge;)s 220 fnt35 6061 5133(|0.3ix)m +240 fnt82 6678 5136(produces)m 7632(a)s 7837(0.3)s 8220(inch)s +8728(g)s 1(ap)k 0 4848(measured)m 972(from)s 1493(mark)s +2043(to)s 2279(mark)s 2829(and)s 3230(widened)s 4097(if)s +4311(necessary)s 5292(to)s 5528(pre)s 6(v)k 3(ent)k +6294(o)s 3(v)k 3(erstriking;)k 7552(and)s 220 fnt35 +7954 4845(|2.5it)m 240 fnt82 8478 4848(places)m 0 4560(its)m 273(right)s +781(parameter)s 1792(2.5)s 2135(inches)s 2794(from)s 3314(the)s +3659(current)s 4392(left)s 4766(mar)s 4(gin,)k 5543(irrespecti)s 6(v)k 3(e)k +6699(of)s 6967(the)s 7312(position)s 8137(of)s 8405(the)s +8749(left)s 0 4272(parameter)m 13(.)k 1098(There)s 1704(is)s +1907(also)s 2338(a)s 2496(choice)s 3169(of)s 3433(ele)s 6(v)k 3(en)k +4098(units)s 4606(of)s 4870(measurement)s 6197(\(inches,)s 6987(centimetres,)s +8186(multiples)s 0 3984(of)m 288(the)s 654(current)s 1407(font)s +1870(size,)s 2365(etc.\),)s 2907(the)s 3272(most)s 3815(interesting)s +4894(being)s 5496(the)s 220 fnt35 5862 3981(r)m 240 fnt82 +6012 3984(unit:)m 6568(one)s 220 fnt35 6987 3981(r)m 240 fnt82 +7138 3984(is)m 7365(the)s 7731(column)s 8524(width)s 0 3696(minus)m +635(the)s 982(width)s 1583(of)s 1852(the)s 2199(follo)s 6(wing)k +3175(object,)s 3864(so)s 4129(that)s 220 fnt35 4546 3693(|1r)m -8(t)k +240 fnt82 4921 3696(produces)m 5835(suf\207cient)s 6783(space)s 7368(to)s +7606(right)s 8116(justify)s 8778(the)s 0 3408(follo)m 6(wing)k +987(object,)s 1688(and)s 220 fnt35 2103 3405(|0.5r)m -8(t)k +240 fnt82 2673 3408(to)m 2923(center)s 3576(it.)s 3883(These)s +4520(features)s 5337(implement)s 6429(spacings)s 7315(needed)s 8061(in)s +8315(practice)s 0 3120(rather)m 608(than)s 1069(suggested)s 2063(by)s +2349(theory)s 15(.)k 3101(The)s 3(y)k 3636(w)s 2(ork)k +4179(with)s 4653(all)s 4938(\207v)s 3(e)k 5342(concatenation)s +6719(operators,)s 7707(horizontal)s 8722(and)s 0 2832(v)m 3(ertical.)k +480 2458(When)m 1113(we)s 1452(construct)s 2392(a)s 2562(b)s 4(uilt-up)k +3372(fraction,)s 4225(the)s 4577(result)s 5171(has)s 5545(three)s +6082(ro)s 6(w)k 6506(marks,)s 7201(b)s 4(ut)k +7567(only)s 8051(the)s 8403(second)s 0 2170(should)m 697(be)s +979(visible)s 1672(outside)s 2419(the)s 2767(object:)s gsave +480 1339 translate +240 fnt83 156 491 0 288 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +156 491 0 288 240 288 12 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +156 491 0 288 240 288 12 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +0 336(X)m +156 0 0 0 240 288 12 0 288 LoutGr2 +0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke +grestore + +grestore +2 68(Y)m +grestore + +grestore +end end restore +grestore +0 888(This)m 493(is)s 721(a)s 905(common)s +1817(problem,)s 2739(and)s 3161(accordingly)s 4361(a)s 220 fnt35 +4545 885(@OneRo)m 3(w)k 240 fnt82 5694 888(operator)m 6567(w)s 2(as)k +7006(introduced)s 8105(for)s 8461(hiding)s 0 600(all)m 291(b)s 4(ut)k +650(one)s 1050(of)s 1318(the)s 1663(ro)s 6(w)k +2081(marks)s 2713(of)s 2981(its)s 3255(parameter)s 13(.)k +4357(Normally)s 15(,)k 5363(the)s 5708(\207rst)s 6136(mark)s +6686(is)s 6893(the)s 7238(survi)s 6(v)k 4(or)k 9(,)k +8121(b)s 4(ut)k 8480(a)s 8643(later)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 7 8 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +%%+ font Symbol +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4351 13848(-)m 4479(7)s 4647(-)s 6693 8221 0 8221 240 288 60 1186 5201 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +0 7447(Edge-to-edge)m 220 fnt35 +1786 7444(|)m 240 fnt83 1843 7449(length)m 220 fnt35 2456 7444(e)m +240 fnt82 0 6238(Hyphenation)m 220 fnt35 1786 6235(|)m 240 fnt83 +1843 6240(length)m 220 fnt35 2456 6235(h)m 240 fnt82 0 5029(Ov)m 3(erstrik)k 2(e)k +220 fnt35 1786 5026(|)m 240 fnt83 1843 5031(length)m 220 fnt35 +2456 5026(o)m 240 fnt82 0 3820(Mark-to-mark)m 220 fnt35 1786 3817(|)m +240 fnt83 1843 3822(length)m 220 fnt35 2456 3817(x)m 240 fnt82 +0 2611(K)m 6(erning)k 220 fnt35 1786 2608(|)m 240 fnt83 +1843 2613(length)m 220 fnt35 2456 2608(k)m 240 fnt82 0 1402(T)m 19(ab)k 4(ulation)k +220 fnt35 1786 1399(|)m 240 fnt83 1843 1404(length)m 220 fnt35 +2456 1399(t)m gsave +3291 0 translate +240 fnt82 3402 8221 0 8221 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +567 7485 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 7371 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 7485 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 7371 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2267 7395 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 1020 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +1247 7395 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +1247 7395 translate +180 fnt82 1020 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +1247 7395 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +180 fnt83 1534 7192(length)m gsave +567 6304 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 6190 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 6304 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 6190 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2267 6214 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 1020 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +1247 6214 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +1247 6214 translate +180 fnt82 1020 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +1247 6214 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +1534 6011(length)m gsave +567 5123 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 5009 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 5123 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 5009 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2551 4976 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +680 4976 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +680 4976 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +680 4976 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +1392 4774(length)m +gsave +567 3886 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 3772 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 3886 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 3772 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2551 3739 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +680 3739 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +680 3739 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +680 3739 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +180 fnt82 941 3536(max)m 180 fnt78 1256 3531(\()m 180 fnt83 +1319 3537(length)m 180 fnt78 1774 3531(,)m 180 fnt83 1854 3537(a)m +180 fnt78 1994 3531(+)m 180 fnt83 2145 3537(b)m 180 fnt78 +2240 3531(\))m gsave +1247 4363 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 567 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +680 4363 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +680 4363 translate +180 fnt82 567 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +680 4363 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +180 fnt83 920 4431(a)m gsave +2551 4363 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 283 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +2268 4363 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +2268 4363 translate +180 fnt82 283 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +2268 4363 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +2366 4387(b)m gsave +567 2590 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 2476 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 2590 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 2476 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2551 2443 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +680 2443 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +680 2443 translate +180 fnt82 1871 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +680 2443 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +180 fnt82 +999 2240(max)m 180 fnt78 1314 2235(\()m 180 fnt83 1377 2241(length)m +180 fnt78 1832 2235(,)m 180 fnt83 1912 2241(a)m 180 fnt78 +2007 2235(,)m 180 fnt83 2087 2241(b)m 180 fnt78 2182 2235(\))m +gsave +1247 3067 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 567 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +680 3067 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +680 3067 translate +180 fnt82 567 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +680 3067 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +180 fnt83 920 3135(a)m gsave +2551 3067 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 283 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +2268 3067 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +2268 3067 translate +180 fnt82 283 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +2268 3067 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +2366 3091(b)m gsave +567 1438 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +680 1324 translate +180 fnt82 2722 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 1438 translate +180 fnt82 680 340 0 340 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto +xsize ysize lineto 0 ysize lineto closepath +gsave 0.9 setgray fill grestore stroke +grestore + +grestore +gsave +2551 1324 translate +180 fnt82 851 567 0 567 180 288 45 LoutGraphic +gsave +0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke +grestore + +grestore +gsave +2268 1234 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 2268 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +0 1234 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 1234 translate +180 fnt82 2268 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 1234 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +1587 1032(length)m gsave +3402 734 translate +180.0000 rotate +gsave +0 0 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 0 translate +180 fnt82 3402 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 0 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore + +grestore +gsave +0 734 translate +30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +gsave +0 734 translate +180 fnt82 3402 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +gsave +0 734 translate +-30.0000 rotate +gsave +0 0 translate +180 fnt82 68 0 0 0 180 288 45 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore + +grestore +1189 523(curr)m 6(ent)k +1759(bound)s +grestore +end end restore +grestore +240 fnt84 0 4610(Figur)m 4(e)k 774(2.)s +1110(The)s 1610(six)s 1991(gap)s 2462(modes)s 3212(\()s +240 fnt83 3285 4613(length)m 240 fnt84 3984 4610(is)m 4242(any)s +4716(length\).)s 5648(Hyphenation)s 7078(mode)s 7737(has)s 8182(an)s +8537(extra)s 0 4322(pr)m 4(operty)k 955(not)s 1347(sho)s 2(wn)k +2053(her)s 4(e.)k 240 fnt82 0 3685(mark)m 552(can)s +941(be)s 1223(chosen)s 1945(by)s 2239(pre\207xing)s 220 fnt35 +3156 3682(^)m 240 fnt82 3322 3685(to)m 3561(the)s 3909(preceding)s +4905(concatenation)s 6290(operator:)s 220 fnt35 480 3184(@OneRo)m 3(w { X ^/2p @HLine /2p )k 19(Y })k +240 fnt82 0 2688(has)m 396(the)s 770(desired)s 1545(result,)s +2208(where)s 220 fnt35 2874 2685(2p)m 240 fnt82 3197 2688(is)m +3433(tw)s 2(o)k 3870(points)s 4532(and)s 220 fnt35 +4962 2685(@HLine)m 240 fnt82 5836 2688(is)m 6072(an)s 6381(easy)s +6887(combination)s 8166(of)s 8464(Lout')s 13(s)k 0 2400(graphics)m +861(operators.)s 1914(A)s 2144(similar)s 2866(operator)s 9(,)k +220 fnt35 3760 2397(@OneCol)m 240 fnt82 4712 2400(,)m 4819(hides)s +5375(column)s 6150(marks.)s 480 2026(A)m 728(v)s 6(ariant)k +1463(of)s 220 fnt35 1753 2023(/)m 240 fnt82 1895 2026(called)m +220 fnt35 2542 2023(//)m 240 fnt82 2745 2026(is)m 2974(pro)s 3(vided)k +3898(which)s 4558(performs)s 5490(v)s 3(ertical)k 6275(concatenation)s +7679(b)s 4(ut)k 8059(ignores)s 8833(all)s 0 1738(column)m +775(marks)s 1410(and)s 1814(simply)s 2519(left-justi\207es)s 3709(its)s +3985(tw)s 2(o)k 4395(parameters:)s 220 fnt35 480 1237(Heading //0.1i)m +480 949(A |0.2i B /0.1i)m 480 661(C | D)m 240 fnt82 0 206(has)m 370(result)s + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 8 9 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Symbol +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4351 13844(-)m 4479(8)s 4646(-)s 480 13253(Heading)m 480 12896(A)m +938(B)s 480 12590(C)m 938(D)s 0 12136(sho)m 6(wing)k +883(that)s 1325(spanning)s 2267(columns)s 3153(in)s 3420(tables)s +4052(moti)s 6(v)k 6(ate)k 4956(the)s 5328(inclusion)s +6286(of)s 6581(this)s 7001(operator)s 13(.)k 7972(There)s +8609(is)s 8843(an)s 0 11848(analogous)m 220 fnt35 1029 11845(||)m +240 fnt82 1191 11848(operator)m 13(.)k 2145(The)s 2581(author)s +3259(w)s 2(ould)k 3922(ha)s 4(v)k 3(e)k +4430(preferred)s 5370(to)s 5616(lea)s 4(v)k 3(e)k +6177(out)s 6550(these)s 7105(operators,)s 8108(since)s 8663(the)s 3(y)k +0 11560(complicate)m 1104(the)s 1452(implementation,)s 3059(and)s 3463(it)s +3655(is)s 3865(interesting)s 4926(to)s 5165(e)s 3(xamine)k +6028(the)s 6376(prospects)s 7330(of)s 7601(doing)s 8200(so.)s +480 11186(The)m 220 fnt35 953 11183(//)m 240 fnt82 1184 11186(operator)m +2086(is)s 2342(formally)s 3263(redundant,)s 4373(because)s 5232(in)s +5521(general)s 6324(the)s 6718(e)s 3(xpression)k 220 fnt35 +7841 11183(x // y)m 240 fnt82 8409 11186(can)m 8844(be)s 0 10898(replaced)m +867(by)s 220 fnt35 480 10397(@OneCol { | x } /)m 480 10109(@OneCol { | y })m 240 fnt82 +0 9611(for)m 338(an)s 3(y)k 734(objects)s 220 fnt35 +1462 9608(x)m 240 fnt82 1629 9611(and)m 220 fnt35 2032 9608(y)m +240 fnt82 2140 9611(.)m 2304(By)s 2637(concatenating)s 4017(an)s +4300(empty)s 4951(object)s 5594(at)s 5826(the)s 6173(left)s +6549(of)s 220 fnt35 6820 9608(x)m 240 fnt82 6987 9611(and)m +7390(hiding)s 8055(all)s 8347(b)s 4(ut)k 8708(that)s +0 9323(empty)m 641(object')s 13(s)k 1423(column)s 2186(mark,)s +2772(we)s 3095(ef)s 6(fecti)k 6(v)k 3(ely)k +4143(shift)s 220 fnt35 4615 9320(x)m 240 fnt82 4723 9323(')m 13(s)k +4921(column)s 5684(mark)s 6224(to)s 6452(its)s 6716(left)s +7081(edge.)s 7685(The)s 8101(same)s 8636(goes)s 0 9035(for)m +220 fnt35 349 9032(y)m 240 fnt82 457 9035(,)m 575(so)s +852(the)s 220 fnt35 1211 9032(/)m 240 fnt82 1347 9035(operator)m +2214(has)s 2595(just)s 3011(one)s 3424(column)s 4211(mark)s +4774(to)s 5024(mer)s 4(ge,)k 5735(at)s 5978(the)s +6338(e)s 3(xtreme)k 7171(left,)s 7606(and)s 8021(its)s +8308(ef)s 6(fect)k 8916(is)s 0 8747(indistinguishable)m 1690(from)s +220 fnt35 2214 8744(//)m 240 fnt82 2339 8747(.)m 480 8373(Unfortunately)m 15(,)k +1915(if)s 220 fnt35 2134 8370(y)m 240 fnt82 2304 8373(consists)m +3114(of)s 3387(tw)s 2(o)k 3799(ro)s 6(ws)k +4311(separated)s 5274(by)s 220 fnt35 5570 8370(/)m 240 fnt82 +5634 8373(,)m 5743(as)s 5995(in)s 6240(the)s 6590(e)s 3(xample)k +7455(abo)s 3(v)k 3(e,)k 8130(both)s 8616(ro)s 6(ws)k +0 8085(must)m 533(be)s 823(placed)s 1513(inside)s 2148(the)s +220 fnt35 2504 8082(@OneCol)m 240 fnt82 3456 8085(,)m 3571(and)s +3983(the)s 4340(table)s 4868(cannot)s 5574(be)s 5864(entered)s +6633(in)s 6884(the)s 7240(simple)s 7942(ro)s 6(w-by-ro)k 6(w)k +0 7797(manner)m 777(that)s 1194(non-e)s 3(xpert)k 2287(users)s +2828(naturally)s 3731(e)s 3(xpect.)k 4515(Another)s 5359(adv)s 6(antage)k +6378(of)s 220 fnt35 6649 7794(//)m 240 fnt82 6833 7797(is)m +7043(that)s 7460(its)s 7736(left)s 8112(parameter)s 0 7509(can)m +382(be)s 657(printed)s 1385(before)s 2044(its)s 2313(right)s +2817(parameter)s 3824(is)s 4027(kno)s 6(wn;)k 4779(this)s +5168(is)s 5371(important)s 6353(when)s 6922(the)s 7263(left)s +7633(parameter)s 8640(is)s 8843(an)s 0 7221(entire)m 599(page.)s +480 6847(The)m 960(\207fth)s 1468(and)s 1924(\207nal)s 2457(concatenation)s +3895(operator)s 9(,)k 220 fnt35 4841 6844(&)m 240 fnt82 +4983 6847(,)m 5143(is)s 5405(an)s 5741(e)s 3(xplicit)k +6567(v)s 3(ersion)k 7377(of)s 7701(the)s 8102(horizontal)s +0 6559(concatenation)m 1402(operator)s 2275(interpolated)s 3492(when)s 4085(objects)s +4830(are)s 5195(separated)s 6172(by)s 6483(white)s 7088(space.)s +7800(It)s 8022(is)s 8250(formally)s 0 6271(identical)m 907(to)s +220 fnt35 1177 6268(|)m 240 fnt82 1305 6271(e)m 3(xcept)k +2017(for)s 2386(taking)s 3068(higher)s 3770(precedence)s 4932(and)s +5367(being)s 5983(subject)s 6751(to)s 7021(replacement)s 8279(by)s +220 fnt35 8604 6268(//1vx)m 240 fnt82 0 5983(during)m 678(paragraph)s +1691(breaking)s 2581(\(Section)s 3434(2.5\).)s 240 fnt84 0 5334(2.4.)m +471(Implementation)s 2159(of)s 2431(objects)s 3201(and)s 3642(concatenation)s +240 fnt82 480 4857(In)m 738(this)s 1136(section)s 1872(we)s +2210(discuss)s 2954(the)s 3304(implementation)s 4863(of)s 5137(objects)s +5867(and)s 6273(concatenation,)s 7710(and)s 8117(especially)s 0 4569(mark)m +552(alignment.)s 1672(The)s 2100(\207rst)s 2531(step)s 2969(is)s +3179(to)s 3418(use)s 3793(an)s 4076(operator)s 4932(precedence)s +6063(parser)s 6706(to)s 6945(con)s 9(v)k 3(ert)k +7710(input)s 8262(such)s 8758(as)s 220 fnt35 480 4068(a |0.5i b /0.2i c | d)m +240 fnt82 0 3613(into)m 425(parse)s 985(trees)s 1486(such)s +1982(as)s gsave +480 1919 translate +240 fnt83 3396 1354 0 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1867 338 56 282 240 288 12 1529 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 136 106(\244)m +grestore +(T) lfigpromotelabels +grestore +1413 846 0 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +876 338 56 282 240 288 12 537 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m + +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +511 338 56 282 240 288 12 451 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +511 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +511 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 56 105(0)m 192 fnt83 +195 111(.)m 192 fnt78 270 105(5)m 192 fnt83 404 111(i)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 962 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 1075 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1413 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1413 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +517 846 56 790 240 288 12 1526 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 56 105(0)m 192 fnt83 +195 111(.)m 192 fnt78 270 105(2)m 192 fnt83 410 111(i)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2043 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1240 846 0 790 240 288 12 2156 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +789 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 451 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 789 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 902 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1240 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3396 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 1468(Missing)m 879(objects)s 1662(are)s 2065(replaced)s +2987(by)s 3336(empty)s 4044(objects,)s 4883(and)s 5342(sequences)s +6419(of)s 6745(concatenation)s 8186(operators)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 9 10 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Symbol +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4349 13844(-)m 4477(9)s 4648(-)s 0 13251(are)m 347(consolidated:)s +gsave +480 11602 translate +240 fnt83 2492 1359 0 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1415 338 56 282 240 288 12 1077 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +517 846 56 790 240 288 12 451 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 +56 105(0)m 192 fnt83 195 111(.)m 192 fnt78 270 105(2)m +192 fnt83 410 111(i)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 968 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1411 846 0 790 240 288 12 1081 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +875 338 56 282 240 288 12 536 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +509 338 56 282 240 288 12 451 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +509 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +509 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 56 105(0)m 192 fnt83 195 111(.)m +192 fnt78 270 105(3)m 192 fnt83 402 111(i)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 960 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 1073 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1411 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2492 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +240 fnt78 3284 12840(\336)m gsave +3825 11602 translate +240 fnt83 2492 1359 0 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1415 338 56 282 240 288 12 1077 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m + +grestore +(T) lfigpromotelabels +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +517 846 56 790 240 288 12 451 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +517 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 56 105(0)m 192 fnt83 +195 111(.)m 192 fnt78 270 105(2)m 192 fnt83 410 111(i)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 968 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 846 56 790 240 288 12 1081 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1419 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +509 846 56 790 240 288 12 1532 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +509 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +509 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt78 56 105(0)m 192 fnt83 +195 111(.)m 192 fnt78 270 105(3)m 192 fnt83 402 111(i)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2041 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 846 56 790 240 288 12 2154 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2492 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +240 fnt82 0 11151(to)m 239(mak)s 2(e)k +811(manifest)s 1693(their)s 2190(associati)s 6(vity)k 3432(and)s +3836(reduce)s 4529(the)s 4877(depth)s 5466(of)s 5737(the)s +6085(tree)s 6498(for)s 6836(ef\207cienc)s 3(y)k 7829(later)s 13(.)k +480 10777(The)m 970(required)s 1887(semantic)s 2851(information)s 4099(is)s +4371(the)s 4782(size)s 5271(of)s 5605(each)s 6162(subobject,)s +7249(consisting)s 8334(of)s 8668(four)s 0 10489(inte)m 3(gers:)k +920(width)s 1524(to)s 1765(left)s 2144(and)s 2550(right)s +3062(of)s 3335(the)s 3685(distinguished)s 5021(column)s 5798(mark,)s +6397(and)s 6803(height)s 7463(abo)s 3(v)k 3(e)k +8087(and)s 8493(belo)s 6(w)k 0 10201(the)m 368(distinguished)s +1722(ro)s 6(w)k 2162(mark.)s 2837(These)s 3484(numbers)s +4379(are)s 4746(al)s 2(w)k 2(ays)k 5477(non-ne)s 3(g)k 1(ati)k 6(v)k 3(e)k +6789(in)s 7052(Basser)s 7769(Lout,)s 8348(b)s 4(ut)k +8730(this)s 0 9913(restriction)m 1024(is)s 1234(unnecessary)s 2457(and)s +2861(should)s 3558(be)s 3840(dropped.)s 480 9539(F)m 3(or)k +867(the)s 1212(lea)s 4(v)k 3(es,)k 1907(which)s +2546(are)s 2890(simple)s 3581(w)s 2(ords,)k 4268(the)s +4614(numbers)s 5486(are)s 5830(obtained)s 6710(from)s 7231(font)s +7674(tables.)s 8392(F)s 3(or)k 8778(the)s 0 9251(higher)m +678(le)s 6(v)k 3(els)k 1285(we)s 1628(apply)s +2222(recursi)s 6(v)k 3(e)k 3152(rules.)s 3788(Suppose)s +4664(that)s 240 fnt83 5090 9253(hgap)m 240 fnt78 5583 9245(\()m +240 fnt83 5675 9253(x)m 240 fnt78 5801 9245(,)m 240 fnt83 +5932 9253(g)m 240 fnt78 6066 9245(,)m 240 fnt83 6197 9253(y)m +240 fnt78 6319 9245(\))m 240 fnt82 6453 9251(returns)m 7175(the)s +7531(desired)s 8287(distance)s 0 8963(between)m 846(the)s 1186(column)s +1952(marks)s 2579(of)s 2841(objects)s 240 fnt83 3561 8965(x)m +240 fnt82 3719 8963(and)m 240 fnt83 4114 8965(y)m 240 fnt82 +4268 8963(when)m 4835(the)s 3(y)k 5290(are)s 5629(separated)s +6580(by)s 6866(g)s 1(ap)k 240 fnt83 7255 8965(g)m +240 fnt82 7369 8963(:)m 240 fnt83 7527 8965(right)m 240 fnt78 +8000 8957(\()m 240 fnt83 8075 8965(x)m 240 fnt78 8185 8957(\))m +8298(+)s 240 fnt83 8473 8965(length)m 240 fnt78 0 8669(\()m +240 fnt83 89 8677(g)m 240 fnt78 221 8669(\))m 376(+)s +240 fnt83 594 8677(left)m 240 fnt78 920 8669(\()m 240 fnt83 +1009 8677(y)m 240 fnt78 1129 8669(\))m 240 fnt82 1261 8675(when)m +1842(the)s 2196(g)s 1(ap)k 2600(mode)s 3193(is)s +3409(edge-to-edge,)s 4770(the)s 5124(lar)s 4(ger)k 5741(of)s +240 fnt83 6018 8677(length)m 240 fnt78 6629 8669(\()m 240 fnt83 +6718 8677(g)m 240 fnt78 6850 8669(\))m 240 fnt82 6982 8675(and)m +240 fnt83 7391 8677(right)m 240 fnt78 7878 8669(\()m 240 fnt83 +7968 8677(x)m 240 fnt78 8091 8669(\))m 8246(+)s 240 fnt83 +8464 8677(left)m 240 fnt78 8790 8669(\()m 240 fnt83 8880 8677(y)m +240 fnt78 9000 8669(\))m 240 fnt82 0 8387(when)m 576(the)s +924(mode)s 1512(is)s 1722(mark-to-mark,)s 3155(and)s 3559(so)s +3825(on.)s 4229(Gi)s 6(v)k 3(en)k 4862(an)s +5145(object)s 240 fnt83 480 7892(X)m 240 fnt78 720 7884(=)m +240 fnt83 933 7892(x)m 168 fnt78 1039 7799(1)m 240 fnt78 +1249 7884(|)m 240 fnt83 1294 7892(g)m 168 fnt78 1405 7799(1)m +240 fnt78 1615 7884(\274)m 200 fnt83 1973 7900(^)m 240 fnt78 +2069 7884(|)m 240 fnt83 2114 7892(g)m 168 fnt83 2225 7805(i)m +168 fnt78 2291 7799(-)m 2403(1)s 240 fnt83 2613 7892(x)m +168 fnt83 2719 7805(i)m 240 fnt78 2907 7884(\274)m 3265(|)s +240 fnt83 3310 7892(g)m 168 fnt83 3421 7805(n)m 168 fnt78 +3523 7799(-)m 3635(1)s 240 fnt83 3845 7892(x)m 168 fnt83 +3951 7805(n)m 240 fnt82 0 7348(we)m 335(may)s 801(calculate)s +1705(its)s 1981(size)s 2408(as)s 2658(follo)s 6(ws:)k +240 fnt83 740 6845(left)m 240 fnt78 1060 6837(\()m 240 fnt83 +1144 6845(X)m 240 fnt78 1312 6837(\))m 1474(=)s 240 fnt83 +1687 6845(left)m 240 fnt78 2007 6837(\()m 240 fnt83 2091 6845(x)m +168 fnt78 2197 6752(1)m 240 fnt78 2275 6837(\))m 2413(+)s +240 fnt83 2614 6845(hgap)m 240 fnt78 3099 6837(\()m 240 fnt83 +3183 6845(x)m 168 fnt78 3289 6752(1)m 240 fnt78 3367 6837(,)m +240 fnt83 3474 6845(g)m 168 fnt78 3585 6752(1)m 240 fnt78 +3663 6837(,)m 240 fnt83 3770 6845(x)m 168 fnt78 3876 6752(2)m +240 fnt78 3968 6837(\))m 4106(+)s 4307(\274)s 4593(+)s +240 fnt83 4794 6845(hgap)m 240 fnt78 5279 6837(\()m 240 fnt83 +5363 6845(x)m 168 fnt83 5469 6758(i)m 168 fnt78 5535 6752(-)m +5647(1)s 240 fnt78 5725 6837(,)m 240 fnt83 5832 6845(g)m +168 fnt83 5943 6758(i)m 168 fnt78 6009 6752(-)m 6121(1)s +240 fnt78 6199 6837(,)m 240 fnt83 6306 6845(x)m 168 fnt83 +6412 6758(i)m 240 fnt78 6468 6837(\))m 240 fnt83 579 6442(right)m +240 fnt78 1060 6434(\()m 240 fnt83 1144 6442(X)m 240 fnt78 +1312 6434(\))m 1474(=)s 240 fnt83 1687 6442(hgap)m 240 fnt78 +2172 6434(\()m 240 fnt83 2256 6442(x)m 168 fnt83 2362 6355(i)m +240 fnt78 2418 6434(,)m 240 fnt83 2525 6442(g)m 168 fnt83 +2636 6355(i)m 240 fnt78 2692 6434(,)m 240 fnt83 2799 6442(x)m +168 fnt83 2905 6355(i)m 168 fnt78 2971 6349(+)m 3084(1)s +240 fnt78 3162 6434(\))m 3300(+)s 3501(\274)s 3787(+)s +240 fnt83 3988 6442(hgap)m 240 fnt78 4473 6434(\()m 240 fnt83 +4557 6442(x)m 168 fnt83 4663 6355(n)m 168 fnt78 4765 6349(-)m +4877(1)s 240 fnt78 4955 6434(,)m 240 fnt83 5062 6442(g)m +168 fnt83 5173 6355(n)m 168 fnt78 5275 6349(-)m 5387(1)s +240 fnt78 5465 6434(,)m 240 fnt83 5572 6442(x)m 168 fnt83 +5678 6355(n)m 240 fnt78 5770 6434(\))m 5908(+)s 240 fnt83 +6109 6442(right)m 240 fnt78 6590 6434(\()m 240 fnt83 6674 6442(x)m +168 fnt83 6780 6355(n)m 240 fnt78 6872 6434(\))m 240 fnt83 +485 6039(abo)m 2(ve)k 240 fnt78 1060 6031(\()m 240 fnt83 +1144 6039(X)m 240 fnt78 1312 6031(\))m 1474(=)s 240 fnt83 +1687 6039(abo)m 2(ve)k 240 fnt78 2262 6031(\()m 240 fnt83 +2346 6039(x)m 168 fnt78 2452 5944(1)m 240 fnt78 2530 6031(\))m +2680(\255)s 2901(\274)s 3199(\255)s 240 fnt83 3420 6039(abo)m 2(ve)k +240 fnt78 3995 6031(\()m 240 fnt83 4079 6039(x)m 168 fnt83 +4185 5950(n)m 240 fnt78 4277 6031(\))m 240 fnt83 480 5636(below)m +240 fnt78 1060 5628(\()m 240 fnt83 1144 5636(X)m 240 fnt78 +1312 5628(\))m 1474(=)s 240 fnt83 1687 5636(below)m 240 fnt78 +2267 5628(\()m 240 fnt83 2351 5636(x)m 168 fnt78 2457 5541(1)m +240 fnt78 2535 5628(\))m 2685(\255)s 2906(\274)s 3204(\255)s +240 fnt83 3425 5636(below)m 240 fnt78 4005 5628(\()m 240 fnt83 +4089 5636(x)m 168 fnt83 4195 5547(n)m 240 fnt78 4287 5628(\))m +240 fnt82 0 5041(where)m 240 fnt78 693 5035(\255)m 240 fnt82 +943 5041(returns)m 1678(the)s 2046(lar)s 4(ger)k 2679(of)s +2971(its)s 3267(tw)s 2(o)k 3698(parameters.)s 4930(Similar)s +5712(formulas)s 6633(are)s 7001(easily)s 7632(deri)s 6(v)k 3(ed)k +8419(for)s 8778(the)s 0 4753(other)m 551(operators.)s 480 4379(F)m 3(or)k +866(purposes)s 1765(of)s 2033(e)s 3(xposition)k 3081(we)s +3412(will)s 3835(no)s 6(w)k 4293(mak)s 2(e)k +4862(the)s 5207(simplifying)s 6358(assumptions)s 7589(that)s 8004(all)s +8294(g)s 1(aps)k 8779(are)s 220 fnt35 0 4088(0i)m +240 fnt82 156 4091(,)m 248(all)s 525(column)s 1285(marks)s +1904(lie)s 2183(at)s 2399(the)s 2732(left)s 3093(edge,)s +3637(and)s 4025(all)s 4303(ro)s 6(w)k 4707(marks)s +5327(lie)s 5605(at)s 5822(the)s 6154(top)s 6498(edge.)s +7098(Then)s 7632(the)s 7964(size)s 8376(of)s 8631(each)s +0 3803(object)m 644(can)s 1033(be)s 1315(e)s 3(xpressed)k +2313(by)s 2607(just)s 3012(tw)s 2(o)k 3422(numbers,)s +4353(width)s 4955(and)s 5359(height,)s 6064(and)s 6468(the)s +6816(four)s 7274(formulas)s 8174(reduce)s 8867(to)s 240 fnt83 +555 3300(width)m 240 fnt78 1094 3292(\()m 240 fnt83 1178 3300(x)m +168 fnt78 1284 3207(1)m 240 fnt78 1434 3292(|)m 1551(\274)s +1849(|)s 240 fnt83 1966 3300(x)m 168 fnt83 2072 3213(n)m +240 fnt78 2164 3292(\))m 2326(=)s 240 fnt83 2539 3300(width)m +240 fnt78 3078 3292(\()m 240 fnt83 3162 3300(x)m 168 fnt78 +3268 3207(1)m 240 fnt78 3346 3292(\))m 3484(+)s 3685(\274)s +3971(+)s 240 fnt83 4172 3300(width)m 240 fnt78 4711 3292(\()m +240 fnt83 4795 3300(x)m 168 fnt83 4901 3213(n)m 240 fnt78 +4993 3292(\))m 240 fnt83 480 2897(height)m 240 fnt78 1094 2889(\()m +240 fnt83 1178 2897(x)m 168 fnt78 1284 2804(1)m 240 fnt78 +1434 2889(|)m 1551(\274)s 1849(|)s 240 fnt83 1966 2897(x)m +168 fnt83 2072 2810(n)m 240 fnt78 2164 2889(\))m 2326(=)s +240 fnt83 2539 2897(height)m 240 fnt78 3153 2889(\()m 240 fnt83 +3237 2897(x)m 168 fnt78 3343 2804(1)m 240 fnt78 3421 2889(\))m +3571(\255)s 3792(\274)s 4090(\255)s 240 fnt83 4311 2897(height)m +240 fnt78 4925 2889(\()m 240 fnt83 5009 2897(x)m 168 fnt83 +5115 2810(n)m 240 fnt78 5207 2889(\))m 240 fnt82 0 2353(The)m +428(corresponding)s 1850(formulas)s 2750(for)s 3088(v)s 3(ertical)k +3855(concatenation)s 5240(are)s 240 fnt83 555 1803(width)m 240 fnt78 +1094 1795(\()m 240 fnt83 1178 1803(x)m 168 fnt78 1284 1710(1)m +240 fnt83 1434 1803(/)m 240 fnt78 1609 1795(\274)m 240 fnt83 +1907 1803(/)m 2082(x)s 168 fnt83 2188 1716(n)m 240 fnt78 +2280 1795(\))m 2442(=)s 240 fnt83 2655 1803(width)m 240 fnt78 +3194 1795(\()m 240 fnt83 3278 1803(x)m 168 fnt78 3384 1710(1)m +240 fnt78 3462 1795(\))m 3612(\255)s 3833(\274)s 4131(\255)s +240 fnt83 4352 1803(width)m 240 fnt78 4891 1795(\()m 240 fnt83 +4975 1803(x)m 168 fnt83 5081 1716(n)m 240 fnt78 5173 1795(\))m +240 fnt83 480 1400(height)m 240 fnt78 1094 1392(\()m 240 fnt83 +1178 1400(x)m 168 fnt78 1284 1307(1)m 240 fnt83 1434 1400(/)m +240 fnt78 1609 1392(\274)m 240 fnt83 1907 1400(/)m 2082(x)s +168 fnt83 2188 1313(n)m 240 fnt78 2280 1392(\))m 2442(=)s +240 fnt83 2655 1400(height)m 240 fnt78 3269 1392(\()m 240 fnt83 +3353 1400(x)m 168 fnt78 3459 1307(1)m 240 fnt78 3537 1392(\))m +3675(+)s 3876(\274)s 4162(+)s 240 fnt83 4363 1400(height)m +240 fnt78 4977 1392(\()m 240 fnt83 5061 1400(x)m 168 fnt83 +5167 1313(n)m 240 fnt78 5259 1392(\))m +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 10 11 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Symbol +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4287 13844(-)m 4415(10)s 4710(-)s 0 13253(According)m 1063(to)s +1302(these)s 1849(formulas,)s 2805(the)s 3153(height)s 3811(of)s +gsave +480 11559 translate +240 fnt83 3044 1354 56 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1240 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 789 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 902 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1240 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 1353 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 136 106(\244)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1691 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1240 846 56 790 240 288 12 1804 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m + +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 789 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 902 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1240 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3044 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 11108(is)m +240 fnt78 480 10600([)m 240 fnt83 563 10608(height)m 240 fnt78 +1177 10600(\()m 240 fnt83 1261 10608(a)m 240 fnt78 1388 10600(\))m +1538(\255)s 240 fnt83 1759 10608(height)m 240 fnt78 2373 10600(\()m +240 fnt83 2457 10608(b)m 240 fnt78 2583 10600(\))m 2661(])s +2792(+)s 2993([)s 240 fnt83 3076 10608(height)m 240 fnt78 +3690 10600(\()m 240 fnt83 3774 10608(c)m 240 fnt78 3888 10600(\))m +4038(\255)s 240 fnt83 4259 10608(height)m 240 fnt78 4873 10600(\()m +240 fnt83 4957 10608(d)m 240 fnt78 5095 10600(\))m 5173(])s +240 fnt82 0 10104(which)m 642(is)s 852(correct,)s 1621(b)s 4(ut)k +1983(for)s 2321(width)s 2923(the)s 3(y)k 3386(yield)s +240 fnt78 480 9546([)m 240 fnt83 563 9554(width)m 240 fnt78 +1102 9546(\()m 240 fnt83 1186 9554(a)m 240 fnt78 1313 9546(\))m +1451(+)s 240 fnt83 1652 9554(width)m 240 fnt78 2191 9546(\()m +240 fnt83 2275 9554(b)m 240 fnt78 2401 9546(\))m 2479(])s +2622(\255)s 2843([)s 240 fnt83 2926 9554(width)m 240 fnt78 +3465 9546(\()m 240 fnt83 3549 9554(c)m 240 fnt78 3663 9546(\))m +3801(+)s 240 fnt83 4002 9554(width)m 240 fnt78 4541 9546(\()m +240 fnt83 4625 9554(d)m 240 fnt78 4763 9546(\))m 4841(])s +240 fnt82 0 9050(which)m 645(is)s 859(not,)s 1276(since)s +1827(it)s 2023(does)s 2517(not)s 2887(tak)s 2(e)k +3343(the)s 3694(mer)s 4(ging)k 4544(of)s 4819(column)s +5598(marks)s 6237(into)s 6666(account.)s 7578(The)s 8010(asymmetry)s +0 8762(between)m 874(horizontal)s 1918(and)s 2342(v)s 3(ertical)k +3130(has)s 3520(come)s 4114(about)s 4726(because)s 5560(the)s +5928(ro)s 6(w)k 6368(entries,)s 7131(such)s 7648(as)s +240 fnt83 7918 8764(a)m 240 fnt82 8113 8762(and)m 240 fnt83 +8537 8764(b)m 240 fnt82 8651 8762(,)m 8779(are)s 0 8474(adjacent)m +849(in)s 1085(the)s 1426(tree,)s 1883(b)s 4(ut)k +2238(the)s 2579(column)s 3346(entries,)s 4082(such)s 4571(as)s +240 fnt83 4814 8476(a)m 240 fnt82 4982 8474(and)m 240 fnt83 +5379 8476(c)m 240 fnt82 5481 8474(,)m 5581(are)s 5920(not.)s +6383(It)s 6581(w)s 2(ould)k 7229(be)s 7504(possible)s +8337(to)s 8568(solv)s 3(e)k 0 8186(this)m 395(cross-linking)s +1694(problem)s 2550(by)s 2842(augmenting)s 4024(the)s 4370(size)s +4795(information)s 5979(stored)s 6619(in)s 6861(each)s 7354(node)s +7875(to)s 8112(record)s 8778(the)s 0 7898(number)m 791(of)s +1063(marks)s 1698(and)s 2103(the)s 2451(size)s 2879(of)s +3150(each,)s 3696(b)s 4(ut)k 4058(the)s 4407(author)s +5078(has)s 5449(preferred)s 6381(the)s 6730(follo)s 6(wing)k +7707(method)s 8484(which)s 0 7610(mak)m 2(es)k 660(structural)s +1616(changes)s 2438(to)s 2677(the)s 3025(tree)s 3438(instead.)s +480 7236(If)m 240 fnt83 715 7238(a)m 240 fnt82 896 7236(and)m +240 fnt83 1305 7238(c)m 240 fnt82 1473 7236(share)m 2038(a)s +2210(column)s 2990(mark,)s 3594(the)s 3(y)k 4063(each)s +4563(might)s 5187(as)s 5442(well)s 5914(ha)s 4(v)k 3(e)k +6420(width)s 240 fnt83 7028 7238(width)m 240 fnt78 7572 7230(\()m +240 fnt83 7662 7238(a)m 240 fnt78 7795 7230(\))m 7961(\255)s +240 fnt83 8199 7238(width)m 240 fnt78 8743 7230(\()m 240 fnt83 +8833 7238(c)m 240 fnt78 8953 7230(\))m 240 fnt82 9019 7236(,)m +0 6948(since)m 547(all)s 840(width)s 1442(calculations)s 2635(apply)s +3221(to)s 3460(entire)s 4060(columns.)s 5035(Accordingly)s 15(,)k +6323(we)s 6659(introduce)s 7618(a)s 7784(ne)s 6(w)k +8232(operator)s 9(,)k 240 fnt83 0 6662(COL)m 240 fnt82 +466 6660(,)m 573(de\207ned)s 1336(by)s 240 fnt83 480 6110(width)m +240 fnt78 1019 6102(\()m 240 fnt83 1103 6110(x)m 168 fnt78 +1209 6017(1)m 240 fnt83 1347 6110(COL)m 240 fnt78 1885 6102(\274)m +240 fnt83 2171 6110(COL)m 2709(x)s 168 fnt83 2815 6023(n)m +240 fnt78 2907 6102(\))m 3057(=)s 240 fnt83 3270 6110(width)m +240 fnt78 3809 6102(\()m 240 fnt83 3893 6110(x)m 168 fnt78 +3999 6017(1)m 240 fnt78 4077 6102(\))m 4227(\255)s 4448(\274)s +4746(\255)s 240 fnt83 4967 6110(width)m 240 fnt78 5506 6102(\()m +240 fnt83 5590 6110(x)m 168 fnt83 5696 6023(n)m 240 fnt78 +5788 6102(\))m 240 fnt82 0 5566(and)m 440(replace)s 1221(both)s +240 fnt83 1741 5568(a)m 240 fnt82 1952 5566(and)m 240 fnt83 +2393 5568(c)m 240 fnt82 2591 5566(by)m 240 fnt83 2922 5568(a)m +3218(COL)s 3865(c)s 240 fnt82 3967 5566(.)m 4168(T)s 19(o)k +4504(pre)s 6(v)k 3(ent)k 240 fnt83 5309 5568(COL)m +240 fnt82 5871 5566(operators)m 6848(from)s 7408(disturbing)s 8468(height)s +0 5278(calculations,)m 1248(we)s 1583(de\207ne)s 2224(a)s 2390(binary)s +3055(operator)s 3911(called)s 240 fnt83 4539 5280(SPLIT)m 240 fnt82 +5228 5278(by)m 240 fnt83 555 4775(width)m 240 fnt78 1094 4767(\()m +240 fnt83 1178 4775(x)m 1356(SPLIT)s 2057(y)s 240 fnt78 +2171 4767(\))m 2333(=)s 240 fnt83 2546 4775(width)m 240 fnt78 +3085 4767(\()m 240 fnt83 3169 4775(x)m 240 fnt78 3287 4767(\))m +240 fnt83 480 4372(height)m 240 fnt78 1094 4364(\()m 240 fnt83 +1178 4372(x)m 1356(SPLIT)s 2057(y)s 240 fnt78 2171 4364(\))m +2333(=)s 240 fnt83 2546 4372(height)m 240 fnt78 3160 4364(\()m +240 fnt83 3244 4372(y)m 240 fnt78 3358 4364(\))m 240 fnt82 +0 3868(which)m 642(switches)s 1516(height)s 2174(and)s 2578(width)s +3180(calculations)s 4372(onto)s 4851(dif)s 6(ferent)k 5726(subtrees.)s +6673(Then)s 7222(the)s 7570(transformation)s gsave +480 2169 translate +240 fnt83 338 1359 56 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +338 1359 56 1298 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 1016 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m + +grestore +(T) lfigpromotelabels +grestore +end end restore +grestore +240 fnt78 1130 3407(\336)m gsave +1671 2169 translate +240 fnt83 2564 1359 56 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1386 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +484 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +484 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 +56 107(COL)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 935 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 1048 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1386 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(L) lfigpromotelabels +grestore +614 338 56 282 240 288 12 1499 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +614 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(SPLIT)m + +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2113 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 846 56 790 240 288 12 2226 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 508 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 2564 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +240 fnt82 0 1669(widens)m 240 fnt83 +740 1671(a)m 240 fnt82 926 1669(to)m 240 fnt83 1176 1671(width)m +240 fnt78 1726 1663(\()m 240 fnt83 1821 1671(a)m 240 fnt78 +1959 1663(\))m 2142(\255)s 240 fnt83 2396 1671(width)m 240 fnt78 +2946 1663(\()m 240 fnt83 3041 1671(c)m 240 fnt78 3166 1663(\))m +240 fnt82 3303 1669(without)m 4105(af)s 6(fecting)k 5011(its)s +5298(height;)s 6019(it)s 6222(is)s 6443(applied)s 7216(to)s +7466(e)s 6(v)k 3(ery)k 8053(object)s 8708(that)s +0 1381(shares)m 638(its)s 904(column)s 1669(mark)s 2211(with)s +2683(at)s 2905(least)s 3392(one)s 3784(other)s 4325(object.)s +5063(A)s 5283(similar)s 5995(transformation)s 7448(in)s 9(v)k 4(olving)k +8396(a)s 240 fnt83 8552 1383(R)m 9(O)k 12(W)k +240 fnt82 0 1093(operator)m 856(deals)s 1398(with)s 1880(shared)s +2562(ro)s 6(w)k 2982(marks.)s 3730(The)s 4158(ef)s 6(fect)k +4754(on)s 5051(our)s 5430(little)s 5922(table)s 6442(is)s +6652(to)s 6891(replace)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 11 12 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Symbol +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4297 13844(-)m 4425(11)s 4700(-)s gsave +480 12065 translate +240 fnt83 3044 1354 56 1298 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1240 846 56 790 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m + +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 789 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 902 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1240 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 1353 1016 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 +136 106(\244)m +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1691 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1240 846 56 790 240 288 12 1804 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +338 338 56 282 240 288 12 451 508 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m + +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 12 789 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 902 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1240 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3044 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 11614(by)m gsave +480 8904 translate +240 fnt83 6248 2370 0 2314 240 288 12 LoutGraphic +gsave +grestore save gsave 70 dict begin lfigdict begin +grestore +3293 338 56 282 240 288 12 2955 2032 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 136 106(\244)m + +grestore +(T) lfigpromotelabels +grestore +3096 1862 0 1806 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1717 338 56 282 240 288 12 1379 1524 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 156 121(|)m +grestore +(T) lfigpromotelabels +grestore +1520 1354 0 1298 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1067 338 56 282 240 288 12 453 1016 LoutGr2 +currentdict end 70 dict begin begin +grestore +614 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(SPLIT)m +grestore +(T) lfigpromotelabels +grestore +732 846 0 790 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +608 338 56 282 240 288 12 124 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +484 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 +56 107(COL)m +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +732 846 0 790 240 288 12 788 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +628 338 56 282 240 288 12 104 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +524 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(R)m 7(O)k 9(W)k +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1520 1354 0 1298 240 288 12 1576 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1067 338 56 282 240 288 12 453 1016 LoutGr2 +currentdict end 70 dict begin begin +grestore +614 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(SPLIT)m + +grestore +(T) lfigpromotelabels +grestore +732 846 0 790 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +608 338 56 282 240 288 12 124 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +484 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(COL)m +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +732 846 0 790 240 288 12 788 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +628 338 56 282 240 288 12 104 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +524 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(R)m 7(O)k 9(W)k + +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3096 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3096 1806 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +3096 1862 0 1806 240 288 12 3152 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1717 338 56 282 240 288 12 1379 1524 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt78 +156 121(|)m +grestore +(T) lfigpromotelabels +grestore +1520 1354 0 1298 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1067 338 56 282 240 288 12 453 1016 LoutGr2 +currentdict end 70 dict begin begin +grestore +614 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(SPLIT)m +grestore +(T) lfigpromotelabels +grestore +732 846 0 790 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +608 338 56 282 240 288 12 124 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +484 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(COL)m + +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +732 846 0 790 240 288 12 788 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +628 338 56 282 240 288 12 104 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +524 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 +56 107(R)m 7(O)k 9(W)k +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1520 1354 0 1298 240 288 12 1576 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +1067 338 56 282 240 288 12 453 1016 LoutGr2 +currentdict end 70 dict begin begin +grestore +614 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(SPLIT)m +grestore +(T) lfigpromotelabels +grestore +732 846 0 790 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +608 338 56 282 240 288 12 124 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +484 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 +56 107(COL)m +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 105(b)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +732 846 0 790 240 288 12 788 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +628 338 56 282 240 288 12 104 508 LoutGr2 +currentdict end 70 dict begin begin +grestore +524 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +192 fnt83 56 107(R)m 7(O)k 9(W)k +grestore +(T) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +128 128(c)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 338 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +338 338 56 282 240 288 12 394 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 70 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 732 282 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 1520 790 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 3096 1298 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 12 6248 1806 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 8453(In)m 244(f)s 2(act,)k +693(common)s 1576(sube)s 3(xpressions)k 3060(are)s 3395(identi\207ed)s +4343(\(tri)s 6(vially\))k 5286(and)s 5678(the)s 6013(result)s +6591(is)s 6788(a)s 6942(directed)s 7756(ac)s 3(yclic)k +8469(graph;)s 0 8165(each)m 486(af)s 6(fected)k 1296(leaf)s +1716(has)s 2076(tw)s 2(o)k 2477(parents,)s 3264(one)s +3657(for)s 3985(width)s 4578(and)s 4972(one)s 5365(for)s +5693(height;)s 6394(and)s 6788(each)s 240 fnt83 7274 8167(COL)m +240 fnt82 7790 8165(or)m 240 fnt83 8040 8167(R)m 9(O)k 12(W)k +240 fnt82 8604 8165(node)m 0 7877(has)m 360(one)s 752(parent)s +1398(and)s 1792(one)s 2184(child)s 2709(for)s 3037(each)s +3521(object)s 4155(lying)s 4690(on)s 4976(the)s 5314(corresponding)s +6726(mark.)s 7370(The)s 7788(data)s 8235(structure)s 0 7589(roughly)m +799(doubles)s 1595(in)s 1838(size,)s 2316(and)s 2720(this)s +3116(occurs)s 3791(only)s 4271(rarely)s 4881(in)s 5124(practice.)s +480 7215(This)m 956(method)s 1732(can)s 2121(cope)s 2629(with)s +3111(an)s 3(y)k 3508(le)s 3(g)k 1(al)k +4023(input,)s 4622(including)s 220 fnt35 480 6714({ a // c | d } | { b / e })m 480 6426(/ { f / i } | { g | h // j })m +240 fnt82 0 5927(which)m 642(produces)s 1557(o)s 3(v)k 3(erlapping)k +2747(spanning)s 3665(columns:)s gsave +480 3779 translate +240 fnt83 1699 1808 0 1695 240 288 60 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1133 452 113 339 240 288 60 0 1356 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 511 178(a)m +grestore +566 452 113 339 240 288 60 1133 1356 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 +228 150(b)m +grestore +566 452 113 339 240 288 60 0 904 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 234 178(c)m +grestore +566 452 113 339 240 288 60 566 904 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 222 150(d)m + +grestore +566 452 113 339 240 288 60 1132 904 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 235 178(e)m +grestore +566 452 113 339 240 288 60 0 452 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 235 173(f)m +grestore +566 452 113 339 240 288 60 566 452 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 +228 200(g)m +grestore +566 452 113 339 240 288 60 1132 452 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 228 149(h)m +grestore +566 452 113 339 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 253 153(i)m + +grestore +1133 452 113 339 240 288 60 566 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +230 fnt83 535 176(j)m +grestore +end end restore +grestore +0 3328(The)m 428(box)s 3(es)k +1035(ha)s 4(v)k 3(e)k 1536(been)s 2045(added)s +2675(to)s 2914(clarify)s 3590(the)s 3938(structure.)s 4937(The)s +5365(width)s 5967(of)s 6238(this)s 6634(object)s 7278(is)s +7488(formally)s 240 fnt78 480 2770(\()m 564(\()s 240 fnt83 +648 2778(width)m 240 fnt78 1187 2770(\()m 240 fnt83 1271 2778(a)m +240 fnt78 1398 2770(\))m 1548(\255)s 1769(\()s 240 fnt83 +1853 2778(x)m 240 fnt78 2031 2770(+)m 240 fnt83 2232 2778(y)m +240 fnt78 2346 2770(\))m 2424(\))s 2562(+)s 240 fnt83 +2763 2778(z)m 240 fnt78 2866 2770(\))m 3016(\255)s 3237(\()s +240 fnt83 3321 2778(x)m 240 fnt78 3499 2770(+)m 3700(\()s +3784(\()s 240 fnt83 3868 2778(y)m 240 fnt78 4042 2770(+)m +240 fnt83 4243 2778(z)m 240 fnt78 4346 2770(\))m 4496(\255)s +240 fnt83 4717 2778(width)m 240 fnt78 5256 2770(\()m 240 fnt83 +5340 2778(j)m 240 fnt78 5418 2770(\))m 5496(\))s 5574(\))s +240 fnt82 0 2274(where)m 240 fnt83 480 1773(x)m 240 fnt78 +670 1765(=)m 240 fnt83 883 1773(width)m 240 fnt78 1422 1765(\()m +240 fnt83 1506 1773(c)m 240 fnt78 1620 1765(\))m 1770(\255)s +240 fnt83 1991 1773(width)m 240 fnt78 2530 1765(\()m 240 fnt83 +2662 1773(f)m 240 fnt78 2823 1765(\))m 2973(\255)s 240 fnt83 +3194 1773(width)m 240 fnt78 3733 1765(\()m 240 fnt83 3817 1773(i)m +240 fnt78 3892 1765(\))m 240 fnt83 480 1222(y)m 240 fnt78 +666 1214(=)m 240 fnt83 879 1222(width)m 240 fnt78 1418 1214(\()m +240 fnt83 1502 1222(d)m 240 fnt78 1688 1214(\))m 1838(\255)s +240 fnt83 2059 1222(width)m 240 fnt78 2598 1214(\()m 240 fnt83 +2682 1222(g)m 240 fnt78 2808 1214(\))m 240 fnt83 480 671(z)m +240 fnt78 655 663(=)m 240 fnt83 868 671(width)m 240 fnt78 +1407 663(\()m 240 fnt83 1491 671(b)m 240 fnt78 1617 663(\))m +1767(\255)s 240 fnt83 1988 671(width)m 240 fnt78 2527 663(\()m +240 fnt83 2611 671(e)m 240 fnt78 2722 663(\))m 2872(\255)s +240 fnt83 3093 671(width)m 240 fnt78 3632 663(\()m 240 fnt83 +3716 671(h)m 240 fnt78 3843 663(\))m +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 12 13 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(12)s 4710(-)s 0 12968(It)m 224(seems)s +878(clear)s 1420(that)s 240 fnt83 1857 12970(y)m 240 fnt82 +2038 12968(at)m 2289(least)s 2805(must)s 3349(appear)s 4065(twice)s +4657(in)s 4919(an)s 3(y)k 5335(e)s 3(xpression)k +6431(for)s 6788(the)s 7155(width)s 7776(of)s 8066(this)s +8482(object)s 0 12680(made)m 602(out)s 997(of)s 1297(simple)s +2019(addition)s 2889(and)s 3322(maxing)s 4121(operations,)s 5253(sho)s 6(wing)k +6141(that)s 6588(an)s 6900(ordinary)s 7793(tree)s 8235(structure)s +0 12392(is)m 227(insuf\207cient)s 1379(for)s 1734(o)s 3(v)k 3(erlapping)k +2941(spanning)s 3876(columns.)s 4868(The)s 5313(Basser)s 6027(Lout)s +6556(interpreter)s 7626(actually)s 8453(rejects)s 0 12104(such)m 521(structures,)s +1581(o)s 6(wing)k 2252(to)s 2517(the)s 2890(author')s 13(s)k +3736(doubts)s 4451(about)s 5069(the)s 5442(implementability)s 7153(of)s +240 fnt83 7449 12106(Constr)m 3(ained)k 240 fnt82 8722 12104(and)m +240 fnt83 0 11818(AdjustSize)m 240 fnt82 1049 11816(\(Section)m 1902(5.3\))s +2330(on)s 2627(them;)s 3217(b)s 4(ut)k 3579(with)s +4061(hindsight)s 5012(this)s 5408(caution)s 6169(w)s 2(as)k +6590(unnecessary)s 15(.)k 480 11442(The)m 915(directed)s 1749(ac)s 3(yclic)k +2482(graph)s 3091(is)s 3308(ordered)s 4104(in)s 4354(the)s +4709(sense)s 5290(that)s 5715(the)s 6071(order)s 6642(of)s +6920(the)s 7275(edges)s 7878(entering)s 8722(and)s 0 11154(lea)m 4(ving)k +746(each)s 1234(node)s 1748(matters.)s 2607(The)s 3028(structure)s +3911(is)s 4114(highly)s 4773(dynamic,)s 5696(and)s 6093(tra)s 4(v)k 3(ersals)k +7044(both)s 7519(with)s 7994(and)s 8390(ag)s 1(ainst)k +0 10866(the)m 349(arro)s 6(ws)k 1045(are)s 1394(required.)s +2355(After)s 2920(a)s 3087(fe)s 6(w)k 3494(ad-)s +3788(hoc)s 4189(attempts)s 5050(to)s 5291(e)s 3(xtend)k +5985(the)s 6334(usual)s 6896(tree)s 7310(representation)s 8722(had)s +0 10578(f)m 2(ailed,)k 665(the)s 1030(author)s 1718(de)s 6(v)k 3(eloped)k +2769(a)s 2952(representation)s 4379(based)s 5000(on)s 5314(doubly)s +6051(link)s 2(ed)k 6723(lists)s 7175(of)s 7463(records)s +8235(denoting)s 0 10290(links,)m 578(whose)s 1253(\210e)s 3(xibility)k +2240(more)s 2794(than)s 3270(compensated)s 4584(for)s 4929(the)s +5284(some)s 6(what)k 6315(e)s 3(xcessi)k 6(v)k 3(e)k +7282(memory)s 8140(consump)s 8998(-)s 0 10002(tion.)m 536(F)s 3(or)k +925(e)s 3(xample,)k gsave +480 8136 translate +240 fnt83 3282 1526 0 1470 240 288 12 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +338 338 56 282 240 288 12 0 1188 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 123 128(a)m +grestore +(A) lfigpromotelabels +grestore +338 338 56 282 240 288 12 2944 1188 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 +123 105(b)m +grestore +(B) lfigpromotelabels +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 128 128(c)m +grestore +(C) lfigpromotelabels +grestore +338 338 56 282 240 288 12 1472 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +338 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore +192 fnt83 118 105(d)m + +grestore +(D) lfigpromotelabels +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR C@CTR lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +C@CTR C@CTR A@CTR lfigangle C@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR D@CTR lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +D@CTR D@CTR A@CTR lfigangle D@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ B@CTR B@CTR D@CTR lfigangle B@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +D@CTR D@CTR B@CTR lfigangle D@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 7685(is)m 210(represented)s 1369(by)s gsave +1135 3169 translate +240 fnt83 6796 4176 0 4120 240 288 12 LoutGraphic +gsave +grestore save gsave 300 dict begin lfigdict begin +grestore +452 1014 0 958 240 288 12 0 3162 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 180 128(a)m + +grestore +(BASE) lfigpromotelabels +grestore +(A) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 6344 3162 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 180 105(b)m +grestore +(BASE) lfigpromotelabels +grestore +(B) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 0 1581 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 104 107(LK)m +grestore +(BASE) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 1586 1581 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 +104 107(LK)m +grestore +(BASE) lfigpromotelabels +grestore +(M) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 4758 1581 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 104 107(LK)m +grestore +(BASE) lfigpromotelabels +grestore +(N) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 185 128(c)m + +grestore +(BASE) lfigpromotelabels +grestore +(C) lfigpromotelabels +grestore +452 1014 0 958 240 288 12 3172 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 676 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +gsave +206 150 translate +192 fnt83 39 39 0 39 192 288 48 LoutGraphic +gsave +/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigcircle ] lfigdopath +pop pop +grestore + +grestore + +grestore +(TOP) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 338 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(MID) lfigpromotelabels +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 +currentdict end 300 dict begin begin +grestore +452 338 56 282 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +192 fnt83 175 105(d)m +grestore +(BASE) lfigpromotelabels +grestore +(D) lfigpromotelabels +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ 0.5 cm 0 A@MID@CTR L@MID@CTR A@MID@CTR M@MID@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef +A@MID@CTR L@MID@CTR A@MID@CTR M@MID@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef +BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef +BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef +BL +BR [ BR 0 0.5 cm lfigpadd ] +BR 0.5 cm 0.5 cm lfigpadd +TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ] +TR +TL [ 0 0.5 cm TL lfigpsub ] +0.5 cm 0.5 cm TL lfigpsub +BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ] +BL ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ 0.5 cm 0 L@TOP@CTR C@TOP@CTR L@TOP@CTR C@TOP@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef +L@TOP@CTR C@TOP@CTR L@TOP@CTR C@TOP@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef +BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef +BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef +BL +BR [ BR 0 0.5 cm lfigpadd ] +BR 0.5 cm 0.5 cm lfigpadd +TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ] +TR +TL [ 0 0.5 cm TL lfigpsub ] +0.5 cm 0.5 cm TL lfigpsub +BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ] +BL ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ 0.5 cm 0 M@TOP@CTR D@TOP@CTR N@TOP@CTR D@TOP@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef +M@TOP@CTR D@TOP@CTR N@TOP@CTR D@TOP@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef +BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef +BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef +BL +BR [ BR 0 0.5 cm lfigpadd ] +BR 0.5 cm 0.5 cm lfigpadd +TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ] +TR +TL [ 0 0.5 cm TL lfigpsub ] +0.5 cm 0.5 cm TL lfigpsub +BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ] +BL ] lfigdopath +pop pop +grestore + +grestore +0 0 0 0 240 288 12 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ 0.5 cm 0 B@MID@CTR N@MID@CTR B@MID@CTR N@MID@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef +B@MID@CTR N@MID@CTR B@MID@CTR N@MID@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef +BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef +BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef +BL +BR [ BR 0 0.5 cm lfigpadd ] +BR 0.5 cm 0.5 cm lfigpadd +TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ] +TR +TL [ 0 0.5 cm TL lfigpsub ] +0.5 cm 0.5 cm TL lfigpsub +BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ] +BL ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 2718(where)m 240 fnt83 645 2720(LK)m +240 fnt82 1017 2718(tags)m 1458(a)s 1630(record)s 2304(representing)s +3543(a)s 3715(link.)s 4257(The)s 4690(\207rst)s 5127(list)s +5484(in)s 5732(an)s 3(y)k 6135(node)s 6663(contains)s +7516(all)s 7815(the)s 8169(incoming)s 0 2430(links,)m 577(the)s +931(second)s 1660(contains)s 2514(the)s 2867(outgoing)s 3778(ones.)s +4387(The)s 4821(node)s 5348(serv)s 3(es)k 5999(as)s +6255(the)s 6609(header)s 7311(for)s 7655(both)s 8144(lists.)s +8698(The)s 0 2142(required)m 890(operations)s 1974(reduce)s 2704(to)s +2979(simple)s 3709(appends,)s 4638(deletes,)s 5444(and)s 5885(tra)s 4(v)k 3(ersals)k +6880(of)s 7187(doubly)s 7944(link)s 2(ed)k 8635(lists,)s +0 1854(all)m 325(ha)s 4(ving)k 1058(small)s 1663(constant)s +2552(cost.)s 3133(There)s 3779(is)s 4021(a)s 4219(highly)s +4918(tuned)s 5540(memory)s 6423(allocator)s 9(,)k 7389(and)s +7825(care)s 8310(is)s 8553(tak)s 2(en)k 0 1566(to)m +269(dispose)s 1073(of)s 1374(each)s 1900(node)s 2452(when)s +3058(the)s 3436(last)s 3858(incoming)s 4845(link)s 5308(is)s +5549(deleted,)s 6376(so)s 6672(that)s 7120(there)s 7684(is)s +7924(no)s 8247(need)s 8788(for)s 0 1278(g)m 1(arbage)k +812(collection.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 13 14 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Helvetica +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4293 13844(-)m 4421(13)s 4705(-)s 480 13253(In)m 739(normal)s +1475(use)s 1854(the)s 2205(number)s 3000(of)s 3275(nodes)s +3888(at)s 4124(higher)s 4799(le)s 6(v)k 3(els)k +5402(of)s 5676(the)s 6028(dag)s 6431(is)s 6644(small)s +7220(in)s 7467(comparison)s 8644(with)s 0 12965(the)m 351(lea)s 4(v)k 3(es)k +995(and)s 1402(their)s 1903(incoming)s 2863(links,)s 3438(so)s +3707(we)s 4046(may)s 4515(estimate)s 5369(the)s 5720(space)s +6311(comple)s 3(xity)k 7441(at)s 7676(about)s 8271(60)s +8570(bytes)s 0 12677(per)m 355(input)s 896(w)s 2(ord)k +1433(\(20)s 1797(bytes)s 2342(per)s 2696(link,)s 3165(40)s +3449(per)s 3803(leaf)s 4222(node\).)s 4920(Careful)s 5680(optimization)s +6935(could)s 7514(easily)s 8114(halv)s 3(e)k 8674(this,)s +0 12389(b)m 4(ut)k 362(since)s 909(memory)s 1760(is)s +1970(reclaimed)s 2969(after)s 3465(printing)s 4275(each)s 4770(page)s +5278(there)s 5811(is)s 6021(little)s 6513(need.)s 240 fnt84 +0 11740(2.5.)m 471(Context-sensiti)s 2(v)k 2(e)k 2274(attrib)s 4(utes)k +3318(of)s 3590(objects)s 240 fnt82 480 11264(Although)m 1466(we)s +1826(are)s 2198(free)s 2649(to)s 2913(place)s 3498(an)s 3(y)k +3920(object)s 4588(in)s 4856(an)s 3(y)k 5278(conte)s 3(xt,)k +6111(the)s 6484(conte)s 3(xt)k 7270(must)s 7820(in\210uence)s +8778(the)s 0 10976(appearance)m 1131(of)s 1402(the)s 1750(object,)s +2441(since)s 2988(otherwise)s 220 fnt35 480 10477(A shor)m -8(t par)k 2(ag)k 2(r)k 2(aph of te)k 6(xt.)k +240 fnt82 0 9978(could)m 588(not)s 952(appear)s 1647(in)s +1887(a)s 2051(v)s 6(ariety)k 2760(of)s 3028(fonts,)s +3611(column)s 4384(widths,)s 5126(etc.)s 5566(This)s 6040(in\210uence)s +6970(cannot)s 7666(tak)s 2(e)k 8116(the)s 8461(purely)s +0 9690(static)m 569(form)s 1106(that)s 1538(block-structured)s 3175(languages)s +4196(use)s 4585(to)s 4837(associate)s 5769(v)s 6(alues)k +6438(with)s 6933(identi\207ers,)s 8009(for)s 8360(then)s 8843(an)s +0 9402(operator)m 850(could)s 1434(not)s 1794(in\210uence)s 2721(the)s +3063(appearance)s 4188(of)s 4453(its)s 4723(parameters;)s 5876(and)s +6274(a)s 6434(state)s 6921(v)s 6(ariable)k 7734(solution)s +8556(is)s 8760(not)s 0 9114(compatible)m 1118(with)s 1600(the)s +1948(o)s 3(v)k 3(erall)k 2660(functional)s 3684(design.)s +480 8740(The)m 914(information)s 2105(needed)s 2848(from)s 3378(the)s +3733(conte)s 3(xt)k 4500(seems)s 5141(quite)s 5682(limited,)s +6471(comprising)s 7607(the)s 7961(font)s 8413(f)s 2(amily)k 15(,)k +0 8452(f)m 2(ace,)k 525(and)s 952(size)s 1402(to)s +1664(use,)s 2114(the)s 2485(style)s 3015(of)s 3309(paragraph)s +4345(breaking)s 5259(required,)s 6185(ho)s 6(w)k 6669(much)s +7281(space)s 7891(to)s 8154(substitute)s 0 8164(between)m 873(the)s +1240(w)s 2(ords)k 1893(of)s 2184(paragraphs,)s 3359(and)s +3782(ho)s 6(w)k 4263(much)s 4871(horizontal)s 5914(and)s +6337(v)s 3(ertical)k 7124(space)s 7730(is)s 7959(a)s 4(v)k 6(ailable)k +8887(to)s 0 7876(recei)m 6(v)k 3(e)k 763(the)s +1139(object.)s 1914(These)s 2569(four)s 3054(items)s 3650(constitute)s +4662(the)s 5038(so-called)s 5985(`style)s 6599(information')s 7866(of)s +8165(Lout.)s 8809(As)s 0 7588(graphics)m 902(rendering)s 1912(hardw)s 2(are)k +2896(impro)s 3(v)k 3(es,)k 3928(the)s 4317(style)s +4865(information)s 6091(will)s 6558(probably)s 7504(gro)s 6(w)k +8085(to)s 8366(include)s 0 7300(colour)m 671(and)s 1075(te)s 3(xture)k +1791(information.)s 480 6926(The)m 908(w)s 2(ay)k 1359(to)s +1598(deal)s 2051(with)s 2533(fonts)s 3062(at)s 3294(least)s +3791(is)s 4001(v)s 3(ery)k 4477(clear:)s 220 fnt35 +480 6425({ )m 11(Times Slope 12p } @F)k 6(ont { Hello)k 8(, w)k 2(or)k -3(ld })k +240 fnt82 0 5929(should)m 697(ha)s 4(v)k 3(e)k +1198(result)s 240 fnt83 480 5475(Hello,)m 1104(world)s 240 fnt82 +0 4993(Lout)m 528(also)s 983(pro)s 3(vides)k 220 fnt35 +1872 4990(@Break)m 240 fnt82 2745 4993(and)m 220 fnt35 3166 4990(@Space)m +240 fnt82 4080 4993(symbols)m 4946(for)s 5301(controlling)s 6420(the)s +6785(paragraph)s 7815(breaking)s 8722(and)s 0 4705(space)m 610(styles)s +1229(mentioned)s 2320(abo)s 3(v)k 3(e.)k 3074(These)s +3724(w)s 2(ork)k 4299(in)s 4565(the)s 4937(same)s +5507(w)s 2(ay)k 15(,)k 6020(returning)s 6972(their)s +7493(right)s 8028(parameters)s 0 4417(in)m 261(the)s 627(style)s +1152(of)s 1441(their)s 1956(left.)s 2455(The)s 2901(implementation)s +4476(is)s 4704(v)s 3(ery)k 5198(simple:)s 6019(one)s +6439(merely)s 7174(broadcasts)s 8252(the)s 8619(style)s 0 4129(information)m +1183(do)s 6(wn)k 1765(into)s 2188(the)s 2533(parse)s +3091(tree)s 3502(of)s 3771(the)s 4116(right)s 4625(parameter)s 13(.)k +5728(A)s 5956(font,)s 6445(for)s 6781(e)s 3(xample,)k +7693(is)s 7901(con)s 9(v)k 3(erted)k 8887(to)s +0 3841(an)m 278(8-bit)s 783(internal)s 1562(name)s 2130(and)s +2529(stored)s 3165(in)s 3403(each)s 3892(leaf,)s 4351(while)s +4932(a)s 5093(breaking)s 5977(style)s 6479(is)s 6683(stored)s +7320(in)s 7557(the)s 7900(root)s 8339(node)s 8855(of)s +0 3553(each)m 495(paragraph.)s 480 3179(The)m 954(same)s 1547(language)s +2514(design)s 3242(can)s 3677(be)s 4006(used)s 4549(for)s +4933(a)s 4(v)k 6(ailable)k 5888(width)s 6536(and)s +6986(height,)s 7738(only)s 8264(here)s 8778(the)s 0 2891(implementation)m +1557(is)s 1767(much)s 2356(more)s 2903(demanding:)s 220 fnt35 +480 2390(2i @Wide {)m 480 2102(\(1\) |0.1i An e)m 6(xample)k 480 1814(containing a small)m 480 1526(par)m 2(ag)k 2(r)k 2(aph of \207lled te)k 6(xt.)k +480 1238(})m +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 14 15 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(14)s 4710(-)s 0 13256(is)m 210(guaranteed)s +1317(to)s 1556(be)s 1838(tw)s 2(o)k 2248(inches)s +2910(wide:)s 480 12753(\(1\))m 891(An)s 1270(e)s 3(xample)k +2162(containing)s 3254(a)s 891 12465(small)m 1504(paragraph)s 2558(of)s +2871(\207lled)s 891 12177(te)m 3(xt.)k 0 11724(One)m 448(must)s +966(calculate)s 1863(that)s 2273(1.9)s 2617(inches)s 3272(minus)s +3900(the)s 4241(width)s 4836(of)s 220 fnt35 5100 11721(\(1\))m +240 fnt82 5406 11724(is)m 5609(a)s 4(v)k 6(ailable)k +6510(to)s 6741(the)s 7082(paragraph,)s 8138(and)s 8534(break)s +0 11436(it)m 186(accordingly;)s 1421(Basser)s 2111(Lout)s 2617(does)s +3100(this)s 3490(in)s 3727(tw)s 2(o)k 4130(stages.)s +4872(In)s 5121(the)s 5463(\207rst,)s 5935(upw)s 2(ard-mo)k 3(ving)k +7505(stage,)s 8097(widths)s 8779(are)s 0 11148(calculated)m 1018(using)s +1581(the)s 1920(formulae)s 2829(of)s 3091(Section)s 3856(2.3,)s +4254(which)s 4887(assume)s 5638(that)s 6047(a)s 4(v)k 6(ailable)k +6946(space)s 7524(is)s 7725(in\207nite.)s 8557(If)s 8778(the)s +0 10860(upw)m 2(ard)k 763(mo)s 3(v)k 3(ement)k +1815(reaches)s 2570(a)s 240 fnt83 2724 10862(WIDE)m 240 fnt82 +3375 10860(node,)m 3936(corresponding)s 5346(to)s 5573(a)s 220 fnt35 +5728 10857(@Wide)m 240 fnt82 6490 10860(operator)m 9(,)k 7372(and)s +7764(the)s 8100(calculated)s 0 10572(width)m 627(e)s 3(xceeds)k +1457(that)s 1900(allo)s 6(wed,)k 2784(a)s 2975(second,)s +3772(do)s 6(wnw)k 2(ard-mo)k 3(ving)k 5661(stage)s +6234(is)s 6469(initiated)s 7334(which)s 8001(attempts)s 8887(to)s +0 10284(reduce)m 681(the)s 1017(width)s 1606(by)s 1888(\207nding)s +2607(and)s 2999(breaking)s 3877(paragraphs.)s 5077(This)s 5541(second)s +6251(stage)s 6786(is)s 6984(quite)s 7505(routine)s 8226(e)s 3(xcept)k +8894(at)s 220 fnt35 0 9993(|)m 240 fnt82 84 9996(nodes,)m +736(whose)s 1390(children)s 2216(are)s 2549(the)s 2883(columns)s +3731(of)s 3988(a)s 4141(table.)s 4755(It)s 4946(is)s +5142(necessary)s 6111(to)s 6336(apportion)s 7296(the)s 7630(a)s 4(v)k 6(ailable)k +8524(width)s 0 9708(\(minus)m 727(inter)s 4(-column)k 2026(g)s 1(aps\))k +2604(among)s 3321(the)s 3681(columns.)s 4668(Basser)s 5377(Lout)s +5901(lea)s 4(v)k 3(es)k 6554(narro)s 6(w)k +7291(columns)s 8166(unbrok)s 2(en)k 0 9420(and)m 404(breaks)s +1079(the)s 1427(remaining)s 2449(columns)s 3311(to)s 3550(equal)s +4123(width,)s 4775(using)s 5347(up)s 5640(all)s 5933(of)s +6204(the)s 6552(a)s 4(v)k 6(ailable)k 7460(space.)s +480 9046(The)m 897(size)s 1313(of)s 1572(an)s 1844(object)s +2476(is)s 2675(not)s 3029(clearly)s 3721(determined)s 4843(when)s +5407(the)s 5744(upw)s 2(ard-mo)k 3(ving)k 7309(size)s +7725(is)s 7923(less)s 8321(than)s 8778(the)s 0 8758(do)m 6(wnw)k 2(ard-mo)k 3(ving)k +1871(a)s 4(v)k 6(ailable)k 2786(space,)s 3431(and)s +3842(the)s 4197(object)s 4849(contains)s 5704(constructs)s 6731(that)s +7156(depend)s 7913(on)s 8218(a)s 4(v)k 6(ailable)k +0 8470(space)m 587(\(e.g.)s 1056(right)s 1567(justi\207cation\).)s 2938(F)s 3(or)k +3327(e)s 3(xample,)k 4241(in)s 220 fnt35 480 7969(2i @Wide { Heading // a |1r)m -8(t b })k +240 fnt82 0 7470(it)m 211(seems)s 865(natural)s 1603(to)s +1861(assign)s 2536(a)s 2721(width)s 3342(of)s 3633(tw)s 2(o)k +4062(inches)s 4744(to)s 5002(the)s 5369(subobject)s 220 fnt35 +6366 7467(a |1r)m -8(t b)k 240 fnt82 7124 7470(because)m 7957(of)s +8247(the)s 8615(right)s 0 7182(justi\207cation,)m 1270(b)s 4(ut)k +1667(it)s 1895(w)s 2(ould)k 2585(be)s 2903(equally)s +3696(plausible)s 4650(if)s 4903(the)s 5286(width)s 5924(of)s +220 fnt35 6230 7179(Heading)m 240 fnt82 7129 7182(w)m 2(as)k +7586(assigned)s 8503(to)s 8778(the)s 0 6894(subobject)m 989(instead.)s +1843(The)s 2284(author)s 2968(is)s 3191(conscious)s 4199(of)s +4483(ha)s 4(ving)k 5197(f)s 2(ailed)k 5809(to)s +6061(resolv)s 3(e)k 6817(this)s 7226(matter)s 7908(properly;)s +8843(an)s 0 6606(e)m 3(xtra)k 534(operator)s 1390(for)s +1728(controlling)s 2830(a)s 4(v)k 6(ailable)k 3738(space)s +4325(is)s 4535(probably)s 5440(necessary)s 15(.)k 480 6232(The)m +930(actual)s 1578(paragraph)s 2614(breaking)s 3527(is)s 3759(just)s +4187(a)s 4376(simple)s 5092(transformation)s 6578(on)s 6897(the)s +7268(parse)s 7851(tree;)s 8343(the)s 8714(real)s 0 5944(issue)m +544(is)s 764(ho)s 6(w)k 1235(to)s 1484(describe)s +2346(the)s 2704(v)s 6(arious)k 3463(styles:)s 4183(ragged)s +4902(right,)s 5470(adjusted,)s 6384(outdented,)s 7445(and)s 7859(so)s +8135(on.)s 8549(Their)s 0 5656(di)m 6(v)k 3(ersity)k +874(suggests)s 1729(that)s 2140(the)s 3(y)k 2596(should)s +3286(someho)s 6(w)k 4245(be)s 4519(de\207ned)s 5275(using)s +5840(more)s 6380(basic)s 6917(features;)s 7777(b)s 4(ut)k +8132(then)s 8593(there)s 0 5368(are)m 367(algorithms)s 1461(for)s +1820(high-quality)s 3064(paragraph)s 4098(breaking,)s 5063(which)s 5726(presumably)s +6917(must)s 7463(be)s 7766(b)s 4(uilt-in.)k 8650(This)s +0 5080(dilemma)m 915(w)s 2(as)k 1355(not)s 1741(clearly)s +2463(grasped)s 3285(by)s 3598(the)s 3966(author)s 4656(in)s +4919(1985,)s 5525(and)s 5949(he)s 6250(included)s 7152(a)s +7337(b)s 4(uilt-in)k 8113(paragraph)s 0 4792(break)m 2(er)k 9(,)k +818(with)s 1306(the)s 220 fnt35 1660 4789(@Break)m 240 fnt82 +2522 4792(operator)m 3384(selecting)s 4292(from)s 4822(a)s 4995(\207x)s 3(ed)k +5535(set)s 5866(of)s 6143(styles.)s 6857(A)s 7093(much)s +7688(better)s 8298(solution)s 0 4504(based)m 603(on)s 900(g)s 1(alle)k 3(ys)k +1624(will)s 2050(be)s 2332(gi)s 6(v)k 3(en)k +2912(in)s 3155(Section)s 3929(5.5,)s 4336(b)s 4(ut,)k +4745(re)s 3(grettably)k 15(,)k 5868(it)s 6060(is)s +6270(not)s 6636(implemented.)s 240 fnt84 0 3711(3.)m 291(De\207nitions)s +240 fnt82 480 3280(The)m 936(need)s 1474(to)s 1741(pro)s 3(vide)k +2554(a)s 2748(means)s 3438(of)s 3737(packaging)s 4803(useful)s +5470(pieces)s 6146(of)s 6445(code)s 6982(for)s 7348(easy)s +7855(repeated)s 8751(use)s 0 2992(w)m 2(as)k 440(recognised)s +1554(in)s 1816(the)s 2184(v)s 3(ery)k 2679(earliest)s +3447(programming)s 4822(languages.)s 5962(This)s 6458(need)s 6987(is)s +7217(e)s 6(v)k 3(en)k 7736(more)s 8303(acute)s +8883(in)s 0 2704(document)m 1004(formatting,)s 2118(if)s 2335(that)s +2752(is)s 2962(possible,)s 3852(because)s 4664(the)s 5012(majority)s +5874(of)s 6145(users)s 6686(are)s 7033(not)s 7398(programmers)s +8722(and)s 0 2416(do)m 293(not)s 659(understand)s 1767(the)s +2115(code)s 2623(the)s 3(y)k 3086(in)s 9(v)k 4(ok)k 2(e.)k +240 fnt84 0 1767(3.1.)m 471(Operators)s 240 fnt82 480 1290(It)m +680(is)s 885(e)s 6(vident)k 1637(from)s 2156(the)s +2498(e)s 3(xample)k 3356(of)s 3621(Eqn)s 4059(that)s +4471(user)s 4(-de\207ned)k 5702(operators)s 6636(are)s 6978(needed)s +7708(that)s 8121(mimic)s 8778(the)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 15 16 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Symbol +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4292 13841(-)m 4420(15)s 4706(-)s 0 13250(primiti)m 6(v)k 3(e)k +929(ones)s 1426(in)s 1677(taking)s 2335(objects)s 3071(as)s +3328(parameters)s 4434(and)s 4845(returning)s 5781(objects)s 6517(as)s +6774(results.)s 7569(F)s 3(or)k 7965(e)s 3(xample,)k +8887(to)s 0 12962(de\207ne)m 641(a)s 807(superscript)s 1915(operator)s +2771(so)s 3037(that)s 220 fnt35 480 12468(2 sup n)m 240 fnt82 +0 11943(appears)m 781(as)s 168 fnt82 1145 12059(n)m 240 fnt78 +1031 11937(2)m 240 fnt82 1227 11943(,)m 1334(the)s 1682(follo)s 6(wing)k +2659(operator)s 3515(de\207nition)s 4489(may)s 4955(be)s 5237(used:)s +220 fnt35 480 11444(def sup)m 480 11156( precedence 50)m 480 10868( associativity r)m -3(ight)k +480 10580( left x)m 480 10292( r)m -3(ight y)k 480 10004({)m 480 9716( @OneRo)m 3(w { | {-2p @F)k 6(ont y} ^/0.5fk x })k +480 9428(})m 240 fnt82 0 8932(The)m 220 fnt35 481 8929(sup)m +240 fnt82 940 8932(operator)m 1850(has)s 2273(precedence)s 3458(50,)s +3858(is)s 4122(right)s 4686(associati)s 6(v)k 3(e,)k +5886(tak)s 2(es)k 6479(tw)s 2(o)k 6943(objects)s +7724(as)s 8028(parameters)s 0 8644(passed)m 720(on)s 1041(the)s +1413(left)s 1814(and)s 2242(right,)s 2825(and)s 3253(returns)s +3991(the)s 4363(object)s 5031(between)s 5910(braces)s 6595(as)s +6869(result.)s 7587(This)s 8087(object)s 8756(has)s 0 8356(the)m +348(structure)s gsave +608 7875 translate +280 fnt83 128 191 0 123 280 288 70 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +128 191 0 123 280 288 70 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +128 191 0 123 280 288 70 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +260 fnt35 0 56(y)m +grestore + +grestore +end end restore +grestore +gsave +480 7740 translate +280 fnt83 128 135 0 67 280 288 70 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +128 135 0 67 280 288 70 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +128 135 0 67 280 288 70 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +260 fnt35 0 0(x)m + +grestore + +grestore +end end restore +grestore +0 7289(b)m 4(ut)k 381(with)s 882(the)s 1249(\207rst)s +1699(ro)s 6(w)k 2138(mark)s 2709(hidden)s 3437(by)s +3751(the)s 220 fnt35 4118 7286(@OneRo)m 3(w)k 240 fnt82 +5268 7289(operator)m 9(,)k 6181(and)s 220 fnt35 6604 7286(y)m +240 fnt82 6791 7289(tw)m 2(o)k 7220(points)s 7875(smaller)s +8657(than)s 0 7001(it)m 220(w)s 2(ould)k 904(otherwise)s +1917(ha)s 4(v)k 3(e)k 2447(been.)s 3091(The)s +3548(length)s 220 fnt35 4231 6998(0.5f)m 240 fnt82 4683 7001(speci\207es)m +5585(half)s 6057(the)s 6433(current)s 7198(font)s 7671(size;)s +8243(Figure)s 8952(2)s 0 6713(describes)m 936(the)s 220 fnt35 +1280 6710(k)m 240 fnt82 1446 6713(g)m 1(ap)k 1840(mode.)s +2532(In)s 2784(the)s 3128(Eq)s 3448(equation)s 4325(formatting)s +5382(package)s 6218([10])s 6651(the)s 6995(equation)s 7872(as)s +8118(a)s 8280(whole)s 8916(is)s 0 6425(set)m 331(in)s +580(italic)s 1116(font,)s 1614(and)s 220 fnt35 2024 6422(2)m +240 fnt82 2203 6425(is)m 2419(an)s 2709(identi\207er)s 3637(whose)s +4311(body)s 4852(contains)s 5706(a)s 5879(font)s 6330(change)s +7070(back)s 7590(to)s 7835(Roman.)s 8698(The)s 0 6137(digits)m +220 fnt35 586 6134(0)m 240 fnt82 765 6137(to)m 220 fnt35 +1009 6134(9)m 240 fnt82 1186 6137(are)m 1538(classed)s 2291(as)s +2546(punctuation)s 3737(characters,)s 4816(permitting)s 220 fnt35 5869 6134(234)m +240 fnt82 6293 6137(for)m 6635(e)s 3(xample)k 7503(to)s +7747(be)s 8034(interpreted)s 0 5849(as)m 250(a)s 416(sequence)s +1349(of)s 1620(three)s 2153(identi\207ers.)s 480 5475(These)m 1152(de\207nitions)s +2258(are)s 2650(easily)s 3307(implemented)s 4658(by)s 4997(a)s +5208(standard)s 6122(symbol)s 6927(table)s 7492(and)s 7941(an)s +8270(operator)s 0 5187(precedence)m 1155(parser)s 13(.)k 1914(Algol)s +2539(block)s 3157(structure)s 4073(with)s 4580(the)s 4953(usual)s +5538(scope)s 6164(rules)s 6704(w)s 2(as)k 7150(adopted)s +7991(as)s 8266(a)s 8457(matter)s 0 4899(of)m 271(course.)s +480 4525(Operators)m 1481(are)s 1837(limited)s 2580(to)s 2828(at)s +3069(most)s 3603(tw)s 2(o)k 4022(parameters,)s 5185(left)s +5571(and)s 5984(right,)s 6551(and)s 6964(the)s 7321(parameters)s +8428(cannot)s 0 4237(be)m 282(gi)s 6(v)k 3(en)k +862(def)s 2(ault)k 1583(v)s 6(alues.)k 240 fnt83 +2352 4239(Named)m 240 fnt82 3097 4237(parameters)m 4195(solv)s 3(e)k +4753(both)s 5236(problems:)s 220 fnt35 480 3736(def @Pref)m 6(ace)k +480 3448( named @T)m 26(ag {})k 480 3160( named @Title { Pref)m 6(ace })k 480 2872( r)m -3(ight @Body)k +480 2584({)m 480 2296( Bold @F)m 6(ont @Title)k 480 2008( //0.3v @Body)m 480 1720(})m +240 fnt82 0 1226(The)m 452(def)s 2(ault)k 1197(v)s 6(alue)k +1789(appears)s 2594(just)s 3023(after)s 3543(the)s 3915(parameter')s 13(s)k +5103(declaration,)s 6295(between)s 7173(braces.)s 7972(In)s 9(v)k 4(ocations)k + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 16 17 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13842(-)m 4416(16)s 4709(-)s 0 13251(ha)m 4(v)k 3(e)k +501(a)s 667(natural)s 1385(syntax:)s 220 fnt35 480 12750(@Pref)m 6(ace)k +480 12462( @Title { About this book })m 480 12174({)m 480 11886( F)m 6(e)k 4(w obser)k -6(v)k 5(ers w)k 2(ould ha)k 4(v)k 5(e supposed in 1984, that ...)k +480 11598(})m 240 fnt82 0 11104(with)m 481(the)s 827(actual)s +1450(named)s 2145(parameters)s 3241(follo)s 6(wing)k 4216(directly)s +4998(after)s 5492(the)s 5838(operator)s 9(,)k 6731(before)s +7395(an)s 3(y)k 7790(right)s 8299(parame)s 8998(-)s +0 10816(ter)m 13(.)k 400(In)s 653(this)s 1046(e)s 3(xample,)k +220 fnt35 1958 10813(@T)m 26(ag)k 240 fnt82 2578 10816(will)m +3001(recei)s 6(v)k 3(e)k 3735(its)s 4008(def)s 2(ault)k +4726(v)s 6(alue,)k 5342(and)s 5744(a)s 5907(less)s +6313(e)s 3(xpert)k 6965(user)s 7420(could)s 8007(safely)s +8628(omit)s 0 10528(the)m 220 fnt35 348 10525(@Title)m 240 fnt82 +1036 10528(parameter)m 2050(as)s 2300(well.)s 480 10154(Lout)m 1007(permits)s +1790(named)s 2502(parameters)s 3616(to)s 3870(ha)s 4(v)k 3(e)k +4387(parameters,)s 5557(a)s 5739(feature)s 6472(with)s 6970(applications)s +8192(to)s 8447(biblio)s 8998(-)s 0 9866(graphic)m 781(databases,)s +1816(running)s 2626(headers,)s 3475(and)s 3891(other)s 4454(places)s +5114(where)s 5766(a)s 5944(format)s 6652(has)s 7034(to)s +7285(be)s 7579(supplied)s 8460(before)s 0 9578(content)m 760(is)s +965(kno)s 6(wn.)k 1771(One)s 2221(could)s 2806(go)s +3094(further)s 3798(and)s 4197(pro)s 3(vide)k 4976(a)s +5137(complete)s 6064(lambda)s 6823(calculus,)s 7708(with)s 8185(functions)s +0 9290(as)m 250(\207rst-)s 689(class)s 1204(objects,)s 1988(pro)s 3(vided)k +2894(care)s 3347(w)s 2(as)k 3768(tak)s 2(en)k +4341(not)s 4707(to)s 4946(intimidate)s 5970(the)s 6318(non-)s +6746(e)s 3(xpert)k 7400(user)s 13(.)k 240 fnt84 +0 8641(3.2.)m 471(Recursion)s 1563(and)s 2004(page)s 2539(lay)s 6(out)k +240 fnt82 480 8164(Design)m 1302(and)s 1794(implementation)s 3439(should)s +4223(proceed)s 5126(together)s 6057(in)s 6387(e)s 3(xploratory)k +7628(projects,)s 8579(since)s 0 7876(otherwise)m 988(the)s 1340(design)s +2025(too)s 2388(easily)s 3003(becomes)s 3894(unrealistic.)s 5056(Sometimes)s +6173(the)s 6524(implementation)s 8085(does)s 8579(more)s 0 7588(than)m +469(its)s 745(designer)s 1615(intended.)s 2603(The)s 3031(author)s +3702(wrote)s 4302(the)s 4650(follo)s 6(wing)k 5627(purely)s +6292(as)s 6542(a)s 6708(testing)s 7398(scaf)s 6(fold:)k +220 fnt35 480 7087(def @P)m 8(age r)k -3(ight x)k 480 6799({)m +480 6511( 8i @Wide 11i @High)m 480 6223( {)m 480 5935( //1i ||1i x ||1i)m 480 5647( //1i)m 480 5359( })m +480 5071(})m 240 fnt82 0 4577(Only)m 518(afterw)s 2(ards)k +1558(did)s 1906(he)s 2172(realize)s 2848(its)s 3108(signi\207cance:)s +4400(the)s 4732(concept)s 5521(of)s 5776(a)s 5926(page)s +6418(had)s 6807(been)s 7300(de\207ned)s 8047(outside)s 8778(the)s +0 4289(implementation,)m 1619(remo)s 3(ving)k 2598(the)s 2959(need)s +3481(for)s 3831(commands)s 4932(for)s 5282(setting)s 5984(page)s +6505(width)s 7119(and)s 7535(height,)s 8253(mar)s 4(gins,)k +0 4001(and)m 404(so)s 670(on.)s 480 3627(De\207ning)m 1393(a)s +1582(sequence)s 2538(of)s 2831(pages)s 3450(is)s 3683(harder)s 9(,)k +4414(since)s 4983(their)s 5503(number)s 6317(is)s 6550(not)s +6938(kno)s 6(wn)k 7665(in)s 7931(adv)s 6(ance.)k +8896(A)s 0 3339(simple)m 693(v)s 3(ersion)k 1451(of)s +1722(this)s 2118(same)s 2665(problem)s 3522(is)s 3732(af)s 6(forded)k +4593(by)s 4887(the)s 5235(leaders)s 5962(found)s 6579(in)s +6822(tables)s 7430(of)s 7701(contents:)s 480 2834(Chapter)m 1297(7)s +1525(..)s 1809(..)s 2093(..)s 2377(..)s 2661(..)s +2945(..)s 3229(..)s 3513(..)s 3797(..)s 4081(..)s +4365(..)s 4649(..)s 4933(..)s 5217(..)s 5501(..)s +5785(..)s 6009(53)s 0 2331(This)m 476(seemed)s 1251(to)s +1490(require)s 2222(recursion,)s 3218(speci\207cally)s 4360(the)s 4708(de\207nition)s +220 fnt35 480 1830(def @Leaders { ..)m 13( @Leaders })k 240 fnt82 0 1336(Note)m +535(that)s 968(both)s 220 fnt35 1465 1333(..)m 240 fnt82 +1643 1336(and)m 220 fnt35 2061 1333(@Leaders)m 240 fnt82 3145 1336(are)m +3506(objects,)s 4305(so)s 4585(the)s 4948(tw)s 2(o)k +5372(spaces)s 6062(separating)s 7111(them)s 7664(are)s 8026(signi\207cant.)s +0 1048(No)m 361(base)s 858(case)s 1341(is)s 1567(gi)s 6(v)k 3(en,)k +2213(and)s 2633(indeed)s 3345(we)s 3696(ha)s 4(v)k 3(e)k +4213(no)s 4522(boolean)s 5353(or)s 5628(conditional)s 6775(operators)s +7731(with)s 8229(which)s 8887(to)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 17 18 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4291 13844(-)m 4419(17)s 4707(-)s 0 13255(e)m 3(xpress)k +757(it;)s 993(b)s 4(ut)k 1346(we)s 1673(can)s +2053(adopt)s 2637(the)s 2977(implicit)s 3770(base)s 4243(`if)s +4530(space)s 5109(is)s 5311(not)s 5668(suf\207cient,)s 6656(delete)s +220 fnt35 7273 13252(@Leaders)m 240 fnt82 8334 13255(and)m 8729(an)s 3(y)k +0 12967(preceding)m 996(space'.)s 1770(Then)s 2319(the)s 2667(e)s 3(xpression)k +220 fnt35 480 12466(4i @Wide { Chapter 7 @Leaders 53 })m 240 fnt82 0 11970(will)m 417(produce)s +1234(the)s 1572(object)s 2206(sho)s 6(wn)k 2873(abo)s 3(v)k 3(e.)k +3593(It)s 3788(is)s 3988(hard)s 4461(to)s 4691(see)s +5042(ho)s 6(w)k 5493(this)s 5879(base)s 6350(could)s +6930(be)s 7202(made)s 7766(e)s 3(xplicit,)k 8576(with)s +8998(-)s 0 11682(out)m 348(violating)s 1232(the)s 1561(general)s +2301(principle)s 3187(of)s 3439(k)s 2(eeping)k 4230(all)s +4504(size)s 4912(information)s 6079(internal.)s 6953(In)s 7190(the)s +7519(implementation,)s 220 fnt35 0 11391(@Leaders)m 240 fnt82 1071 11394(remains)m +1881(une)s 3(xpanded)k 3097(while)s 3686(sizes)s 4204(are)s +4554(being)s 5142(calculated;)s 6224(then)s 6696(it)s 6891(is)s +7103(treated)s 7813(similarly)s 8718(to)s 8960(a)s 0 11106(recepti)m 6(v)k 3(e)k +922(symbol,)s 1734(with)s 2216(its)s 2492(body)s 3026(as)s +3276(an)s 3559(incoming)s 4516(g)s 1(alle)k 3(y)k +5150(\(Section)s 6003(5.2\).)s 480 10732(W)m 9(ith)k 1014(this)s +1418(settled,)s 2156(it)s 2356(is)s 2574(no)s 6(w)k +3044(clear)s 3575(ho)s 6(w)k 4044(to)s 4291(de\207ne)s +4940(a)s 5115(document)s 6127(which)s 6777(is)s 6995(a)s +7169(numbered)s 8193(sequence)s 0 10444(of)m 271(pages.)s 980(Let)s +220 fnt35 1358 10441(@Ne)m 6(xt)k 240 fnt82 2082 10444(be)m +2364(a)s 2530(pre\207x)s 3143(operator)s 3999(which)s 4641(returns)s +5355(its)s 5631(parameter)s 6645(plus)s 7095(one.)s 7605(Then)s +220 fnt35 480 9943(def @P)m 8(ageList)k 480 9655( r)m -3(ight @P)k 8(ageNum)k +480 9367({)m 480 9079( @P)m 8(age {)k 480 8791( |0.5r)m -8(t - @P)k 8(ageNum -)k +480 8503( //1v @T)m 26(e)k 6(xtPlace)k 480 8215( //1r)m -8(t @F)k 6(ootSect)k +480 7927( })m 480 7639( //)m 480 7351( @P)m 8(ageList @Ne)k 6(xt @P)k 8(ageNum)k +480 7063(})m 240 fnt82 0 6569(when)m 576(in)s 9(v)k 4(ok)k 2(ed)k +1391(in)s 1634(the)s 1982(e)s 3(xpression)k 220 fnt35 +3059 6566(@P)m 8(ageList 1)k 240 fnt82 4267 6569(,)m 4374(has)s +4744(for)s 5082(its)s 5358(result)s 5948(the)s 6296(potentially)s +7372(in\207nite)s 8105(object)s 1927 2494 0 2494 240 288 60 480 3735 LoutGr2 +0 0 moveto xsize 0 lineto xsize ysize lineto +0 ysize lineto closepath stroke +grestore +160 fnt82 845 2216(-)m 931(1)s +1035(-)s 140 fnt35 170 2000(@T)m 16(e)k 4(xtPlace)k +170 173(@F)m 4(ootSect)k +grestore +1927 2494 0 2494 240 288 60 480 1241 LoutGr2 +0 0 moveto xsize 0 lineto xsize ysize lineto +0 ysize lineto closepath stroke +grestore +160 fnt82 839 2216(-)m 925(2)s +1041(-)s 140 fnt35 170 2000(@T)m 16(e)k 4(xtPlace)k +170 173(@F)m 4(ootSect)k +grestore +140 fnt35 480 1026(@P)m 5(ageList 3)k + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 18 19 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4291 13844(-)m 4419(18)s 4706(-)s 0 13253(Similarly)m 15(,)k +980(we)s 1315(may)s 1781(de\207ne)s 220 fnt35 2422 13250(@F)m 6(ootSect)k +240 fnt82 3573 13253(lik)m 2(e)k 3985(this:)s 220 fnt35 +480 12752(def @F)m 6(ootSect)k 480 12464({)m 480 12176( def @F)m 6(ootList)k +480 11888( r)m -3(ight @Num)k 480 11600( {)m 480 11312( @F)m 6(ootPlace)k +480 11024( //1v)m 480 10736( @F)m 6(ootList @Ne)k 6(xt @Num)k 480 10448( })m +480 9872( 1i @Wide @HLine)m 480 9584( //1v)m 480 9296( @F)m 6(ootList 1)k 480 9008(})m +240 fnt82 0 8514(so)m 266(that)s 684(an)s 967(in)s 9(v)k 4(ocation)k +2021(of)s 220 fnt35 2292 8511(@F)m 6(ootSect)k 240 fnt82 +3443 8514(produces)m gsave +480 8174 translate +220 fnt35 1440 0 0 0 220 288 61 LoutGraphic +gsave +0 0 moveto xsize 0 lineto stroke +grestore + +grestore +220 fnt35 480 7829(@F)m 6(ootPlace)k 480 7541(@F)m 6(ootPlace)k +480 7253(@F)m 6(ootPlace)k 480 6965(...)m 240 fnt82 0 6514(The)m +476(e)s 3(xpansion)k 1550(process)s 2367(is)s 2626(v)s 3(ery)k +3150(similar)s 3921(to)s 4209(a)s 4424(BNF)s 4997(deri)s 6(v)k 6(ation,)k +6109(and)s 6562(w)s 2(ould)k 7266(be)s 7597(attempted)s +8646(only)s 0 6226(on)m 297(demand.)s 480 5852(Clearly)m 15(,)k +1276(deciding)s 2154(which)s 2797(e)s 3(xpansions)k 3910(to)s +4150(tak)s 2(e)k 4603(and)s 5008(replacing)s 220 fnt35 +5951 5849(@T)m 26(e)k 6(xtPlace)k 240 fnt82 7170 5852(and)m +220 fnt35 7575 5849(@F)m 6(ootPlace)k 240 fnt82 8832 5852(by)m +0 5564(the)m 338(appropriate)s 1471(actual)s 2085(te)s 3(xt)k +2489(will)s 2904(not)s 3259(be)s 3530(easy;)s 4056(this)s +4441(is)s 4640(the)s 4977(subject)s 5703(of)s 5963(Section)s +6726(5.1.)s 7179(The)s 7596(important)s 8574(point)s 0 5276(for)m +331(no)s 6(w)k 784(is)s 986(that)s 1397(we)s +1724(ha)s 4(v)k 3(e)k 2217(here)s 2677(a)s +2835(v)s 3(ery)k 3303(simple)s 3989(and)s 4385(\210e)s 3(xible)k +5147(method)s 5916(of)s 6179(specifying)s 7220(the)s 7561(layout)s +8211(of)s 8474(pages,)s 0 4988(which)m 642(requires)s 1462(no)s +1755(specialized)s 2874(language)s 3794(features.)s 240 fnt84 0 4340(3.3.)m +471(Modules)s 240 fnt82 480 3909(It)m 679(is)s 882(well)s +1342(accepted)s 2229(that)s 2641(the)s 2982(visibility)s 3879(of)s +4143(symbols)s 4986(is)s 5189(not)s 5549(adequately)s 6632(controlled)s +7653(by)s 7940(Algol)s 8533(block)s 0 3621(structure.)m 999(The)s +1427(author)s 2098(is)s 2308(a)s 3(w)k 2(are)k +2929(of)s 3200(se)s 6(v)k 3(eral)k 3922(major)s +4539(problems)s 5480(of)s 5751(this)s 6147(kind)s 6631(in)s +6874(document)s 7878(formatting.)s 480 3247(One)m 976(problem)s 1874(is)s +2126(that)s 2585(some)s 3187(symbols)s 4078(should)s 4816(be)s +5139(visible)s 5874(only)s 6395(within)s 7104(restricted)s 8091(parts)s +8647(of)s 8960(a)s 0 2959(document.)m 1108(F)s 3(or)k +1497(e)s 3(xample,)k 2411(we)s 2746(naturally)s 3649(e)s 3(xpect)k +4330(equation)s 5211(formatting)s 6272(to)s 6511(be)s 6793(accomplished)s +8166(lik)s 2(e)k 8578(this:)s 220 fnt35 480 2462(surrounding te)m 6(xt)k +480 2174(@Eq { {x sup 2 + 1} o)m 3(v)k 5(er 4 })k 480 1886(surrounding te)m 6(xt)k +240 fnt82 0 1387(with)m 482(the)s 830(symbols)s 220 fnt35 +1679 1384(sup)m 240 fnt82 2025 1387(,)m 220 fnt35 2132 1384(o)m 3(v)k 5(er)k +240 fnt82 2551 1387(,)m 2658(etc.,)s 3103(visible)s 3796(only)s +4276(within)s 4944(the)s 5292(equation,)s 6223(not)s 6589(in)s +6832(the)s 7180(surrounding)s 8390(te)s 3(xt.)k 480 1013(It)m +695(seems)s 1341(natural)s 2069(to)s 2319(de\207ne)s 2970(these)s +3528(symbols)s 4387(within)s 220 fnt35 5066 1010(@Eq)m 240 fnt82 +5544 1013(,)m 5661(since)s 6219(the)s 3(y)k 6692(are)s +7050(local)s 7579(to)s 7829(equations.)s 8921(It)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 19 20 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4289 13844(-)m 4417(19)s 4708(-)s 0 13251(only)m 494(remains)s +1316(then)s 1799(to)s 2053(decree)s 2746(that)s 3179(symbols)s +4043(local)s 4576(to)s 220 fnt35 4830 13248(@Eq)m 240 fnt82 +5382 13251(are)m 5744(to)s 5998(be)s 6294(visible)s 7002(within)s +7684(its)s 7975(actual)s 8615(right)s 0 12963(parameter)m 9(,)k +1052(and)s 1456(this)s 1852(is)s 2062(done)s 2584(by)s +2878(replacing)s 3820(the)s 4168(right)s 4679(formal)s 5370(parameter)s +6384(with)s 6866(a)s 240 fnt83 7032 12965(body)m 240 fnt82 +7554 12963(parameter:)m 220 fnt35 480 12477(e)m 6(xpor)k -8(t sup o)k 3(v)k 5(er)k +480 12189(def @Eq)m 480 11901( body @Body)m 480 11613({)m 480 11325( def sup ...)m 480 11037( def o)m 3(v)k 5(er ...)k +480 10461( Slope @F)m 6(ont @Body)k 480 10173(})m 240 fnt82 0 9679(The)m +220 fnt35 426 9676(e)m 6(xpor)k -8(t)k 240 fnt82 +1092 9679(clause)m 1743(lists)s 2176(the)s 2522(identi\207ers)s 3526(which)s +4166(are)s 4511(permitted)s 5482(to)s 5719(be)s 5999(visible)s +6690(outside)s 7435(their)s 7930(usual)s 8488(range,)s 0 9391(the)m +359(body)s 905(of)s 220 fnt35 1188 9388(@Eq)m 240 fnt82 +1666 9391(;)m 1790(and)s 2206(the)s 220 fnt35 2566 9388(body)m +240 fnt82 3112 9391(declaration)m 4241(imports)s 5034(them)s 5584(into)s +6021(\(mak)s 2(es)k 6772(them)s 7322(visible)s 8027(within\))s +8778(the)s 0 9103(actual)m 614(right)s 1114(parameter)s 2117(of)s +2376(each)s 2860(in)s 9(v)k 4(ocation)k 3903(of)s +220 fnt35 4162 9100(@Eq)m 240 fnt82 4640 9103(.)m 4793(This)s +5258(arrangement)s 6500(has)s 6859(pro)s 3(v)k 3(en)k +7564(v)s 3(ery)k 8028(con)s 9(v)k 3(enient)k +0 8815(for)m 338(de\207ning)s 1176(a)s 1342(v)s 6(ariety)k +2053(of)s 2324(special-purpose)s 3880(packages.)s 480 8441(Another)m 1361(problem)s +2256(arises)s 2888(when)s 3502(global)s 4193(symbols,)s 5136(such)s +5669(as)s 5957(the)s 6343(ones)s 6871(used)s 7406(for)s +7782(headings)s 8722(and)s 0 8153(paragraph)m 1034(separators,)s 2130(call)s +2550(on)s 2868(v)s 6(alues)k 3545(that)s 3984(the)s +4353(non-e)s 3(xpert)k 5468(user)s 5947(will)s 6394(need)s +6925(to)s 7185(modify)s 15(,)k 7989(such)s 8506(as)s +8778(the)s 0 7865(initial)m 605(font)s 1044(or)s 1297(paragraph)s +2303(indent.)s 3059(These)s 3680(v)s 6(alues)k 4329(are)s +4670(lik)s 2(e)k 5076(parameters)s 6167(of)s 6432(the)s +6774(document)s 7771(as)s 8015(a)s 8175(whole,)s 8860(so)s +0 7577(it)m 192(is)s 402(natural)s 1120(to)s 1359(try)s +1678(this:)s 220 fnt35 480 7076(e)m 6(xpor)k -8(t @Heading @PP ...)k +480 6788(def @BookLa)m 6(y)k 4(out)k 480 6500( named @InitialF)m 6(ont { )k 11(Times Base 12p })k +480 6212( named @InitialBreak { adjust 14p })m 480 5924( named @ColumnWidth { 6i })m 480 5636( ...)m 480 5348({)m 480 5060( def @Heading ...)m +480 4772( def @PP ...)m 480 4484(})m 240 fnt82 0 3990(No)m 6(w)k +220 fnt35 579 3987(@Heading)m 240 fnt82 1732 3990(and)m 220 fnt35 +2202 3987(@PP)m 240 fnt82 2833 3990(may)m 3365(in)s 9(v)k 4(ok)k 2(e)k +220 fnt35 4124 3987(@InitialF)m 6(ont)k 240 fnt82 5411 3990(and)m +5881(the)s 6295(other)s 6911(parameters.)s 8188(T)s 19(o)k +8554(mak)s 2(e)k 220 fnt35 0 3699(@Heading)m 240 fnt82 +1100 3702(and)m 220 fnt35 1517 3699(@PP)m 240 fnt82 2096 3702(visible)m +2802(throughout)s 3926(the)s 4287(document,)s 5352(we)s 5700(need)s +6223(only)s 6716(add)s 7133(a)s 7312(body)s 7859(parameter)s +8887(to)s 220 fnt35 0 3411(@BookLa)m 6(y)k 4(out)k +240 fnt82 1428 3414(and)m 1832(present)s 2582(the)s 2930(entire)s +3529(document)s 4533(as)s 220 fnt35 480 2913(@BookLa)m 6(y)k 4(out)k +480 2625( @InitialF)m 6(ont { Helv)k 5(etica Base 10p })k 480 2337( @InitialBreak { adjust 12p })m 480 2049({)m +480 1761( )m 11(The document.)k 480 1473(})m 240 fnt82 0 979(b)m 4(ut)k +383(for)s 742(practical)s 1639(reasons)s 2429(gi)s 6(v)k 3(en)k +3030(belo)s 6(w)k 3684(we)s 4040(prefer)s 4691(not)s +5078(to)s 5338(enclose)s 6132(the)s 6502(entire)s 7122(document)s +8147(in)s 8412(braces.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 20 21 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4287 13844(-)m 4415(20)s 4710(-)s 0 13253(Instead,)m 797(we)s +1132(write)s 220 fnt35 480 12771(@Use { @BookLa)m 6(y)k 4(out)k +480 12483( @InitialF)m 6(ont { Helv)k 5(etica Base 10p })k 480 12195( @InitialBreak { adjust 12p })m 480 11907(})m +480 11619(The document.)m 240 fnt82 0 11165(which)m 643(has)s 1015(the)s +1365(same)s 1914(ef)s 6(fect:)k 220 fnt35 2617 11162(@Use)m +240 fnt82 3284 11165(mak)m 2(es)k 3946(the)s 4296(e)s 3(xported)k +5190(symbols)s 6040(of)s 220 fnt35 6313 11162(@BookLa)m 6(y)k 4(out)k +240 fnt82 7743 11165(visible)m 8438(for)s 8778(the)s 0 10877(remainder)m +1028(of)s 1299(the)s 1647(document,)s 2698(and)s 3102(is)s +3312(permitted)s 4285(only)s 4765(at)s 4997(the)s 5345(be)s 3(ginning.)k +480 10503(The)m 925(third)s 1451(feature)s 2187(that)s 2622(af)s 6(fects)k +3319(visibility)s 15(,)k 4278(and)s 4699(which)s 5359(will)s +5802(pro)s 3(v)k 3(e)k 6414(useful)s 7071(for)s +7426(cross)s 7986(referencing)s 0 10215(\(Section)m 851(6.1\),)s 1335(is)s +1543(the)s 220 fnt35 1889 10212(@Open)m 240 fnt82 2693 10215(symbol.)m +3560(It)s 3763(mak)s 2(es)k 4421(the)s 4767(e)s 3(xported)k +5657(symbols)s 6504(of)s 6773(its)s 7047(left)s 7422(parameter)s +8433(visible)s 0 9927(within)m 668(its)s 944(right)s 1455(parameter)s 9(,)k +2507(and)s 2911(is)s 3121(therefore)s 4038(similar)s 4760(to)s +4999(the)s 5347(P)s 3(ascal)k 220 fnt35 6009 9924(with)m +240 fnt82 6444 9927(statement.)m 480 9553(It)m 698(could)s 1301(be)s +1596(ar)s 4(gued)k 2314(that)s 2745(Lout)s 3270(is)s +3493(o)s 3(v)k 3(er)k 4(-supplied)k 4869(with)s +5364(these)s 5924(visibility)s 6840(modifying)s 7903(features:)s 8778(the)s +0 9265(body)m 544(parameter)s 9(,)k 220 fnt35 1606 9262(@Use)m +240 fnt82 2282 9265(and)m 220 fnt35 2696 9262(@Open)m 240 fnt82 +3513 9265(do)m 3816(not)s 4193(seem)s 4754(suf\207ciently)s 5894(dif)s 6(ferent)k +6779(from)s 7314(each)s 7819(another)s 13(.)k 8698(The)s +220 fnt35 0 8974(@Open)m 240 fnt82 806 8977(symbol)m 1566(is)s +1776(the)s 2124(most)s 2649(general,)s 3459(being)s 4044(capable)s +4830(of)s 5101(replacing)s 6043(the)s 6391(other)s 6942(tw)s 2(o.)k +7463(F)s 3(or)k 7852(e)s 3(xample,)k 220 fnt35 +480 8476(@Use { x })m 480 8188(@Use { y })m 480 7900(Body of document)m 240 fnt82 0 7402(can)m +389(be)s 671(replaced)s 1538(by)s 220 fnt35 480 6901(x @Open {)m +480 6613(y @Open {)m 480 6325(Body of document)m 480 6037(}})m 240 fnt82 0 5543(and,)m +453(taking)s 1104(the)s 220 fnt35 1452 5540(@Eq)m 240 fnt82 +1990 5543(symbol)m 2750(abo)s 3(v)k 3(e)k 3372(as)s +3622(e)s 3(xample,)k 4536(we)s 4871(could)s 5461(eliminate)s +6405(its)s 6681(body)s 7215(parameter)s 9(,)k 8267(add)s +220 fnt35 480 5042(def @Body r)m -3(ight x { Slope @F)k 6(ont x })k 240 fnt82 +0 4543(to)m 239(the)s 587(e)s 3(xported)k 1479(de\207nitions)s +2540(of)s 220 fnt35 2811 4540(@Eq)m 240 fnt82 3289 4543(,)m +3396(and)s 3800(replace)s 220 fnt35 480 4042(@Eq { object })m 240 fnt82 +0 3545(by)m 220 fnt35 480 3044(@Eq @Open { @Body { object } })m 240 fnt82 0 2544(If)m +220 fnt35 232 2541(@Eq)m 240 fnt82 772 2544(is)m 985(a)s +1153(g)s 1(alle)k 3(y)k 1790(\(Section)s 2645(5.1\),)s +220 fnt35 3133 2541(@Body)m 240 fnt82 3917 2544(must)m 4444(tak)s 2(e)k +4899(o)s 3(v)k 3(er)k 5380(that)s 5800(function.)s +6764(But)s 7172(one)s 7577(w)s 2(ould)k 8234(not)s +8603(w)s 2(ant)k 0 2256(to)m 253(write)s 813(these)s +1374(clumsy)s 2133(e)s 3(xpressions)k 3311(in)s 3568(practice,)s +4444(and)s 4862(the)s 5224(enclosure)s 6210(of)s 6495(lar)s 4(ge)k +7038(quantities)s 8032(of)s 8317(input)s 8883(in)s 0 1968(e)m 3(xtra)k +534(braces)s 1195(could)s 1785(cause)s 2372(Basser)s 3069(Lout)s +3581(to)s 3820(run)s 4196(out)s 4562(of)s 4833(memory)s +5684(\(Section)s 6537(5.4\).)s 480 1594(A)m 700(quite)s 1224(separate)s +2052(kind)s 2526(of)s 2786(visibility)s 3679(problem)s 4526(arises)s +5110(when)s 5676(e)s 3(xpert)k 6319(users)s 6851(wish)s +7350(to)s 7579(de\207ne)s 8210(an)s 8482(object)s 0 1306(or)m +259(operator)s 1115(for)s 1453(repeated)s 2320(use)s 2695(within,)s +3413(say)s 15(,)k 3824(equations:)s 220 fnt35 480 807(def isum { sum from i=1 to n })m +240 fnt82 0 313(As)m 338(it)s 551(stands)s 1221(this)s +1638(can)s 2048(only)s 2549(be)s 2852(placed)s 3555(within)s +4244(the)s 220 fnt35 4613 310(@Eq)m 240 fnt82 5172 313(package)m +6033(itself,)s 6637(where)s 220 fnt35 7298 310(sum)m 240 fnt82 +7780 313(and)m 8205(the)s 8575(other)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 21 22 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4297 13844(-)m 4425(21)s 4700(-)s 0 13256(symbols)m 841(are)s +1179(visible,)s 1915(b)s 4(ut)k 2268(it)s 2451(is)s +2653(not)s 3010(desirable)s 3919(to)s 4150(modify)s 4886(the)s +5225(source)s 5897(code)s 6396(of)s 6658(a)s 6816(standard)s +7675(package.)s 8614(Lout)s 0 12968(pro)m 3(vides)k 872(an)s +220 fnt35 1155 12965(impor)m -8(t)k 240 fnt82 1828 12968(clause)m +2481(to)s 2720(solv)s 3(e)k 3278(this)s 3674(problem:)s +220 fnt35 480 12467(impor)m -8(t @Eq)k 480 12179(def isum { sum from i=1 to n })m 240 fnt82 +0 11685(may)m 469(appear)s 1169(after)s 220 fnt35 1669 11682(@Eq)m +240 fnt82 2210 11685(is)m 2423(de\207ned,)s 3239(and)s 3646(it)s +3842(will)s 4271(mak)s 2(e)k 4846(the)s 5198(e)s 3(xported)k +6093(symbols)s 6945(of)s 220 fnt35 7220 11682(@Eq)m 240 fnt82 +7761 11685(visible)m 8458(within)s 0 11397(the)m 335(body)s 855(of)s +220 fnt35 1112 11394(isum)m 240 fnt82 1561 11397(.)m 1711(This)s +2174(feature)s 2878(complicates)s 4056(the)s 4390(treatment)s 5337(of)s +5595(en)s 9(vironments)k 6925(\(Section)s 7764(3.4\),)s 8236(and)s +8626(e)s 6(v)k 3(en)k 0 11109(introduces)m 1050(an)s +1336(insecurity)s 15(,)k 2373(when)s 220 fnt35 2952 11106(isum)m +240 fnt82 3464 11109(is)m 3677(in)s 9(v)k 4(ok)k 2(ed)k +4495(outside)s 5245(an)s 5531(equation.)s 6522(A)s 6755(simpler)s +7534(approach)s 8471(w)s 2(ould)k 0 10821(be)m 290(to)s +538(allo)s 6(w)k 1126(only)s 1615(one)s 2026(symbol)s +2795(in)s 3047(an)s 220 fnt35 3339 10818(impor)m -8(t)k +240 fnt82 4020 10821(clause,)m 4733(and)s 5146(treat)s 5638(the)s +5995(follo)s 6(wing)k 6981(de\207nition)s 7964(e)s 3(xactly)k +8714(lik)s 2(e)k 0 10533(a)m 174(local)s 702(de\207nition)s +1684(of)s 1964(that)s 2390(symbol;)s 3216(b)s 4(ut)k +3587(then)s 4064(it)s 4265(w)s 2(ould)k 4928(not)s +5303(be)s 5594(possible)s 6442(to)s 6690(de\207ne)s 7339(symbols)s +8197(using)s 8778(the)s 0 10245(resources)m 953(of)s 1224(more)s +1771(than)s 2240(one)s 2642(of)s 2913(the)s 3261(standard)s +4129(packages.)s 240 fnt84 0 9596(3.4.)m 471(Implementation)s 2159(of)s +2431(de\207nitions)s 240 fnt82 480 9119(Input)m 1089(is)s 1343(processed)s +2388(by)s 2726(a)s 2936(h)s 1(ybrid)k 3663(parser)s +4350(which)s 5036(emplo)s 2(ys)k 5940(operator)s 6840(precedence)s +8015(for)s 8398(objects)s 0 8831(and)m 433(simple)s 1156(recursi)s 6(v)k 3(e)k +2108(descent)s 2915(for)s 3283(the)s 3661(headers)s 4472(of)s +4772(de\207nitions.)s 5976(A)s 6236(symbol)s 7026(table)s 7576(stores)s +8214(the)s 8592(body)s 0 8543(of)m 278(each)s 780(de\207nition)s +1761(as)s 2018(a)s 2191(parse)s 2758(tree,)s 3229(e)s 3(xcept)k +3917(for)s 4263(macros)s 5011(which)s 5660(are)s 6014(lists)s +6456(of)s 6734(tok)s 2(ens,)k 7471(and)s 7882(manages)s +8778(the)s 0 8255(usual)m 564(stack)s 1121(of)s 1397(static)s +1958(scopes,)s 2708(accepting)s 240 fnt83 3682 8257(PushScope)m 240 fnt82 +4791 8255(and)m 240 fnt83 5200 8257(P)m 19(opScope)k 240 fnt82 +6197 8255(operations)m 7249(as)s 7504(the)s 7857(parser)s 8505(enters)s +0 7967(and)m 447(lea)s 4(v)k 3(es)k 1131(scope)s +1775(re)s 3(gions,)k 2626(including)s 3627(actual)s 4295(body)s +4872(parameters)s 6013(and)s 6461(the)s 6852(right)s 7406(parameter)s +8463(of)s 8778(the)s 220 fnt35 0 7676(@Open)m 240 fnt82 +806 7679(operator)m 13(.)k 480 7305(As)m 818(the)s 1187(parse)s +1769(proceeds,)s 2747(a)s 2934(complete)s 3888(call)s 4308(graph)s +4932(is)s 5163(constructed,)s 6393(recording,)s 7438(for)s 7797(each)s +8314(symbol,)s 0 7017(which)m 633(symbols)s 1473(are)s 1810(in)s 9(v)k 4(ok)k 2(ed)k +2616(within)s 3274(its)s 3541(body)s 15(.)k 4160(Immediately)s +5412(after)s 5898(the)s 6237(last)s 6618(de\207nition)s 7583(is)s +7783(read,)s 8292(the)s 8630(tran)s 8998(-)s 0 6729(siti)m 6(v)k 3(e)k +565(closure)s 1312(of)s 1584(the)s 1933(call)s 2334(graph)s +2937(is)s 3148(computed,)s 4200(and)s 4605(used)s 5104(to)s +5344(determine)s 6356(whether)s 7187(each)s 7684(non-)s 8112(parameter)s +0 6441(symbol)m 775(is)s 1001(recursi)s 6(v)k 3(e)k +1939(or)s 2214(recepti)s 6(v)k 3(e)k 3151(\(Section)s +4020(5.1\),)s 4522(and)s 4942(whether)s 5787(each)s 6298(parameter)s +7328(is)s 7554(in)s 9(v)k 4(ok)k 2(ed)k +8385(e)s 3(xactly)k 0 6153(once)m 508(or)s 767(not.)s +480 5779(Purely)m 1188(functional)s 2243(systems)s 3082(may)s 3579(e)s 6(v)k 6(aluate)k +4450(symbol)s 5240(in)s 9(v)k 4(ocations)k 6412(in)s +6686(applicati)s 6(v)k 3(e)k 7812(order)s 8407(\(where)s +0 5491(parameters)m 1092(are)s 1433(e)s 6(v)k 6(aluated)k +2389(before)s 3049(substitution)s 4216(into)s 4635(bodies\),)s 5440(or)s +5693(in)s 5930(normal)s 6656(order)s 7214(\(substitution)s 8460(before)s +0 5203(e)m 6(v)k 6(aluation\),)k 1164(and)s 1562(the)s 3(y)k +2018(may)s 2478(also)s 2909(share)s 3463(the)s 3804(v)s 6(alue)k +4366(of)s 4630(a)s 4790(parameter)s 5798(among)s 6496(all)s +6783(uses)s 7239(of)s 7504(it.)s 7793(But)s 8193(in)s +8429(Basser)s 0 4915(Lout,)m 603(the)s 996(presence)s 1932(of)s +2248(conte)s 3(xt-sensiti)k 6(v)k 3(e)k 3955(style)s +4507(information)s 5736(\(Section)s 6634(2.5\))s 7106(forces)s 7785(normal)s +8562(order)s 0 4627(e)m 6(v)k 6(aluation)k 1041(and)s +1445(pre)s 6(v)k 3(ents)k 2297(sharing)s 3054(of)s +3325(parameter)s 4339(v)s 6(alues.)k 480 4253(T)m 19(o)k +780(e)s 6(v)k 6(aluate)k 1620(an)s 1903(unsized)s +2692(object)s 3336(\(pure)s 3896(parse)s 4456(tree\),)s 4999(its)s +240 fnt83 5275 4255(en)m 9(vir)k 10(onment)k 240 fnt82 +6456 4253(,)m 6563(the)s 6911(equi)s 6(v)k 6(alent)k +7955(of)s 8226(the)s 8574(stack)s 0 3965(frames)m 728(in)s +999(Algol-lik)s 2(e)k 2064(languages,)s 3156(must)s 3710(be)s +4020(a)s 4(v)k 6(ailable,)k 5008(containing)s 6099(the)s +6476(actual)s 7129(v)s 6(alues)k 7814(of)s 8113(all)s +8435(formal)s 0 3677(parameters)m 1119(that)s 1558(are)s 1927(visible)s +2641(within)s 3330(the)s 3700(unsized)s 4510(object.)s 5279(En)s 9(vironment)k +6601(handling)s 7513(is)s 7744(a)s 7932(well-kno)s 6(wn)k +0 3389(implementation)m 1557(technique,)s 2594(so)s 2860(it)s 3052(will)s +3478(be)s 3760(discussed)s 4735(only)s 5215(brie\210y)s 5893(here.)s +480 3015(En)m 9(vironments)k 1894(are)s 2272(e)s 3(xtra)k +2837(subtrees)s 3702(hung)s 4265(from)s 4820(the)s 5199(objects)s +5958(the)s 3(y)k 6451(refer)s 6991(to.)s 7372(This)s +7879(or)s 4(g)k 1(anization)k 0 2727(mak)m 2(es)k +668(e)s 3(xcellent)k 1595(use)s 1978(of)s 2257(the)s +2613(ordered)s 3409(dag)s 3816(to)s 4063(permit)s 4754(en)s 9(vironments)k +6106(to)s 6353(be)s 6643(shared,)s 7382(and)s 7794(deleted)s +8550(when)s 0 2439(the)m 339(last)s 721(reference)s 1655(to)s +1885(them)s 2413(is)s 2614(remo)s 3(v)k 3(ed.)k +3600(Se)s 6(v)k 3(eral)k 4353(optimizations)s 5695(ha)s 4(v)k 3(e)k +6187(been)s 6687(implemented.)s 8090(Actual)s 8772(pa)s 8998(-)s +0 2151(rameters)m 860(kno)s 6(wn)k 1552(to)s 1778(be)s +2048(in)s 9(v)k 4(ok)k 2(ed)k 2850(only)s +3318(once)s 3814(are)s 4148(mo)s 3(v)k 3(ed)k +4840(in)s 5070(from)s 5582(the)s 5918(en)s 9(vironment,)k +7212(not)s 7566(copied;)s 8303(cop)s 2(ying)k 0 1863(could)m +581(lead)s 1028(to)s 1258(quadratic)s 2191(time)s 2662(comple)s 3(xity)k 15(.)k +3875(Actual)s 4558(parameters)s 5647(of)s 5909(the)s 6248(form)s +220 fnt35 6763 1860(@Ne)m 6(xt)k 240 fnt83 7478 1865(object)m +240 fnt82 8117 1863(recei)m 6(v)k 3(e)k 8843(an)s +0 1575(applicati)m 6(v)k 3(e)k 1105(pre-)s 1478(e)s 6(v)k 6(aluation)k +2529(which)s 3181(pre)s 6(v)k 3(ents)k 4044(long)s +4533(chains)s 5205(of)s 220 fnt35 5486 1572(@Ne)m 6(xt)k +240 fnt82 6221 1575(symbols)m 7080(from)s 7614(forming)s 8448(during)s +0 1287(the)m 359(generation)s 1437(of)s 1719(lar)s 4(ge)k +2260(page)s 2779(numbers.)s 3779(Some)s 4391(en)s 9(vironments)k +5747(which)s 6400(pro)s 3(v)k 6(ably)k 7308(contrib)s 4(ute)k +8341(nothing)s 0 999(are)m 344(deleted,)s 1137(most)s 1659(notably)s +2427(when)s 3000(a)s 3162(symbol)s 3918(in)s 9(v)k 4(ocation)k +4969(has)s 5335(no)s 5625(symbols)s 6470(within)s 7135(its)s +7407(actual)s 8028(parameters)s 0 711(and)m 406(no)s 702(import)s +1402(list,)s 1803(so)s 2071(that)s 2492(only)s 2975(the)s +3326(en)s 9(vironment)k 4589(of)s 4862(its)s 5141(body)s +5678(need)s 6191(be)s 6476(k)s 2(ept;)k 7000(this)s +7399(sa)s 4(v)k 3(es)k 7964(a)s 8133(great)s +8673(deal)s 0 423(of)m 271(space)s 858(when)s 1434(objects)s +2162(with)s 2644(en)s 9(vironments)k 3988(are)s 4335(written)s +5068(to)s 5307(auxiliary)s 6210(\207les)s 6659(\(Section)s 7512(6.1\).)s + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 22 23 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(22)s 4710(-)s 240 fnt84 0 12678(4.)m +291(Implementation)s 1979(of)s 2251(the)s 2625(functional)s 3715(subset)s +240 fnt82 480 12201(The)m 941(objects)s 1702(and)s 2139(de\207nitions)s +3233(of)s 3537(Lout)s 4082(are)s 4462(v)s 3(ery)k +4971(similar)s 5726(to)s 5998(those)s 6592(found)s 7242(in)s +7518(other)s 8102(functional)s 0 11913(languages,)m 1085(and)s 1510(the)s 3(y)k +1994(form)s 2539(a)s 2726(natural)s 3465(subset)s 4144(of)s +4436(the)s 4805(language.)s 5854(So)s 6181(we)s 6537(pause)s +7159(here)s 7647(and)s 8072(present)s 8843(an)s 0 11625(o)m 3(v)k 3(ervie)k 6(w)k +932(of)s 1203(the)s 1551(Basser)s 2248(Lout)s 2760(object)s +3404(e)s 6(v)k 6(aluation)k 4445(algorithm.)s 480 11251(The)m +922(problem)s 1794(is)s 2019(to)s 2272(tak)s 2(e)k +2739(an)s 3037(unsized)s 3841(object)s 4499(\(pure)s 5074(parse)s +5649(tree\),)s 6206(its)s 6497(en)s 9(vironment)k 7772(\(Section)s +8640(3.4\),)s 0 10963(and)m 404(its)s 681(style)s 1188(\(Section)s +2042(2.5\),)s 2528(and)s 2933(to)s 3173(produce)s 4000(a)s +4167(PostScript)s 5209(\207le)s 5571(for)s 5910(rendering)s 6879(the)s +7228(object)s 7872(on)s 8170(an)s 8454(output)s 0 10675(de)m 6(vice.)k +786(This)s 1267(\207le)s 1632(is)s 1847(essentially)s 2914(a)s +3084(sequence)s 4022(of)s 4298(instructions)s 5468(to)s 5712(print)s +6227(a)s 6398(gi)s 6(v)k 3(en)k 6983(string)s +7584(of)s 7860(characters)s 8883(in)s 0 10387(a)m 166(gi)s 6(v)k 3(en)k +746(font)s 1191(at)s 1423(a)s 1589(gi)s 6(v)k 3(en)k +2169(point.)s 480 10013(Before)m 1189(the)s 1541(algorithm)s 2534(be)s 3(gins,)k +3266(the)s 3618(parse)s 4182(tree)s 4599(must)s 5127(be)s +5413(obtained,)s 6348(either)s 6955(by)s 7252(parsing)s 8013(input)s +8569(or)s 8832(by)s 0 9725(cop)m 2(ying)k 823(from)s +1347(the)s 1695(symbol)s 2455(table.)s 3082(Afterw)s 2(ards)k +4205(the)s 4553(data)s 5011(structure)s 5901(must)s 6426(be)s +6708(disposed.)s 7710(The)s 8137(algorithm)s 0 9437(proper)m 692(consists)s +1508(of)s 1787(\207v)s 3(e)k 2207(passes,)s 2933(each)s +3437(a)s 3611(recursi)s 6(v)k 3(e)k 4541(tra)s 4(v)k 3(ersal)k +5418(of)s 5697(the)s 6054(structure)s 6953(from)s 7485(the)s +7841(root)s 8294(do)s 6(wn)k 8887(to)s 0 9149(the)m +348(lea)s 4(v)k 3(es)k 989(and)s 1393(back.)s +240 fnt83 0 8695(1.)m 330(Evaluation)s 1490(of)s 1827(unsized)s +2667(objects.)s 240 fnt82 3554 8693(On)m 3960(the)s 4364(w)s 2(ay)k +4871(do)s 6(wn,)k 5561(calculate)s 6521(en)s 9(vironments)k +7921(and)s 8381(replace)s 0 8405(non-recursi)m 6(v)k 3(e,)k +1404(non-recepti)s 6(v)k 3(e)k 2757(symbols)s 3598(by)s +3884(their)s 4373(bodies)s 5041(\(Section)s 5886(3.4\);)s 6369(broadcast)s +7337(fonts)s 7858(to)s 8089(the)s 8429(lea)s 4(v)k 3(es,)k +0 8117(and)m 409(paragraph)s 1427(breaking)s 2322(and)s 2731(spacing)s +3521(styles)s 4121(to)s 4365(the)s 4718(paragraph)s 5736(nodes.)s +6465(On)s 6820(the)s 7173(w)s 2(ay)k 7629(back)s +8147(up,)s 8500(delete)s 240 fnt83 0 7831(FONT)m 240 fnt82 +630 7829(,)m 240 fnt83 737 7831(BREAK)m 240 fnt82 1494 7829(,)m +1601(and)s 240 fnt83 2005 7831(SP)m 21(A)k 7(CE)k +240 fnt82 2760 7829(nodes,)m 3426(and)s 3830(insert)s 240 fnt83 +4420 7831(SPLIT)m 240 fnt82 5049 7829(,)m 240 fnt83 5156 7831(COL)m +240 fnt82 5622 7829(,)m 5729(and)s 240 fnt83 6133 7831(R)m 9(O)k 12(W)k +240 fnt82 6707 7829(nodes)m 7317(\(Section)s 8170(2.3\).)s 240 fnt83 +0 7336(2.)m 293(W)s 13(idth)k 925(calculations)s 2169(and)s +2614(br)s 8(eaking)k 3(.)k 240 fnt82 3628 7334(Calculate)m +4605(the)s 4973(width)s 5594(of)s 5885(e)s 6(v)k 3(ery)k +6480(subobject)s 7477(from)s 8020(the)s 8388(bottom)s 0 7046(up.)m +404(As)s 720(described)s 1693(in)s 1936(Section)s 2709(2.3,)s +240 fnt83 3115 7048(WIDE)m 240 fnt82 3777 7046(nodes)m 4386(may)s +4851(trigger)s 5547(object)s 6190(breaking)s 7079(sub-tra)s 4(v)k 3(ersals)k +8448(during)s 0 6758(this)m 396(pass.)s 240 fnt83 0 6255(3.)m +274(Height)s 989(calculations.)s 240 fnt82 2312 6253(Calculate)m 3270(the)s +3618(height)s 4276(of)s 4547(e)s 6(v)k 3(ery)k +5123(subobject,)s 6147(from)s 6671(the)s 7019(bottom)s 7757(up.)s +240 fnt83 0 5750(4.)m 283(Horizontal)s 1389(coor)s 8(dinates.)k +240 fnt82 2674 5748(Calculate)m 3641(the)s 3998(horizontal)s 5032(coordinate)s +6106(of)s 6386(each)s 6890(subobject)s 7876(from)s 8409(the)s +8767(top)s 0 5460(do)m 6(wn,)k 634(and)s 1038(store)s +1558(each)s 2053(leaf)s -13(')k 13(s)k 2633(coordinate)s +3698(in)s 3941(the)s 4289(leaf.)s 240 fnt83 0 4976(5.)m +295(V)s 26(ertical)k 1119(coor)s 8(dinates)k 2317(and)s +2765(P)s 19(ostScript)k 3827(g)s 2(ener)k 3(ation.)k +240 fnt82 5034 4974(Calculate)m 6013(the)s 6383(v)s 3(ertical)k +7171(coordinate)s 8257(of)s 8550(e)s 6(v)k 3(ery)k +0 4686(subobject)m 981(from)s 1509(the)s 1861(top)s 2224(do)s 6(wn,)k +2862(and)s 3270(at)s 3506(each)s 4005(leaf,)s 4473(retrie)s 6(v)k 3(e)k +5252(the)s 5604(character)s 6542(string,)s 7197(font,)s 7693(and)s +8102(horizontal)s 0 4398(coordinate,)m 1116(and)s 1520(print)s 2031(the)s +2379(PostScript)s 3421(instruction)s 4500(for)s 4838(rendering)s 5807(that)s +6225(leaf.)s 0 3895(Figure)m 692(3)s 869(gi)s 6(v)k 3(es)k +1428(the)s 1789(amount)s 2579(of)s 2863(code)s 3383(required)s +4250(for)s 4600(each)s 5168(pass.)s 5756(Symmetry)s 6819(between)s +7685(horizontal)s 8722(and)s 0 3607(v)m 3(ertical)k 764(is)s +971(e)s 3(xploited)k 1913(throughout)s 3021(Basser)s 3715(Lout,)s +4271(and)s 4672(passes)s 5331(2)s 5502(and)s 5903(3,)s +6127(as)s 6374(well)s 6837(as)s 7084(4)s 7255(and)s +7656(5,)s 7880(are)s 8224(e)s 3(x)k 3(ecuted)k +0 3319(on)m 297(shared)s 979(code.)s 480 2945(The)m 929(author)s +1621(can)s 2031(see)s 2413(no)s 2728(simple)s 3442(w)s 2(ay)k +3914(to)s 4174(reduce)s 4888(the)s 5258(number)s 6070(of)s +6362(passes.)s 7158(The)s 7607(introduction)s 8855(of)s 0 2657(horizontal)m +1027(g)s 1(alle)k 3(ys)k 1755(\(Section)s 2612(5.5\))s +3044(w)s 2(ould)k 3703(remo)s 3(v)k 3(e)k +4474(the)s 4826(need)s 5340(for)s 5682(the)s 6034(object)s +6682(breaking)s 7576(transformations)s 0 2369(within)m 700(this)s 1128(algorithm)s +2149(that)s 2599(are)s 2978(the)s 3359(principal)s 4295(obstacles)s +5254(in)s 5529(the)s 5909(w)s 2(ay)k 6393(of)s +6696(the)s 7076(mer)s 4(ging)k 7954(of)s 8257(passes)s +8952(2)s 0 2081(and)m 404(3.)s 240 fnt84 0 1337(5.)m +291(Galleys)s 240 fnt82 480 860(W)m 9(ith)k 1022(objects)s +1767(and)s 2188(de\207nitions)s 3266(under)s 3888(control,)s 4689(the)s +5053(author)s 5741(f)s 2(aced)k 6331(the)s 6696(problem)s +7570(of)s 7858(getting)s 8592(body)s 0 572(te)m 3(xt,)k +478(footnotes,)s 1491(\210oating)s 2291(\207gures)s 3009(and)s 3429(tables,)s +4109(references,)s 5213(inde)s 3(x)k 5813(entries,)s 6572(and)s +6992(entries)s 7695(in)s 7954(the)s 8318(table)s 8855(of)s +0 284(contents)m 844(into)s 1264(their)s 1757(places.)s 2513(The)s +2937(resulting)s 3821(in)s 9(v)k 3(estig)k 1(ation)k +5095(occupied)s 6013(three)s 6541(months)s 7293(of)s 7559(full-time)s +8444(design)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 23 24 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Times-Bold +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4293 13844(-)m 4421(23)s 4705(-)s 1659 13218(1.)m 2163(Initialization)s +7172(200)s 1659 12930(2.)m 2163(Memory)s 3041(allocation,)s 4090(ordered)s +4878(dag)s 5277(operations)s 7172(400)s 1659 12642(3.)m 2163(Le)s 3(xical)k +2931(analysis,)s 3808(macros,)s 4605(\207le)s 4966(handling)s 6992(1,350)s +1659 12354(4.)m 2163(P)s 3(arsing)k 2930(of)s 3201(objects)s +3929(and)s 4333(de\207nitions)s 6992(1,150)s 1659 12066(5.)m 2163(Symbol)s +2963(table)s 3483(and)s 3887(call)s 4286(graph)s 7172(600)s +1659 11778(6.)m 2163(Ev)s 6(aluation)k 3250(of)s 3521(pure)s +4002(parse)s 4562(trees)s 6992(1,650)s 1659 11490(7.)m 2163(Reading,)s +3068(storing,)s 3839(and)s 4243(scaling)s 4973(of)s 5244(fonts)s +7172(600)s 1659 11202(8.)m 2163(Cross)s 2759(references)s 3790(and)s +4194(databases)s 6992(1,000)s 1659 10914(9.)m 2163(W)s 9(idth)k +2809(and)s 3213(height)s 3871(calculations,)s 5119(and)s 5523(breaking)s +7172(700)s 1539 10626(10.)m 240 fnt83 2163 10628(Constr)m 3(ained)k +240 fnt82 3410 10626(and)m 240 fnt83 3814 10628(AdjustSize)m 240 fnt82 +7172 10626(700)m 1539 10338(11.)m 2163(T)s 8(ransfer)k 3023(of)s +3294(sized)s 3843(objects)s 4571(into)s 4996(g)s 1(alle)k 3(y)k +5630(tree)s 7172(450)s 1539 10050(12.)m 2163(Galle)s 3(y)k +2851(\210ushing)s 3676(algorithm)s 6992(1,500)s 1539 9762(13.)m 2163(Coordinate)s +3282(calculations)s 4474(and)s 4878(PostScript)s 5920(output)s 7172(700)s +1539 9474(14.)m 2163(Deb)s 4(ugging)k 3277(and)s 3681(error)s +4204(handling)s 6992(1,200)s 655 0 0 0 240 288 60 6872 9328 LoutGr2 +0.5 pt ltabhs +grestore + +grestore +6872 9074(12,200)m 240 fnt84 0 8394(Figur)m 4(e)k +761(3.)s 1084(Major)s 1825(components)s 3134(of)s 3438(the)s +3844(Basser)s 4612(Lout)s 5197(inter)s 2(pr)k 4(eter)k 22(,)k +6441(sho)s 2(wing)k 7365(the)s 7772(appr)s 4(oximate)k +0 8106(number)m 868(of)s 1140(lines)s 1658(of)s 1930(C)s +2155(code.)s 240 fnt82 0 7512(w)m 2(ork,)k 612(and)s +1031(proceeded)s 2088(approximately)s 3538(as)s 3803(described)s 4793(in)s +5051(Section)s 5840(5.1;)s 6268(the)s 6631(implementation)s 8204(occupied)s +0 7224(the)m 348(years)s 903(1987-89.)s 240 fnt84 0 6575(5.1.)m +471(The)s 926(galley)s 1580(abstraction)s 240 fnt82 480 6098(Let)m +870(us)s 1147(tak)s 2(e)k 1611(the)s 1972(footnote)s +2838(as)s 3100(a)s 3279(representati)s 6(v)k 3(e)k +4677(e)s 3(xample.)k 5661(At)s 5973(some)s 6546(point)s +7111(in)s 7366(the)s 7727(document,)s 8791(we)s 0 5810(wish)m +509(to)s 748(write)s 220 fnt35 480 5362(preceding te)m 6(xt)k +480 5074(@F)m 6(ootNote { f)k 6(ootnote te)k 6(xt })k 480 4786(f)m 6(ollo)k 3(wing te)k 6(xt)k +240 fnt82 0 4287(and)m 406(we)s 744(e)s 3(xpect)k +1428(the)s 1779(formatter)s 2729(to)s 2971(remo)s 3(v)k 3(e)k +3741(the)s 4092(footnote)s 4947(from)s 5474(this)s 5873(conte)s 3(xt)k +6637(and)s 7044(place)s 7607(it)s 7802(at)s 8037(the)s +8388(bottom)s 0 3999(of)m 281(the)s 639(current)s 1386(page,)s +1955(possibly)s 2817(splitting)s 3664(some)s 4235(or)s 4504(all)s +4808(of)s 5089(it)s 5291(onto)s 5781(a)s 5957(follo)s 6(wing)k +6944(page)s 7463(if)s 7690(space)s 8287(is)s 8508(insuf)s +8998(-)s 0 3711(\207cient.)m 480 3337(An)m 844(object)s 1503(appears)s +2298(in)s 2556(the)s 2918(\207nal)s 3413(document)s 4431(at)s +4678(the)s 5040(point)s 5607(it)s 5813(is)s 6038(in)s 9(v)k 4(ok)k 2(ed,)k +6916(b)s 4(ut)k 7293(this)s 7703(basic)s 8262(property)s +0 3049(does)m 503(not)s 882(hold)s 1379(for)s 1730(footnotes:)s +2799(the)s 3160(point)s 3725(of)s 4009(in)s 9(v)k 4(ocation)k +5076(and)s 5493(the)s 5854(point)s 6419(of)s 6703(appearance)s +7847(are)s 8207(dif)s 6(ferent.)k 0 2761(In)m 254(some)s +813(w)s 2(ay)k 15(,)k 1299(the)s 1645(footnote)s +2496(is)s 2703(attached)s 3555(to)s 3791(the)s 4137(document)s +5139(at)s 5368(both)s 5849(points,)s 6539(introducing)s 7692(a)s +7856(cross)s 8395(linking)s 0 2473(\(Section)m 853(2.1\))s 1281(that)s +1699(cannot)s 2397(be)s 2679(described)s 3653(in)s 3896(purely)s +4561(functional)s 5585(terms.)s 480 2099(Since)m 1069(the)s 1420(interpretation)s +2766(of)s 3040(an)s 3(y)k 3440(object)s 4087(depends)s +4926(on)s 5226(an)s 5512(en)s 9(vironment)k 6775(and)s +7182(style)s 7692(inherited)s 8602(from)s 0 1811(the)m 347(conte)s 3(xt,)k +1153(the)s 1499(\207rst)s 1929(question)s 2795(must)s 3318(be)s +3598(whether)s 4427(the)s 4773(footnote)s 5624(inherits)s 6390(them)s +6926(through)s 7726(the)s 8072(in)s 9(v)k 4(ocation)k +0 1523(point)m 552(or)s 811(through)s 1613(the)s 1961(point\(s\))s +2753(of)s 3024(appearance.)s 480 1149(If)m 697(symbols)s 1533(are)s +1867(to)s 2092(be)s 2361(interpreted)s 3440(statically)s 4341(as)s +4578(heretofore,)s 5653(then)s 6108(en)s 9(vironments)k 7439(must)s +7951(be)s 8219(inherited)s 0 861(through)m 829(the)s 1204(in)s 9(v)k 4(ocation)k +2285(point)s 2865(alone.)s 3574(Dynamic)s 4531(inheritance)s 5675(through)s +6505(the)s 6880(point)s 7459(of)s 7757(appearance)s 8916(is)s +0 573(enticing)m 836(in)s 1092(some)s 1666(w)s 2(ays:)k +2335(it)s 2541(might)s 3172(replace)s 3930(the)s 4291(body)s +4838(parameter)s 9(,)k 5904(and)s 6321(it)s 6526(might)s +7157(help)s 7635(with)s 8131(automatic)s 0 285(numbering,)m 1163(since)s +1730(the)s 2097(number)s 2908(of)s 3198(a)s 3384(footnote)s +4256(is)s 4486(kno)s 6(wn)k 5209(only)s 5709(at)s +5960(the)s 6328(point)s 6899(of)s 7190(appearance;)s 8396(b)s 4(ut)k +8778(the)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 24 25 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(24)s 4710(-)s 0 13256(implementation)m 1606(problems)s +2597(are)s 2993(se)s 6(v)k 3(ere,)k 3751(and)s +4204(static)s 4810(inheritance)s 5976(seems)s 6661(much)s 7299(simpler)s +8125(and)s 8579(more)s 0 12968(comprehensible)m 1572(to)s 1814(the)s +2165(user)s 13(.)k 2716(Style,)s 3317(at)s 3552(least)s +4052(its)s 4330(a)s 4(v)k 6(ailable)k 5241(width)s +5846(and)s 6253(height)s 6913(part,)s 7394(must)s 7922(of)s +8196(necessity)s 0 12680(be)m 268(inherited)s 1160(through)s 1947(the)s +2280(point)s 2817(of)s 3073(appearance.)s 4297(F)s 3(or)k +4671(consistenc)s 3(y)k 15(,)k 5861(the)s 6194(entire)s +6778(style)s 7270(should)s 7952(be)s 8219(inherited)s 0 12392(in)m +256(this)s 666(w)s 2(ay)k 15(.)k 1226(There)s +1853(is)s 2077(a)s 2257(suggesti)s 6(v)k 3(e)k +3328(analogy)s 4154(here)s 4635(with)s 5131(actual)s 5770(parameters,)s +6938(which)s 7594(ha)s 4(v)k 3(e)k 8109(a)s +8289(point)s 8855(of)s 0 12104(in)m 9(v)k 4(ocation)k +1060(from)s 1591(which)s 2240(the)s 3(y)k 2710(inherit)s +3400(an)s 3690(en)s 9(vironment,)k 5004(and)s 5414(a)s +5587(point)s 6146(of)s 6424(appearance)s 7562(within)s 8237(the)s +8592(body)s 0 11816(of)m 265(the)s 606(enclosing)s 1569(de\207nition,)s +2587(from)s 3104(which)s 3739(the)s 3(y)k 4196(inherit)s +4872(a)s 5031(style.)s 5639(It)s 5838(may)s 6297(be)s +6572(possible)s 7406(to)s 7638(treat)s 8114(a)s 8273(footnote)s +0 11528(as)m 250(the)s 598(actual)s 1223(parameter)s 2237(of)s +2508(some)s 3069(symbol,)s 3881(therefore,)s 4849(although)s 5744(the)s +6092(details)s 6766(seem)s 7317(v)s 3(ery)k 7793(obscure.)s +480 11154(But)m 881(the)s 1224(most)s 1744(profound)s 2674(consequence)s +3948(of)s 4214(ha)s 4(ving)k 4910(tw)s 2(o)k +5314(types)s 5865(of)s 6131(attachment)s 7234(point)s 7780(is)s +7985(that)s 8398(it)s 8584(leads)s 0 10866(to)m 261(tw)s 2(o)k +693(distincti)s 6(v)k 3(e)k 1757(tree)s 2192(structures.)s +3306(Considering)s 4551(in)s 9(v)k 4(ocation)k 5627(points)s +6285(only)s 6787(leads)s 7351(to)s 7612(static)s 8190(trees)s +8714(lik)s 2(e)k 0 10578(this)m 396(one:)s gsave +480 8292 translate +240 fnt83 3666 1996 170 1715 240 288 60 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +1117 1273 170 993 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 1273 170 993 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 551 170 272 240 288 60 0 721 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(footnote)m + +grestore +(T) lfigpromotelabels +grestore +(L) lfigpromotelabels +grestore +1206 553 170 272 240 288 60 1230 1443 LoutGr2 +currentdict end 200 dict begin begin +grestore +1206 553 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(body)m 692(te)s 4(xt)k +grestore +(T) lfigpromotelabels +grestore +0 0 0 0 240 288 60 2436 1715 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1117 1273 0 993 240 288 60 2549 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1001 552 170 272 240 288 60 116 721 LoutGr2 +currentdict end 200 dict begin begin +grestore +884 552 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(\207gur)m 8(e)k + +grestore +(T) lfigpromotelabels +grestore +1117 551 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 551 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 551 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(footnote)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 60 1117 272 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +(R) lfigpromotelabels +grestore +0 0 0 0 240 288 60 3666 1715 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 7841(which)m 663(sho)s 6(ws)k 1329(that)s +1769(the)s 2139(body)s 2695(te)s 3(xt)k 3131(contains)s +4001(a)s 4189(footnote)s 5064(and)s 5490(a)s 5677(\207gure,)s +6364(the)s 6734(latter)s 7305(itself)s 7875(containing)s 8960(a)s +0 7553(footnote.)m 961(Considering)s 2184(points)s 2820(of)s 3091(appearance)s +4222(only)s 4702(gi)s 6(v)k 3(es)k 5249(a)s +5415(completely)s 6531(dif)s 6(ferent,)k 7453(dynamic)s 8330(tree:)s +gsave +480 5939 translate +240 fnt83 4663 1274 0 995 240 288 60 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +3382 551 170 272 240 288 60 1281 723 LoutGr2 +currentdict end 200 dict begin begin +grestore +2101 551 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(sequence)m 1100(of)s 1381(pa)s 2(g)k 2(es)k + +grestore +(T) lfigpromotelabels +grestore +1206 553 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1206 553 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1206 553 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(body)m 692(te)s 4(xt)k +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 60 1206 272 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1117 553 170 272 240 288 60 1319 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 553 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 551 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(footnote)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 60 2436 272 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +884 553 170 272 240 288 60 2549 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +884 553 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +884 552 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(\207gur)m 8(e)k + +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 60 3433 272 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +1117 553 170 272 240 288 60 3546 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 553 170 272 240 288 60 0 0 LoutGr2 +currentdict end 200 dict begin begin +grestore +1117 551 170 272 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +170 220(footnote)m +grestore +(T) lfigpromotelabels +grestore +(S) lfigpromotelabels +grestore +0 0 0 0 240 288 60 4663 272 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore + +grestore +end end restore +grestore +0 5488(The)m 468(tree)s 921(can)s 1351(be)s +1673(deeper)s 9(,)k 2448(for)s 2827(e)s 3(xample)k +3730(with)s 4253(sections)s 5114(appearing)s 6150(within)s 6859(chapters)s +7746(which)s 8429(appear)s 0 5200(within)m 680(the)s 1041(body)s +1587(te)s 3(xt,)k 2062(which)s 2717(appears)s 3510(within)s +4191(the)s 4551(\207nal)s 5044(sequence)s 5990(of)s 6273(pages.)s +6995(Document)s 8065(formatting)s 0 4912(languages)m 1024(generally)s 1984(shirk)s +2540(the)s 2905(issues)s 3544(raised)s 4189(by)s 4500(this)s +4912(dual)s 5396(tree)s 5826(structure,)s 6785(by)s 7096(making)s +7884(the)s 8249(dynamic)s 0 4624(tree)m 421(b)s 4(uilt-in,)k +1235(by)s 1537(limiting)s 2354(one)s 2764(or)s 3032(both)s +3523(trees)s 4032(to)s 4279(tw)s 2(o)k 4697(le)s 6(v)k 3(els,)k +5360(and)s 5773(so)s 6047(on,)s 6402(pro)s 3(viding)k +7391(a)s 7565(classic)s 8263(e)s 3(xample)k 0 4336(of)m +295(the)s 667(impo)s 3(v)k 3(erishing)k 2120(ef)s 6(fect)k +2740(of)s 3035(f)s 2(ailing)k 3733(to)s 3997(permit)s +4704(language)s 5648(features)s 6478(to)s 6741(attain)s 7352(their)s +7873(natural)s 8616(le)s 6(v)k 3(el)k 0 4048(of)m +271(generality)s 15(.)k 480 3674(W)m 19(e)k 854(are)s +1206(thus)s 1662(led)s 2017(to)s 2261(propose)s 3081(a)s +3252(second)s 3980(abstraction)s 5091(for)s 5434(document)s 6443(formatting,)s +7564(which)s 8211(we)s 8552(name)s 0 3386(the)m 240 fnt83 +371 3388(galle)m 7(y)k 240 fnt82 1028 3386(in)m 1294(recognition)s +2464(of)s 2759(its)s 3058(similarity)s 4050(to)s 4312(the)s +4684(g)s 1(alle)k 3(ys)k 5432(used)s 5952(in)s +6219(manual)s 7001(typesetting.)s 8238(A)s 8492(g)s 1(alle)k 3(y)k +0 3098(consists)m 817(of)s 1098(an)s 1391(object)s 2045(\(such)s +2630(as)s 2890(a)s 3066(footnote\))s 4001(together)s 4854(with)s +5346(a)s 5522(sequence)s 6465(of)s 6746(places)s 7404(where)s +8054(that)s 8482(object)s 0 2810(may)m 491(appear)s 1214(\(such)s +1814(as)s 2090(the)s 2464(bottoms)s 3311(of)s 3608(the)s +3982(current)s 4743(and)s 5173(follo)s 6(wing)k 6176(pages\).)s +6989(Splitting)s 7891(occurs)s 8592(quite)s 0 2522(naturally)m 903(when)s +1479(space)s 2066(at)s 2298(an)s 3(y)k 2695(place)s +3255(is)s 3465(insuf\207cient)s 4600(to)s 4839(hold)s 5323(the)s +5671(entire)s 6270(object.)s 480 2148(In)m 736(Lout,)s 1295(a)s +1461(footnote)s 2314(g)s 1(alle)k 3(y)k 2948(and)s +3352(its)s 3628(place)s 4188(of)s 4459(appearance)s 5590(are)s +5937(de\207ned)s 6700(as)s 6950(follo)s 6(ws:)k 220 fnt35 +480 1647(def @F)m 6(ootPlace { @Galle)k 4(y })k 480 1071(def @F)m 6(ootNote into { @F)k 6(ootPlace&&f)k 6(ollo)k 3(wing })k +480 783( r)m -3(ight x)k 480 495({ x })m +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 25 26 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4292 13841(-)m 4420(25)s 4706(-)s 0 13250(The)m 220 fnt35 +445 13247(@F)m 6(ootPlace)k 240 fnt82 1719 13250(symbol)m 2496(contains)s +3362(the)s 3727(special)s 4463(symbol)s 220 fnt35 5240 13247(@Galle)m 4(y)k +240 fnt82 6078 13250(,)m 6203(indicating)s 7229(that)s 7665(it)s +7874(is)s 8102(a)s 8285(point)s 8855(of)s 0 12962(appearance)m +1143(for)s 1493(a)s 1672(g)s 1(alle)k 3(y)k 15(.)k +2413(By)s 2759(placing)s 3529(in)s 9(v)k 4(ocations)k +4682(of)s 220 fnt35 4965 12959(@F)m 6(ootPlace)k 240 fnt82 +6234 12962(at)m 6478(the)s 6838(bottoms)s 7673(of)s 7956(pages,)s +8620(as)s 8883(in)s 0 12674(Section)m 801(3.2,)s 1235(we)s +1597(de\207ne)s 2265(the)s 2640(desired)s 3415(points)s 4078(of)s +4376(appearance)s 5534(for)s 5899(footnotes.)s 6980(Symbols)s 7896(whose)s +8592(body)s 0 12386(contains)m 220 fnt35 863 12383(@Galle)m 4(y)k +240 fnt82 1776 12386(either)m 2394(directly)s 3192(or)s 3466(indirectly)s +4450(are)s 4812(called)s 5455(recepti)s 6(v)k 3(e)k +6392(symbols,)s 7312(meaning)s 8204(recepti)s 6(v)k 3(e)k +0 12098(to)m 239(g)s 1(alle)k 3(ys,)k 1019(and)s +1423(the)s 3(y)k 1886(are)s 2233(e)s 3(xpanded)k +3207(only)s 3687(on)s 3984(demand.)s 4906(The)s 5334(ef)s 6(fect)k +5930(of)s 6202(the)s 220 fnt35 6550 12095(into)m 240 fnt82 +6956 12098(clause)m 7609(is)s 7819(to)s 8058(mak)s 2(e)k +8631(each)s 0 11810(in)m 9(v)k 4(ocation)k 1057(of)s +220 fnt35 1332 11807(@F)m 6(ootNote)k 240 fnt82 2506 11810(a)m +2676(g)s 1(alle)k 3(y)k 3313(whose)s 3985(object)s +4632(is)s 4846(the)s 5198(result)s 5791(of)s 6066(the)s +6417(in)s 9(v)k 4(ocation)k 7475(in)s 7721(the)s +8073(usual)s 8637(w)s 2(ay)k 15(,)k 0 11522(and)m +406(whose)s 1076(sequence)s 2011(of)s 2285(points)s 2923(of)s +3196(appearance)s 4329(is)s 4542(speci\207ed)s 5452(by)s 5748(the)s +220 fnt35 6098 11519(into)m 240 fnt82 6507 11522(clause;)m 7218(in)s +7463(this)s 7861(e)s 3(xample,)k 8778(the)s 0 11234(sequence)m +933(of)s 1204(all)s 220 fnt35 1497 11231(@F)m 6(ootPlace)k +240 fnt82 2753 11234(symbols)m 3602(follo)s 6(wing)k 4579(the)s +4927(in)s 9(v)k 4(ocation)k 5981(point.)s 480 10860(Lout)m +995(permits)s 1766(g)s 1(alle)k 3(ys)k 2494(to)s +2737(be)s 3023(in)s 9(v)k 4(ok)k 2(ed)k +3842(within)s 4514(other)s 5069(g)s 1(alle)k 3(ys)k +5797(to)s 6040(arbitrary)s 6919(depth,)s 7562(so)s 7832(that)s +8254(one)s 8660(may)s 0 10572(ha)m 4(v)k 3(e)k +514(footnotes)s 1468(within)s 2149(\207gures)s 2864(within)s 3546(the)s +3907(body)s 4454(te)s 3(xt)k 4882(g)s 1(alle)k 3(y)k 15(,)k +5568(for)s 5919(e)s 3(xample,)k 6846(creating)s 7681(arbitrary)s +8570(static)s 0 10284(trees.)m 649(Recepti)s 6(v)k 3(e)k +1688(symbols)s 2573(lik)s 2(e)k 220 fnt35 3021 10281(@F)m 6(ootPlace)k +240 fnt82 4313 10284(may)m 4815(appear)s 5548(within)s 6252(an)s 3(y)k +6685(g)s 1(alle)k 3(y)k 15(,)k 7393(creating)s +8251(arbitrary)s 0 9996(dynamic)m 912(trees)s 1449(as)s 1734(well.)s +2345(The)s 2808(root)s 3289(of)s 3595(the)s 3979(dynamic)s +4891(tree,)s 5391(which)s 6068(w)s 2(ould)k 6759(normally)s +7711(consist)s 8471(of)s 8778(the)s 0 9708(sequence)m 959(of)s +1257(pages)s 1880(of)s 2178(the)s 2553(complete)s 3512(assembled)s +4593(document,)s 5671(is)s 5908(considered)s 7029(to)s 7295(be)s +7604(a)s 7797(g)s 1(alle)k 3(y)k 8458(whose)s +0 9420(point)m 563(of)s 845(appearance)s 1987(is)s 2208(the)s +2567(output)s 3250(\207le.)s 3730(Points)s 4390(of)s 4672(appearance)s +5814(may)s 6291(be)s 220 fnt35 6584 9417(preceding)m 240 fnt82 +7606 9420(or)m 220 fnt35 7876 9417(f)m 6(ollo)k 3(wing)k +240 fnt82 8778 9420(the)m 0 9132(in)m 9(v)k 4(ocation)k +1054(point;)s 1658(entries)s 2345(in)s 2588(tables)s 3196(of)s +3467(contents)s 4315(are)s 4662(the)s 5010(main)s 5545(users)s +6087(of)s 220 fnt35 6358 9129(preceding)m 240 fnt82 7309 9132(.)m +480 8758(The)m 913(g)s 1(alle)k 3(y)k 1552(abstraction)s +2662(is)s 2877(adequate)s 3788(for)s 4131(all)s 4429(of)s +4706(the)s 5059(applications)s 6270(listed)s 6850(at)s 7087(the)s +7440(be)s 3(ginning)k 8453(of)s 8730(this)s 0 8470(section,)m +808(e)s 3(xcept)k 1514(that)s 1957(there)s 2515(is)s +2749(no)s 3067(pro)s 3(vision)k 4050(for)s 4413(sorting)s +5155(inde)s 3(x)k 5763(entries)s 6475(and)s 6904(references.)s +8073(Sorting)s 8855(of)s 0 8182(g)m 1(alle)k 3(ys)k +715(has)s 1075(been)s 1574(added)s 2194(to)s 2423(Lout)s +2925(as)s 3165(a)s 3321(b)s 4(uilt-in)k 4068(feature,)s +4827(in)s 9(v)k 4(ok)k 2(ed)k 5632(by)s +5916(adding)s 6611(a)s 6767(special)s 220 fnt35 7475 8179(@K)m 8(e)k 4(y)k +240 fnt82 8112 8182(parameter)m 0 7894(to)m 227(the)s 563(g)s 1(alle)k 3(ys,)k +1330(and)s 1722(using)s 2281(its)s 2545(v)s 6(alue)k +3100(as)s 3338(the)s 3673(sort)s 4079(k)s 2(e)k 3(y)k 15(.)k +4556(The)s 4972(author)s 5631(w)s 2(as)k 6039(at)s +6259(a)s 6412(loss)s 6823(to)s 7049(\207nd)s 7468(an)s 3(y)k +7852(other)s 8391(w)s 2(ay)k 15(,)k 8867(or)s +0 7606(an)m 3(y)k 397(useful)s 1036(generalization)s 2446(of)s +2717(this)s 3113(feature.)s 3939(Its)s 4228(implementation)s 5785(will)s +6211(be)s 6493(discussed)s 7468(in)s 7711(Section)s 8485(6.2.)s +240 fnt84 0 6957(5.2.)m 471(The)s 926(galley)s 1580(\210ushing)s +2447(algorithm)s 240 fnt82 480 6480(Galle)m 3(y)k 1177(components)s +2395(are)s 2751(promoted)s 3736(one)s 4148(by)s 4451(one)s +4863(into)s 5298(the)s 5655(point)s 6217(of)s 6498(appearance)s +7638(in)s 7891(the)s 8249(dynamic)s 0 6192(parent)m 672(g)s 1(alle)k 3(y)k 15(,)k +1359(then)s 1843(carried)s 2579(along)s 3179(with)s 3676(it,)s +3931(ultimately)s 4968(to)s 5222(the)s 5586(root)s 6046(g)s 1(alle)k 3(y)k +6695(and)s 7115(the)s 7478(output)s 8165(\207le.)s 8650(This)s +0 5904(process)m 800(is)s 1042(called)s 240 fnt83 1703 5906(galle)m 7(y)k +2368(\210ushing)s 240 fnt82 3121 5904(:)m 3259(the)s 3640(g)s 1(alle)k 3(ys)k +4396(are)s 4775(ri)s 6(v)k 3(ers)k 5393(running)s +6223(together)s 7098(to)s 7370(the)s 7750(sea,)s 8194(and)s +8631(each)s 0 5616(component)m 1124(is)s 1334(a)s 1500(drop)s +1992(of)s 2263(w)s 2(ater)k 13(.)k 480 5242(Here)m +1057(is)s 1324(a)s 1547(snapshot)s 2502(of)s 2830(a)s +3053(small)s 3682(dynamic)s 4616(tree,)s 5137(based)s 5797(on)s +6151(the)s 220 fnt35 6556 5239(@P)m 8(ageList)k 240 fnt82 +7737 5242(de\207nitions)m 8855(of)s 0 4954(Section)m 774(3.2:)s 6982 3257 0 3257 240 288 60 480 1406 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +200 fnt83 +0 3121(output)m 563(\207le)s gsave +860 0 translate +240 fnt82 0 3257 0 3165 240 288 60 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +0 0 0 0 240 288 60 0 3165 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(A) lfigpromotelabels +grestore +1994(r)s 9(oot)k 2370(galle)s 6(y)k +gsave +1994 2967 translate +240 fnt82 1927 0 0 0 240 288 60 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +0 0 0 0 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(B) lfigpromotelabels +grestore +gsave +1994 473 translate +240 fnt82 1927 2494 0 2494 240 288 60 LoutGraphic +gsave +0 0 moveto xsize 0 lineto xsize ysize lineto +0 ysize lineto closepath stroke +grestore +160 fnt82 845 2216(-)m 931(1)s 1035(-)s 410 2000(A)m +563(small)s 140 fnt35 170 1784(@Galle)m 2(y)k 160 fnt82 +743(*)s 904 1617 5 1545 160 180 40 853 275 LoutGr2 +currentdict end 200 dict begin begin +grestore +10 10 5 5 160 180 40 0 1540 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(C) lfigpromotelabels +grestore +140 fnt35 170 173(@F)m 4(ootSect)k +grestore +gsave +1994 0 translate +240 fnt82 1927 473 170 237 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +140 fnt35 +170 201(@P)m 5(ageList 2)k +grestore +5055 2611(body)m 5490(te)s 4(xt)k +gsave +5055 1974 translate +240 fnt82 1927 483 170 240 240 288 60 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +1927 483 170 240 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +160 fnt82 170 204(paragraph)m +grestore +(D) lfigpromotelabels +grestore +gsave +5055 1524 translate +240 fnt82 1927 450 170 207 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +160 fnt82 170 171(of)m 351(te)s 2(xt.)k + +grestore +gsave +5055 1034 translate +240 fnt82 1927 490 170 244 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +160 fnt35 170 203(@Input)m +grestore +gsave +0 0 translate +240 fnt82 0 0 0 0 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ B@W lfigprevious /FROM lfigpointdef +A@E lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +gsave +0 0 translate +240 fnt82 0 0 0 0 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ D@W lfigprevious /FROM lfigpointdef +C@E lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 955(The)m 472(components)s 1724(of)s +2039(the)s 2431(body)s 3009(te)s 3(xt)k 3468(g)s 1(alle)k 3(y)k +4146(are)s 4537(lines,)s 5139(e)s 3(xcept)k 5864(for)s +6246(the)s 6638(special)s 7400(recepti)s 6(v)k 3(e)k +8366(symbol)s 220 fnt35 0 664(@Input)m 240 fnt82 759 667(which)m +1393(is)s 1595(a)s 1753(placeholder)s 2920(for)s 3249(as)s +3491(yet)s 3835(unread)s 4536(input)s 5080(\(Section)s 5924(5.4\).)s +6459(The)s 6879(components)s 8079(of)s 8342(the)s 8681(root)s + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 26 27 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13842(-)m 4416(26)s 4709(-)s 0 13251(g)m 1(alle)k 3(y)k +646(are)s 1006(pages,)s 1671(e)s 3(xcept)k 2364(for)s +2715(the)s 3076(concluding)s 4205(une)s 3(xpanded)k 5431(in)s 9(v)k 4(ocation)k +6498(of)s 220 fnt35 6781 13248(@P)m 8(ageList)k 240 fnt82 +7845 13251(,)m 7965(which)s 8620(is)s 8843(an)s 0 12963(ine)m 3(xhaustible)k +1328(source)s 2008(of)s 2279(more)s 2826(pages,)s 3478(e)s 3(xpanded)k +4451(on)s 4748(demand.)s 480 12589(The)m 923(concrete)s 1804(data)s +2277(structure)s 3184(used)s 3696(by)s 4006(Basser)s 4718(Lout)s +5246(permits)s 6028(the)s 6392(g)s 1(alle)k 3(y)k +7041(\210ushing)s 7882(algorithm)s 8887(to)s 0 12301(na)m 4(vig)k 1(ate)k +861(the)s 1209(dynamic)s 2086(tree)s 2499(and)s 2903(\207nd)s +3334(signi\207cant)s 4390(features)s 5196(quickly:)s gsave +480 4942 translate +200 fnt82 8081 7019 226 7019 200 288 50 LoutGraphic +gsave +grestore save gsave 100 dict begin lfigdict begin +grestore +980 7019 226 6704 200 288 50 0 0 LoutGr2 +currentdict end 100 dict begin begin +grestore +980 585 226 270 200 288 50 0 6434 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 226(HEAD)m + +grestore +(A) lfigpromotelabels +grestore +1927 588 226 273 200 288 50 1830 6431 LoutGr2 +currentdict end 100 dict begin begin +grestore +1631 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 229(RECEIVING)m 1306(*)s +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 6431 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 1830 5503 LoutGr2 +currentdict end 100 dict begin begin +grestore +1498 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 229(RECEPTIVE)m + +grestore +(C) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 5503 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +C@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 0 0 0 200 288 50 1830 5163 LoutGr2 +currentdict end 100 dict begin begin +grestore +0 0 0 0 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +(D) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 5163 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR D@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +D@NW lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 2494 0 2494 200 288 50 1830 2669 LoutGr2 +0 0 moveto xsize 0 lineto xsize ysize lineto +0 ysize lineto closepath stroke +grestore +160 fnt82 845 2216(-)m 931(1)s 1035(-)s 410 2000(A)m +563(small)s 1587 1611 0 1545 160 180 40 170 275 LoutGr2 +currentdict end 100 dict begin begin +grestore +572 132 0 66 160 180 40 0 1479 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +140 fnt35 0 30(@Galle)m 2(y )k +grestore +(E) lfigpromotelabels +grestore +1587 105 0 39 160 180 40 170 170 LoutGr2 +currentdict end 100 dict begin begin +grestore +731 105 0 39 160 180 40 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +140 fnt35 +0 3(@F)m 4(ootSect )k +grestore +(F) lfigpromotelabels +grestore + +grestore +0 0 0 0 200 288 50 1830 2669 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ B@E B@E 0 B@E E@E lfigydistance lfigpadd E@E ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +0 0 0 0 200 288 50 1830 2669 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ C@E C@E 0 C@E F@E lfigydistance lfigpadd F@E ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 1830 1741 LoutGr2 +currentdict end 100 dict begin begin +grestore +839 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 229(GAP)m +grestore +(C) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 1741 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +C@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 1830 813 LoutGr2 +currentdict end 100 dict begin begin +grestore +1498 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 +226 229(RECEPTIVE)m +grestore +(C) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 813 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +C@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 473 170 237 200 288 50 1830 0 LoutGr2 +currentdict end 100 dict begin begin +grestore +1927 473 170 237 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +140 fnt35 170 201(@P)m 5(ageList 2)k +grestore +(D) lfigpromotelabels +grestore +0 0 0 0 200 288 50 1830 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR D@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +D@NW lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +0 0 0 0 200 288 50 1830 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ C@E C@E 0 C@E D@W 1.8 cm 0 lfigpadd lfigydistance lfigpadd D@W 1.8 cm 0 lfigpadd ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +980 7019 226 6704 200 288 50 4324 0 LoutGr2 +currentdict end 100 dict begin begin +grestore +980 585 226 270 200 288 50 0 6434 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 +226 226(HEAD)m +grestore +(A) lfigpromotelabels +grestore +0 0 0 0 200 288 50 5304 6704 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ B@E lfigprevious /FROM lfigpointdef +A@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 483 170 240 200 288 50 6154 6536 LoutGr2 +currentdict end 100 dict begin begin +grestore +1927 483 170 240 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +160 fnt82 170 204(paragraph)m +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 6536 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 6154 5608 LoutGr2 +currentdict end 100 dict begin begin +grestore +839 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 229(GAP)m + +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 5608 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 450 170 207 200 288 50 6154 4818 LoutGr2 +currentdict end 100 dict begin begin +grestore +1927 450 170 207 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +160 fnt82 170 171(of)m 351(te)s 2(xt.)k +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 4818 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@NW lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 6154 3890 LoutGr2 +currentdict end 100 dict begin begin +grestore +839 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 +226 229(GAP)m +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 3890 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 588 226 273 200 288 50 6154 2962 LoutGr2 +currentdict end 100 dict begin begin +grestore +1498 588 226 273 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigellipse ] lfigdopath +pop pop +grestore +200 fnt83 226 229(RECEPTIVE)m +grestore +(B) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 2962 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +B@W lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +1927 471 170 235 200 288 50 6154 2151 LoutGr2 +currentdict end 100 dict begin begin +grestore +1927 471 170 235 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +140 fnt35 170 199(@Input)m + +grestore +(C) lfigpromotelabels +grestore +0 0 0 0 200 288 50 6154 2151 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@CTR A@CTR C@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef +C@NW lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +0 0 0 0 200 288 50 6154 2151 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ B@E B@E 0 B@E C@W 1.2 cm 0 lfigpadd lfigydistance lfigpadd C@W 1.2 cm 0 lfigpadd ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 4491(Each)m 521(g)s 1(alle)k 3(y)k 1140(has)s +1495(a)s 240 fnt83 1647 4493(HEAD)m 240 fnt82 2325 4491(node)m +2832(whose)s 3485(children)s 4311(are)s 4643(its)s 4904(component)s +6013(objects,)s 6783(separated)s 7728(by)s 240 fnt83 8007 4493(GAP)m +240 fnt82 8516 4491(nodes)m 0 4203(recording)m 969(the)s 1317(inter)s 4(-component)k +2953(g)s 1(aps.)k 480 3829(Each)m 1026(component)s 2161(is)s +2383(preceded)s 3315(by)s 3621(zero)s 4096(or)s 4367(more)s +240 fnt83 4925 3831(galle)m 7(y)k 5569(inde)s 4(x)k +6155(nodes)s 240 fnt82 6780 3829(of)m 7063(v)s 6(arious)k +7823(types.)s 8504(Ev)s 3(ery)k 0 3541(recepti)m 6(v)k 3(e)k +922(symbol)s 1681(has)s 2051(a)s 240 fnt83 2216 3543(RECEPTIVE)m +240 fnt82 3529 3541(inde)m 3(x)k 4112(pointing)s 4963(to)s +5201(it,)s 5440(so)s 5705(that)s 6123(it)s 6314(can)s +6703(be)s 6984(found)s 7601(without)s 8391(search)s 8998(-)s +0 3253(ing)m 355(through)s 1152(its)s 1423(component.)s 2646(If)s +2871(the)s 3215(symbol)s 3970(is)s 4175(currently)s 5086(the)s +5429(tar)s 4(get)k 6023(of)s 6290(a)s 6451(g)s 1(alle)k 3(y)k 15(,)k +7118(it)s 7305(has)s 7670(a)s 240 fnt83 7831 3255(RECEIVING)m +240 fnt82 0 2965(inde)m 3(x)k 595(instead)s 1342(which)s +1995(is)s 2217(also)s 2667(link)s 2(ed)k 3332(to)s +3583(the)s 3942(incoming)s 4911(g)s 1(alle)k 3(y)k 15(.)k +5652(Galle)s 3(ys)k 6441(that)s 6871(are)s 7229(currently)s +8157(without)s 8960(a)s 0 2677(tar)m 4(get)k 586(are)s +920(link)s 2(ed)k 1560(to)s 1786(the)s 2120(dynamic)s +2984(tree)s 3383(by)s 240 fnt83 3664 2679(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k +240 fnt82 5215 2677(g)m 1(alle)k 3(y)k 5836(inde)s 3(x)k 3(es,)k +6654(either)s 7244(just)s 7635(after)s 8118(their)s 8601(most)s +0 2389(recent)m 643(tar)s 4(get)k 1242(if)s 1459(there)s +1992(has)s 2362(been)s 2871(one,)s 3324(or)s 3583(else)s +4010(at)s 4242(their)s 4739(point)s 5291(of)s 5562(in)s 9(v)k 4(ocation.)k +480 2015(Each)m 1041(g)s 1(alle)k 3(y)k 1701(should)s +2424(be)s 2732(thought)s 3550(of)s 3847(as)s 4123(a)s +4315(concurrent)s 5423(process,)s 6273(although)s 7194(the)s 7569(implementation)s +0 1727(in)m 268(C)s 506(uses)s 995(coroutines)s 2067(implemented)s +3399(by)s 3719(procedures.)s 4957(A)s 5213(g)s 1(alle)k 3(y)k +5873(may)s 6364(promote)s 7243(its)s 7545(\207rst)s 8002(component)s +0 1439(only)m 499(if)s 735(it)s 946(has)s 1335(a)s +1520(tar)s 4(get,)k 2185(suf\207cient)s 3153(space)s 3759(is)s +3988(a)s 4(v)k 6(ailable)k 4915(at)s 5166(the)s +5533(tar)s 4(get)k 6151(to)s 6409(recei)s 6(v)k 3(e)k +7164(the)s 7531(component,)s 8722(and)s 0 1151(the)m 349(component)s +1475(contains)s 2325(no)s 2620(recepti)s 6(v)k 3(e)k +3544(symbols.)s 4508(This)s 4986(last)s 5379(condition)s 6342(seems)s +6979(to)s 7220(be)s 7504(the)s 7854(k)s 2(e)k 3(y)k +8251(to)s 8492(g)s 1(alle)k 3(y)k 0 863(synchronization:)m +1722(it)s 1943(forces)s 2606(a)s 2801(bottom-up)s 3880(promotion)s +4963(re)s 3(gime,)k 5759(pre)s 6(v)k 3(enting)k +6855(pages)s 7480(from)s 8033(\210ushing)s 8887(to)s 0 575(output)m +672(before)s 1338(te)s 3(xt)k 1753(\210ushes)s 2469(into)s +2894(them,)s 3479(for)s 3817(e)s 3(xample.)k +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 27 28 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4291 13844(-)m 4419(27)s 4707(-)s 480 13255(Each)m 1022(g)s 1(alle)k 3(y)k +1663(contains)s 2519(a)s 2692(number)s 3490(of)s 3769(binary)s +4441(semaphores,)s 5685(sho)s 6(wn)k 6369(as)s 6626(asterisks)s +7507(in)s 7757(our)s 8144(snapshots)s 0 12967(when)m 583(set.)s +1019(At)s 1325(an)s 3(y)k 1730(gi)s 6(v)k 3(en)k +2317(moment,)s 3215(a)s 3389(g)s 1(alle)k 3(y)k +4030(process)s 4805(is)s 5022(either)s 5633(running)s 6438(or)s +6704(else)s 7139(is)s 7356(suspended)s 8419(on)s 8724(one)s +0 12679(of)m 269(its)s 543(o)s 6(wn)k 1005(semaphores.)s +2296(The)s 240 fnt83 2722 12681(HEAD)m 240 fnt82 3413 12679(node)m +3933(contains)s 4779(a)s 4943(semaphore)s 6033(which)s 6673(is)s +6881(set)s 7204(when)s 7778(the)s 8124(g)s 1(alle)k 3(y)k +8756(has)s 0 12391(tried)m 499(to)s 742(\207nd)s 1177(a)s +1347(tar)s 4(get)k 1950(and)s 2359(f)s 2(ailed.)k +3068(Each)s 3607(recepti)s 6(v)k 3(e)k 4533(symbol)s +5297(has)s 5671(a)s 5842(semaphore)s 6938(which)s 7584(is)s +7798(set)s 8127(when)s 8708(that)s 0 12103(symbol)m 760(is)s +970(pre)s 6(v)k 3(enting)k 2037(the)s 2385(\207rst)s +2816(component)s 3940(from)s 4464(being)s 5049(promoted.)s 480 11729(F)m 3(or)k +859(e)s 3(xample,)k 1762(in)s 1994(the)s 2331(snapshot)s +3218(at)s 3439(the)s 3776(be)s 3(ginning)k 4773(of)s +5033(this)s 5418(section,)s 6191(the)s 6528(root)s 6962(g)s 1(alle)k 3(y)k +7585(is)s 7784(suspended)s 8829(on)s 0 11441(the)m 220 fnt35 +351 11438(@Galle)m 4(y)k 240 fnt82 1253 11441(symbol,)m 2069(b)s 4(ut)k +2435(the)s 2787(te)s 3(xt)k 3205(g)s 1(alle)k 3(y)k +3843(is)s 4057(running.)s 4970(It)s 5179(will)s 5608(suspend)s +6442(on)s 6743(the)s 220 fnt35 7095 11438(@Input)m 240 fnt82 +7866 11441(symbol)m 8630(after)s 0 11153(the)m 348(\207rst)s 779(tw)s 2(o)k +1189(components)s 2397(are)s 2744(promoted.)s 480 10779(Ev)m 3(ery)k +1145(g)s 1(alle)k 3(y)k 240 fnt83 1822 10781(G)m +240 fnt82 1995 10779(,)m 2145(be)s 2470(it)s 2705(a)s +2914(list)s 3308(of)s 3623(pages,)s 4318(body)s 4895(te)s 3(xt,)k +5400(a)s 5609(footnote,)s 6556(or)s 6858(whate)s 6(v)k 3(er)k 9(,)k +7866(e)s 3(x)k 3(ecutes)k 8778(the)s 0 10491(follo)m 6(wing)k +977(algorithm)s 1966(in)s 2209(parallel)s 2979(with)s 3461(e)s 6(v)k 3(ery)k +4037(other)s 4588(g)s 1(alle)k 3(y:)k 0 9988(1.)m +303(Initially)s 240 fnt83 1132 9990(G)m 240 fnt82 1384 9988(is)m +1614(unattached.)s 2834(Search)s 3560(forw)s 2(ards)k 4478(or)s +4756(backw)s 2(ards)k 5848(from)s 6392(its)s 240 fnt83 +6687 9990(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k +240 fnt82 8272 9988(inde)m 3(x)k 8876(as)s 0 9700(required,)m +903(to)s 1142(\207nd)s 1573(a)s 1739(recepti)s 6(v)k 3(e)k +2661(symbol)s 240 fnt83 3421 9702(S)m 240 fnt82 3602 9700(which)m +4244(can)s 4633(e)s 3(xpand)k 5380(to)s 5619(re)s 6(v)k 3(eal)k +6248(a)s 6414(tar)s 4(get)k 7013(for)s 240 fnt83 +7351 9702(G)m 240 fnt82 7524 9700(.)m 0 9197(2.)m 284(If)s +514(no)s 240 fnt83 807 9199(S)m 240 fnt82 988 9197(can)m +1377(be)s 1659(found,)s 2325(suspend)s 3155(on)s 3452(the)s +3800(attachment)s 4908(semaphore.)s 6108(Resume)s 6935(later)s 7418(from)s +7942(step)s 8380(1.)s 0 8694(3.)m 281(Expand)s 240 fnt83 +1068 8696(S)m 240 fnt82 1246 8694(to)m 1482(re)s 6(v)k 3(eal)k +2107(the)s 2452(tar)s 4(get)k 3048(of)s 240 fnt83 +3316 8696(G)m 240 fnt82 3489 8694(.)m 3649(Preserv)s 3(e)k +240 fnt83 4521 8696(S)m 240 fnt82 4642 8694(')m 13(s)k +4849(semaphore)s 5938(by)s 6229(mo)s 3(ving)k 7007(it)s +7196(to)s 7432(the)s 7777(\207rst)s 8204(recepti)s 6(v)k 3(e)k +0 8406(symbol)m 760(within)s 1428(the)s 1776(e)s 3(xpansion)k +2801(of)s 240 fnt83 3072 8408(S)m 240 fnt82 3193 8406(.)m +0 7903(4.)m 295(Calculate)s 1264(the)s 1624(a)s 4(v)k 6(ailable)k +2543(width)s 3156(and)s 3572(height)s 4241(at)s 4484(the)s +4844(tar)s 4(get,)k 5501(and)s 5917(if)s 240 fnt83 +6145 7905(G)m 240 fnt82 6389 7903(is)m 6611(still)s 7034(a)s +7211(pure)s 7704(parse)s 8275(tree,)s 8751(use)s 0 7615(the)m +377(en)s 9(vironment)k 1667(attached)s 2550(to)s 240 fnt83 +2819 7617(G)m 240 fnt82 3081 7615(and)m 3515(the)s 3892(style)s +4429(information)s 5643(from)s 6197(the)s 6574(tar)s 4(get)k +7203(to)s 7471(e)s 6(v)k 6(aluate)k 240 fnt83 +8341 7617(G)m 240 fnt82 8603 7615(as)m 8883(in)s 0 7327(Section)m +774(4.)s 0 6871(5.)m 284(Examine)s 1190(the)s 1538(components)s +2746(of)s 240 fnt83 3017 6873(G)m 240 fnt82 3250 6871(one)m +3652(by)s 3946(one.)s 4456(F)s 3(or)k 4845(each)s +5340(component)s 6464(there)s 6997(are)s 7344(three)s 7877(possibilities:)s +240 fnt83 480 6499(A)m 7(CCEPT)k 17(.)k 240 fnt82 +1513 6497(If)m 1756(the)s 2116(component)s 3253(\207ts)s 3609(into)s +4046(the)s 4407(a)s 4(v)k 6(ailable)k 5328(space,)s +5978(and)s 6395(has)s 6778(no)s 7083(other)s 7647(problems,)s +8657(then)s 0 6209(promote)m 875(it)s 1090(into)s 1538(the)s +1909(tar)s 4(get.)k 2635(If)s 2888(this)s 3306(is)s +3539(the)s 3910(\207rst)s 4364(component)s 5511(promoted)s 6509(into)s +6956(this)s 7375(tar)s 4(get,)k 8044(and)s 240 fnt83 +8471 6211(G)m 240 fnt82 8727 6209(is)m 8960(a)s 0 5921(forcing)m +768(g)s 1(alle)k 3(y)k 1428(\(Section)s 2307(5.4\),)s +2819(delete)s 3470(e)s 6(v)k 3(ery)k 4072(recepti)s 6(v)k 3(e)k +5020(symbol)s 5806(preceding)s 6827(the)s 7201(tar)s 4(get)k +7826(in)s 8095(the)s 8469(parent)s 0 5633(g)m 1(alle)k 3(y)k 15(.)k +729(If)s 240 fnt83 959 5635(G)m 240 fnt82 1192 5633(is)m +1402(the)s 1750(root)s 2195(g)s 1(alle)k 3(y)k 15(,)k +2867(render)s 3537(the)s 3885(component)s 5009(on)s 5306(the)s +5654(output)s 6326(\207le)s 6687(and)s 7091(dispose)s 7865(it;)s +240 fnt83 480 5261(REJECT)m 17(.)k 240 fnt82 1490 5259(If)m +1756(the)s 2140(component)s 3300(is)s 3546(too)s 3941(lar)s 4(ge)k +4506(for)s 4880(the)s 5264(a)s 4(v)k 6(ailable)k +6208(space,)s 6882(or)s 7177(a)s 240 fnt83 7379 5261(FOLLO)m 12(WS)k +240 fnt82 8542 5259(inde)m 3(x)k 0 4971(\(described)m 1043(belo)s 6(w\))k +1740(forbids)s 2458(its)s 2723(promotion)s 3767(into)s 4182(this)s +4568(tar)s 4(get,)k 5203(then)s 5662(detach)s 240 fnt83 +6333 4973(G)m 240 fnt82 6556 4971(from)m 7069(the)s 7407(tar)s 4(get.)k +8100(If)s 8320(this)s 8705(w)s 2(as)k 0 4683(the)m +338(\207rst)s 758(component)s 1872(at)s 2093(this)s 2479(tar)s 4(get,)k +240 fnt83 3114 4685(S)m 240 fnt82 3284 4683(has)m 3644(been)s +4142(a)s 4298(complete)s 5219(f)s 2(ailure,)k 5936(so)s +6191(undo)s 6713(step)s 7141(3)s 7294(\(Basser)s 8060(Lout)s +8561(is)s 8760(not)s 0 4395(able)m 454(to)s 693(undo)s +1226(step)s 1664(4\);)s 1975(otherwise)s 2960(delete)s 3586(the)s +3934(tar)s 4(get.)k 4637(Return)s 5345(to)s 5584(step)s +6022(1)s 6177(and)s 6581(continue)s 7461(immediately;)s 240 fnt83 +480 4023(SUSPEND.)m 240 fnt82 1685 4021(If)m 1928(the)s 2289(component)s +3426(contains)s 4287(a)s 4466(recepti)s 6(v)k 3(e)k +5402(symbol,)s 6227(it)s 6432(cannot)s 7143(be)s 7438(promoted)s +8426(yet.)s 8896(If)s 0 3733(this)m 392(symbol)s 1148(is)s +1354(the)s 1697(tar)s 4(get)k 2292(of)s 2559(a)s +2720(g)s 1(alle)k 3(y)k 3350(that)s 3764(w)s 2(as)k +4180(written)s 4909(to)s 5144(an)s 5423(auxiliary)s 6321(\207le)s +6678(on)s 6971(a)s 7132(pre)s 6(vious)k 7997(run,)s +8419(read)s 8883(in)s 0 3445(that)m 427(g)s 1(alle)k 3(y)k +1071(and)s 1484(\210ush)s 2017(it.)s 2322(Otherwise)s 3370(suspend)s +4209(on)s 4516(the)s 4873(recepti)s 6(v)k 3(e)k +5805(symbol')s 13(s)k 6729(semaphore;)s 7887(resume)s 8643(later)s +0 3157(from)m 524(step)s 962(4.)s 0 2653(6.)m 284(T)s 16(erminate)k +1305(when)s 1881(the)s 2229(g)s 1(alle)k 3(y)k +2863(is)s 3073(empty)s 15(.)k 0 2150(At)m 354(v)s 6(arious)k +1158(points)s 1850(in)s 2148(this)s 2599(algorithm,)s 3691(recepti)s 6(v)k 3(e)k +4668(symbols)s 5572(\(and)s 6111(their)s 6663(semaphores\))s 7975(are)s +8378(deleted)s 0 1862(in)m 273(the)s 652(dynamic)s 1560(parent)s +2247(g)s 1(alle)k 3(y)k 15(,)k 2950(possibly)s +3833(permitting)s 4911(it)s 5134(to)s 5404(resume)s 6180(\210ushing.)s +7147(When)s 7807(this)s 8234(happens,)s 0 1574(Basser)m 701(Lout)s +1218(resumes)s 2057(the)s 2410(parent)s 3071(immediately)s 4324(after)s +240 fnt83 4825 1576(G)m 240 fnt82 5063 1574(suspends)m 5983(or)s +6247(terminates.)s 7410(Also,)s 7974(whene)s 6(v)k 3(er)k +8960(a)s 0 1286(component)m 1140(is)s 1366(promoted,)s 2406(an)s 3(y)k +2819(child)s 3371(g)s 1(alle)k 3(ys)k 4111(connected)s +5156(to)s 5411(it)s 5619(by)s 240 fnt83 5929 1288(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k +240 fnt82 7510 1286(inde)m 3(x)k 3(es)k 8302(must)s +8844(be)s 0 998(resumed,)m 918(since)s 1466(these)s 2014(g)s 1(alle)k 3(ys)k +2739(may)s 3206(be)s 3490(able)s 3945(to)s 4185(\207nd)s +4617(a)s 4784(tar)s 4(get)k 5384(no)s 6(w)k 15(.)k +5942(A)s 6173(good)s 6712(e)s 3(xample)k 7576(of)s +7848(this)s 8246(situation)s 0 710(occurs)m 664(when)s 1228(a)s +1382(line)s 1785(of)s 2044(body)s 2566(te)s 3(xt)k +2969(with)s 3440(one)s 3830(or)s 4077(more)s 4613(footnotes)s +5542(is)s 5740(promoted)s 6703(onto)s 7171(a)s 7325(page.)s +7929(Basser)s 8614(Lout)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 28 29 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4291 13844(-)m 4419(28)s 4706(-)s 0 13253(gi)m 6(v)k 3(es)k +547(priority)s 1317(to)s 1556(such)s 2052(children,)s 2942(suspending)s +240 fnt83 4073 13255(G)m 240 fnt82 4306 13253(while)m 4893(each)s +5388(is)s 5598(gi)s 6(v)k 3(en)k 6178(a)s +6344(chance)s 7064(to)s 7303(\210ush.)s 480 12879(Basser)m 1211(Lout)s +1758(searches)s 2653(for)s 3025(the)s 3408(\207rst)s 3874(tar)s 4(get)k +4507(of)s 240 fnt83 4813 12881(G)m 240 fnt82 5081 12879(only)m +5595(in)s 5873(re)s 3(gions)k 6660(of)s 6965(the)s +7348(dynamic)s 8260(tree)s 8708(that)s 0 12591(will)m 437(clearly)s +1152(precede)s 1963(or)s 2233(follo)s 6(w)k 240 fnt83 +2917 12593(G)m 240 fnt82 3090 12591(')m 13(s)k 3312(in)s 9(v)k 4(ocation)k +4378(point)s 4941(in)s 5196(the)s 5556(\207nal)s 6047(printed)s +6794(document,)s 7857(whiche)s 6(v)k 3(er)k 8916(is)s +0 12303(speci\207ed)m 904(in)s 1142(the)s 220 fnt35 1486 12300(into)m +240 fnt82 1887 12303(clause;)m 2591(subsequent)s 3711(tar)s 4(gets)k +4389(are)s 4731(sought)s 5426(later)s 5904(in)s 6142(the)s +6486(same)s 7028(g)s 1(alle)k 3(y)k 7657(as)s +7903(the)s 8246(\207rst.)s 8776(An)s 0 12015(e)m 3(xception)k +982(to)s 1219(this)s 1613(rule,)s 2089(whose)s 2755(necessity)s +3683(will)s 4107(be)s 4387(made)s 4959(clear)s 5480(later)s 9(,)k +5999(is)s 6207(that)s 6623(a)s 6787(\207rst)s 220 fnt35 +7216 12012(f)m 6(ollo)k 3(wing)k 240 fnt82 8104 12015(tar)m 4(get)k +8700(will)s 0 11727(be)m 282(sought)s 981(within)s 1649(a)s +1815(dynamic)s 2692(sibling)s 3396(g)s 1(alle)k 3(y)k +4030(preceding)s 240 fnt83 5026 11729(G)m 240 fnt82 5199 11727(')m 13(s)k +5409(in)s 9(v)k 4(ocation)k 6463(point:)s gsave +480 6741 translate +200 fnt82 5379 4646 0 4646 200 288 50 LoutGraphic +gsave +grestore save gsave 200 dict begin lfigdict begin +grestore +200 fnt83 +0 4510(dynamic)m 722(par)s 7(ent)k gsave +0 1353 translate +200 fnt82 2039 3003 226 2777 200 288 50 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1587 171 0 86 200 288 50 226 2323 LoutGr2 +currentdict end 200 dict begin begin +grestore +796 171 0 86 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +180 fnt35 0 40(@XT)m 21(arget)k + +grestore +(A) lfigpromotelabels +grestore +1587 136 0 47 200 288 50 226 1620 LoutGr2 +currentdict end 200 dict begin begin +grestore +1254 136 0 47 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +200 fnt83 0 3(UN)m 5(A)k 7(TT)k 10(A)k 6(CHED)k + +grestore +(C) lfigpromotelabels +grestore +180 fnt35 226 752(@XT)m 21(arget)k +grestore +gsave +2889 4135 translate +200 fnt82 2490 171 0 86 200 288 50 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +2450 171 0 86 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +180 fnt35 0 40(X into { @XT)m 21(arget&&f)k 5(ollo)k 2(wing })k + +grestore +(B) lfigpromotelabels +grestore +gsave +2889 2720 translate +200 fnt82 2039 1302 226 1076 200 288 50 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +180 fnt35 226 492(@GT)m 21(arget)k +grestore +gsave +2889 1982 translate +200 fnt82 2490 171 0 86 200 288 50 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +2490 171 0 86 200 288 50 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +180 fnt35 0 40(G into { @GT)m 21(arget&&f)k 5(ollo)k 2(wing })k + +grestore +(D) lfigpromotelabels +grestore +gsave +2889 0 translate +200 fnt82 2039 1869 226 1643 200 288 50 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore + +grestore +gsave +0 0 translate +200 fnt82 0 0 0 0 200 288 50 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef +0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +gsave +0 0 translate +200 fnt82 0 0 0 0 200 288 50 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ C@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef +0.2 cm 0 D@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 6290(Here)m 240 fnt83 524 6292(G)m 240 fnt82 762 6290(will)m +1193(\207nd)s 1629(the)s 220 fnt35 1982 6287(@GT)m 26(arget)k +240 fnt82 3045 6290(tar)m 4(get)k 3649(within)s 240 fnt83 +4322 6292(X)m 240 fnt82 4478 6290(.)m 4647(This)s 5128(is)s +5343(dangerous,)s 6439(since)s 6991(if)s 7213(the)s 7566(\207rst)s +8002(component)s 0 6002(of)m 240 fnt83 303 6004(G)m 240 fnt82 +568 6002(is)m 811(then)s 1312(promoted)s 2320(via)s 240 fnt83 +2704 6004(X)m 240 fnt82 2952 6002(into)m 3410(the)s 3790(\207rst)s +220 fnt35 4254 5999(@XT)m 26(arget)k 240 fnt82 5319 6002(rather)m +5967(than)s 6469(into)s 6926(the)s 7307(second,)s 240 fnt83 +8111 6004(G)m 240 fnt82 8284 6002(')m 13(s)k 8527(tar)s 4(get)k +0 5714(will)m 438(not)s 817(appear)s 1526(later)s 2022(in)s +2277(the)s 2638(\207nal)s 3130(printed)s 3878(document)s 4894(than)s +5376(its)s 5664(in)s 9(v)k 4(ocation)k 6731(point,)s +7342(as)s 7605(required)s 8471(by)s 8778(the)s 220 fnt35 +0 5423(into)m 240 fnt82 406 5426(clause.)m 480 5052(Accordingly)m 15(,)k +1753(when)s 2313(such)s 2794(a)s 2944(tar)s 4(get)k +3528(is)s 3722(chosen,)s 4478(tw)s 2(o)k 4873(special)s +5575(g)s 1(alle)k 3(y)k 6194(inde)s 3(x)k 3(es)k +6954(are)s 7286(inserted)s 8084(and)s 8472(link)s 2(ed)k +0 4764(together:)m 898(a)s 240 fnt83 1074 4766(PRECEDES)m 240 fnt82 +2327 4764(inde)m 3(x)k 2921(at)s 240 fnt83 3163 4766(G)m +240 fnt82 3336 4764(')m 13(s)k 3555(in)s 9(v)k 4(ocation)k +4619(point,)s 5227(and)s 5641(a)s 240 fnt83 5817 4766(FOLLO)m 12(WS)k +240 fnt82 6952 4764(inde)m 3(x)k 7546(at)s 7787(the)s +8145(\207rst)s 8586(com)s 8998(-)s 0 4476(ponent)m 720(of)s +240 fnt83 1000 4478(G)m 240 fnt82 1173 4476(.)m 1346(The)s +1783(algorithm)s 2781(checks)s 3492(before)s 4167(promoting)s 5226(an)s 3(y)k +240 fnt83 5632 4478(FOLLO)m 12(WS)k 240 fnt82 6767 4476(inde)m 3(x)k +7360(that)s 7787(its)s 8072(promotion)s 0 4188(w)m 2(ould)k +661(not)s 1033(place)s 1600(it)s 1798(earlier)s 2472(than)s +2948(the)s 3302(corresponding)s 240 fnt83 4730 4190(PRECEDES)m 240 fnt82 +5981 4188(inde)m 3(x)k 6571(in)s 6820(the)s 7175(same)s +7728(g)s 1(alle)k 3(y)k 15(,)k 8406(and)s +8817(re)s 8998(-)s 0 3900(jects)m 486(the)s 831(component)s +1952(if)s 2166(it)s 2355(w)s 2(ould.)k 3113(Since)s +240 fnt83 3697 3902(PRECEDES)m 240 fnt82 4939 3900(and)m 240 fnt83 +5340 3902(FOLLO)m 12(WS)k 240 fnt82 6463 3900(inde)m 3(x)k 3(es)k +7236(are)s 7580(rarely)s 8187(used,)s 8730(this)s 0 3612(check)m +619(can)s 1008(be)s 1290(implemented)s 2596(by)s 2890(linear)s +3493(search.)s 480 3238(When)m 1114(tw)s 2(o)k 1529(components)s +2742(are)s 3094(separated)s 4060(by)s 220 fnt35 4359 3235(/)m +240 fnt82 4423 3238(,)m 4535(as)s 4790(opposed)s 5652(to)s +5897(the)s 6250(more)s 6802(usual)s 220 fnt35 7367 3235(//)m +240 fnt82 7492 3238(,)m 7604(each)s 8105(in\210uences)s 0 2950(the)m +358(horizontal)s 1393(position)s 2232(of)s 2514(the)s 2872(other)s 13(.)k +3525(Because)s 4389(of)s 4671(this,)s 5133(the)s 240 fnt83 +5492 2952(SUSPEND)m 240 fnt82 6596 2950(action)m 7248(is)s 7468(in)s +7722(f)s 2(act)k 8148(tak)s 2(en)k 8732(if)s +8960(a)s 0 2662(recepti)m 6(v)k 3(e)k 930(symbol)s +1698(occurs)s 2382(in)s 2633(an)s 3(y)k 3039(component)s +4171(separated)s 5140(from)s 5672(the)s 6028(\207rst)s 6468(by)s +220 fnt35 6770 2659(/)m 240 fnt82 6903 2662(operators)m 7851(only)s 15(.)k +8435(Ag)s 1(ain,)k 0 2374(linear)m 603(search)s 1270(forw)s 2(ards)k +2168(to)s 2407(the)s 2755(\207rst)s 220 fnt35 3186 2371(//)m +240 fnt82 3371 2374(suf\207ces)m 4152(for)s 4490(this)s 4886(check.)s +480 2000(A)m 740(good)s 1308(illustration)s 2430(of)s 2731(these)s +3308(unusual)s 4139(cases)s 4724(is)s 4964(af)s 6(forded)k +5856(by)s 6180(the)s 220 fnt35 6558 1997(@Align)m 240 fnt82 +7344 2000(symbols)m 8223(from)s 8778(the)s 0 1712(standard)m 867(DocumentLayout)s +2600(package.)s 3546(These)s 4171(are)s 4516(used)s 5012(to)s +5249(produce)s 6074(displayed)s 7047(equations,)s 8069(aligned)s 8829(on)s +0 1424(their)m 497(equals)s 1159(signs)s 1702(despite)s 2435(being)s +3020(separated)s 3980(by)s 4274(arbitrary)s 5149(body)s 5683(te)s 3(xt.)k +480 1050(The)m 220 fnt35 921 1047(@Align)m 240 fnt82 1689 1050(symbols)m +2551(are)s 2911(packaged)s 3886(neatly)s 4537(for)s 4889(the)s +5250(con)s 9(v)k 3(enience)k 6503(of)s 6787(the)s +7148(non-e)s 3(xpert)k 8254(user)s 9(,)k 8764(b)s 4(ut)k +0 762(we)m 335(will)s 761(sho)s 6(w)k 1315(just)s +1720(the)s 2067(essence)s 2853(of)s 3124(the)s 3472(implementation)s +5029(here.)s 5603(First,)s 6147(an)s 220 fnt35 6430 759(@AlignList)m +240 fnt82 7536 762(g)m 1(alle)k 3(y)k 8170(is)s +8379(created)s 0 474(which)m 642(contains)s 1490(an)s 1773(in\207nite)s +2506(supply)s 3199(of)s 220 fnt35 3470 471(@AlignPlace)m 240 fnt82 +4779 474(recepti)m 6(v)k 3(e)k 5701(symbols)s 6550(separated)s +7510(by)s 220 fnt35 7804 471(/)m 240 fnt82 7928 474(operators:)m + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 29 30 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +%%+ font Symbol +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4289 13844(-)m 4417(29)s 4708(-)s 4777 3207 0 3207 240 288 60 480 10207 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +240 fnt83 0 3044(body)m +522(te)s 4(xt)k 926(galle)s 7(y)k gsave +0 161 translate +240 fnt82 2039 2720 226 2494 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1587 1418 0 1314 240 288 60 226 226 LoutGr2 +currentdict end 200 dict begin begin +grestore +838 208 0 104 240 288 60 0 1210 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +220 fnt35 +0 47(@Galle)m 4(y)k +grestore +(A) lfigpromotelabels +grestore + +grestore +gsave +2889 1638 translate +240 fnt82 1888 209 0 105 240 288 60 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +1046 209 0 105 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +220 fnt35 0 48(@AlignList)m +grestore +(B) lfigpromotelabels +grestore +gsave +2889 0 translate +240 fnt82 1888 1525 226 1195 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +220 fnt35 +226 1138(@AlignPlace)m 226 850(@AlignPlace)m 226 562(...)m 226 274(@EndAlignList)m +grestore +gsave +0 0 translate +240 fnt82 0 0 0 0 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef +0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 9756(Then)m +549(equations)s 1517(lik)s 2(e)k 1471 214 393 105 240 288 60 480 9202 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +1471 214 393 105 240 288 60 0 0 LoutGr2 +/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1471 214 393 105 240 288 60 0 0 LoutGr2 + +0.015 cm setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd +[] +xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath +pop pop +grestore +240 fnt83 0 53(f)m +240 fnt78 113 45(\()m 240 fnt83 197 53(x)m 240 fnt78 +315 45(\))m 477(=)s 240 fnt83 690 53(g)m 240 fnt78 +816 45(\()m 240 fnt83 900 53(x)m 240 fnt78 1018 45(\))m +1156(+)s 1357(2)s +grestore + +grestore +end end restore +grestore +0 8751(are)m 358(created)s 1117(and)s +1532(sent)s 1989(to)s 220 fnt35 2239 8748(@AlignPlace&&f)m 6(ollo)k 3(wing)k +240 fnt82 4690 8751(tar)m 4(gets.)k 5498(The)s 3(y)k +6052(collect)s 6760(in)s 7014(the)s 220 fnt35 7374 8748(@AlignList)m +240 fnt82 8492 8751(g)m 1(alle)k 3(y)k 0 8463(and)m +404(are)s 751(aligned)s 1513(there:)s 5836 3212 0 3212 240 288 60 480 4911 LoutGr2 +grestore save gsave 200 dict begin lfigdict begin +grestore +240 fnt83 0 3049(body)m +522(te)s 4(xt)k 926(galle)s 7(y)k gsave +0 166 translate +240 fnt82 2039 2720 226 2494 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +1587 1418 0 1314 240 288 60 226 226 LoutGr2 +currentdict end 200 dict begin begin +grestore +838 208 0 104 240 288 60 0 1210 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +220 fnt35 +0 47(@Galle)m 4(y)k +grestore +(A) lfigpromotelabels +grestore + +grestore +gsave +2889 1643 translate +240 fnt82 2947 209 0 105 240 288 60 LoutGraphic +gsave +currentdict end 200 dict begin begin +grestore +1046 209 0 105 240 288 60 0 0 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfignoline [ lfigbox ] lfigdopath +pop pop +grestore +220 fnt35 0 48(@AlignList)m +grestore +(B) lfigpromotelabels +grestore +gsave +2889 0 translate +240 fnt82 2947 1530 1285 1195 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ lfigbox ] lfigdopath +pop pop +grestore +2495 1078 1059 969 240 288 60 226 226 LoutGr2 + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigdashed [ xmark ysize lfigprevious /FROM lfigpointdef +xmark 0 lfigprevious /TO lfigpointdef ] lfigdopath +pop pop +grestore +240 fnt83 +666 917(f)m 240 fnt78 779 909(\()m 240 fnt83 863 917(x)m +240 fnt78 981 909(\))m 1143(=)s 240 fnt83 1356 917(g)m +240 fnt78 1482 909(\()m 240 fnt83 1566 917(x)m 240 fnt78 +1684 909(\))m 1822(+)s 2023(2)s 240 fnt83 0 629(f)m +240 fnt78 113 621(\()m 240 fnt83 197 629(x)m 240 fnt78 +315 621(\))m 453(-)s 240 fnt83 653 629(g)m 240 fnt78 +779 621(\()m 240 fnt83 863 629(x)m 240 fnt78 981 621(\))m +1143(=)s 1356(2)s 220 fnt35 1059 336(...)m 1059 48(@EndAlignList)m + +grestore + +grestore +gsave +0 0 translate +240 fnt82 0 0 0 0 240 288 60 LoutGraphic +gsave + +0.5 pt setlinewidth lfiground setlinecap +0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef +0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath +0.15 cm /lfigsolid /lfigblack +lfigopen +0.15 cm 0.05 cm lfigforward +grestore + +grestore +end end restore +grestore +0 4460(The)m 220 fnt35 450 4457(@AlignList)m 240 fnt82 1579 4460(g)m 1(alle)k 3(y)k +2236(does)s 2749(not)s 3138(\210ush,)s 3734(because)s 4570(its)s +4868(\207rst)s 5322(component)s 6469(is)s 6702(connected)s 7753(to)s +8015(a)s 8204(recepti)s 6(v)k 3(e)k 0 4172(symbol)m +760(by)s 220 fnt35 1054 4169(/)m 240 fnt82 1178 4172(operators.)m +480 3798(After)m 1048(the)s 1402(last)s 1799(equation,)s 2736(an)s +3025(empty)s 3683(forcing)s 4432(g)s 1(alle)k 3(y)k +5072(is)s 5288(sent)s 5739(to)s 220 fnt35 5984 3795(@EndAlignList)m +240 fnt82 7420 3798(,)m 7533(deleting)s 8362(the)s 8716(tw)s 2(o)k +0 3510(remaining)m 1028(recepti)s 6(v)k 3(e)k 1957(symbols)s +2813(from)s 3344(the)s 220 fnt35 3699 3507(@AlignList)m 240 fnt82 +4812 3510(g)m 1(alle)k 3(y)k 5452(and)s 5863(permitting)s +6918(it)s 7117(to)s 7363(\210ush.)s 240 fnt83 8000 3512(FOLLO)m 12(WS)k +240 fnt82 0 3222(inde)m 3(x)k 3(es)k 797(ensure)s +1499(that)s 1939(each)s 2456(equation)s 3359(\207nds)s 3898(a)s +4086(tar)s 4(get)k 4707(placed)s 5410(in)s 5675(the)s +6045(body)s 6601(te)s 3(xt)k 7038(just)s 7465(after)s +7983(its)s 8281(point)s 8855(of)s 0 2934(in)m 9(v)k 4(ocation,)k +1090(so)s 1341(the)s 1675(equations)s 2628(return,)s 3290(aligned,)s +4087(to)s 4311(approximately)s 5732(the)s 6065(points)s 6686(where)s +7312(the)s 3(y)k 7760(were)s 8265(in)s 9(v)k 4(ok)k 2(ed.)k +0 2646(Notice)m 703(that)s 1131(the)s 1489(\210ushing)s 2324(of)s +2605(body)s 3149(te)s 3(xt)k 3574(is)s 3794(suspended)s +4860(until)s 5363(the)s 5721(list)s 6082(of)s 6363(equations)s +7341(is)s 7561(completed,)s 8674(as)s 8934(it)s 0 2358(must)m +513(be,)s 833(since)s 1367(the)s 1702(horizontal)s 2713(position)s +3528(of)s 3786(the)s 4121(\207rst)s 4539(equation)s 5407(cannot)s +6092(be)s 6361(kno)s 6(wn)k 7052(until)s 7532(the)s +7867(last)s 8245(equation)s 0 2070(is)m 210(added)s 840(to)s +1079(the)s 1427(list.)s 480 1696(Layout)m 1262(quality)s 2025(can)s +2459(occasionally)s 3753(be)s 4080(impro)s 3(v)k 3(ed)k +5094(by)s 5433(rejecting)s 6366(a)s 6577(component)s 7746(that)s +8209(could)s 8844(be)s 0 1408(promoted)m 978(\211)s 1161(for)s +1502(e)s 3(xample,)k 2419(a)s 2588(component)s 3715(of)s +3989(body)s 4526(te)s 3(xt)k 4944(that)s 5365(carries)s +6054(a)s 6223(footnote)s 7079(too)s 7441(lar)s 4(ge)k +7973(to)s 8215(\207t)s 8477(on)s 8778(the)s 0 1120(current)m +747(page.)s 1374(Since)s 1972(Lout)s 2496(does)s 2997(not)s +3374(specify)s 4130(ho)s 6(w)k 4602(breaking)s 5503(decisions)s +6455(are)s 6814(made,)s 7450(be)s 3(yond)k 8222(the)s +8582(basic)s 0 832(constraints)m 1089(imposed)s 1961(by)s 2258(a)s 4(v)k 6(ailable)k +3169(space)s 3759(and)s 220 fnt35 4166 829(into)m 240 fnt82 +4575 832(clauses,)m 5375(in)s 5621(principle)s 6529(such)s 7028(high)s +7514(quality)s 8236(breaking)s 0 544(could)m 592(be)s 877(added)s +1510(to)s 1752(the)s 2102(implementation)s 3662(with)s 4147(no)s +4443(change)s 5180(to)s 5421(the)s 5772(language.)s 6803(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k +7766(the)s 8117(generality)s 0 256(of)m 280(the)s 637(g)s 1(alle)k 3(y)k +1280(\210ushing)s 2115(algorithm,)s 3160(and)s 3573(its)s 3859(already)s +4625(considerable)s 5898(comple)s 3(xity)k 15(,)k 7073(mak)s 2(e)k +7654(this)s 8059(a)s 8235(daunting)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 30 31 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Bold +%%+ font Helvetica +%%+ font Symbol +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4287 13844(-)m 4415(30)s 4710(-)s 0 13253(problem)m 890(in)s +1167(practice,)s 2062(although)s 2991(a)s 3190(f)s 2(ascinating)k +4323(one.)s 4866(T)s 5008 13205(E)m 5151 13253(X)m 5414([9],)s +5832(with)s 6348(its)s 6657(unnested)s 7600(set)s 7958(of)s +8263(`\210oating)s 0 12965(insertions')m 1041(clearly)s 1744(identi\207able)s 2875(as)s +3125(each)s 3620(page)s 4128(is)s 4338(be)s 3(gun,)k +5028(has)s 5398(the)s 5746(adv)s 6(antage)k 6766(in)s +7009(this)s 7405(respect.)s 240 fnt84 0 12316(5.3.)m 471(Size)s +938(constraints)s 2120(and)s 2561(size)s 2988(adjustments)s 240 fnt82 +480 11840(The)m 893(g)s 1(alle)k 3(y)k 1512(\210ushing)s +2321(algorithm)s 3295(needs)s 3876(to)s 4099(kno)s 6(w)k +4665(the)s 4998(a)s 4(v)k 6(ailable)k 5890(width)s +6477(and)s 6866(height)s 7508(at)s 7725(each)s 8204(recepti)s 6(v)k 3(e)k +0 11552(symbol.)m 869(These)s 1496(symbols)s 2346(may)s 2812(lie)s +3106(within)s 3775(arbitrarily)s 4782(comple)s 3(x)k 5659(objects,)s +6443(and)s 6847(the)s 3(y)k 7311(may)s 7777(compete)s +8644(with)s 0 11264(each)m 492(other)s 1040(for)s 1375(a)s 4(v)k 6(ailable)k +2280(space)s 2864(\(as)s 3189(body)s 3720(te)s 3(xt)k +4132(and)s 4533(footnote)s 5383(tar)s 4(gets)k 6062(do\),)s +6485(so)s 6748(this)s 7141(information)s 8323(must)s 8844(be)s +0 10976(e)m 3(xtracted)k 930(from)s 1454(the)s 1802(tree)s +2215(structure)s 3106(when)s 3682(required.)s 480 10602(F)m 3(or)k +869(e)s 3(xample,)k 1783(consider)s 2653(the)s 3001(object)s +220 fnt35 480 10101(5i @Wide { a / b })m 240 fnt82 0 9607(and)m 406(suppose)s +1236(that)s 1656(the)s 2006(width)s 2610(of)s 220 fnt35 +2883 9604(a)m 240 fnt82 3062 9607(is)m 240 fnt78 3274 9601(1)m +240 fnt83 3382 9609(i)m 240 fnt78 3459 9601(,)m 3572(2)s +240 fnt83 3700 9609(i)m 240 fnt82 3825 9607(\()m 240 fnt78 +3898 9601(1)m 240 fnt83 4006 9609(i)m 240 fnt82 4131 9607(to)m +4372(the)s 4722(left)s 5101(of)s 5374(the)s 5724(mark,)s +240 fnt78 6324 9601(2)m 240 fnt83 6452 9609(i)m 240 fnt82 +6577 9607(to)m 6818(the)s 7168(right\).)s 7864(What)s 8444(then)s +8916(is)s 0 9319(the)m 348(a)s 4(v)k 6(ailable)k +1256(width)s 1858(at)s 220 fnt35 2090 9316(b)m 240 fnt82 +2204 9319(?)m 2423(If)s 2653(we)s 2988(let)s 3286(the)s +3634(width)s 4236(of)s 220 fnt35 4507 9316(b)m 240 fnt82 +4681 9319(be)m 240 fnt83 4963 9321(l)m 240 fnt78 5041 9313(,)m +240 fnt83 5148 9321(r)m 240 fnt82 5246 9319(,)m 5353(we)s +5688(must)s 6213(ha)s 4(v)k 3(e)k 240 fnt78 +480 8771(\()m 564(1)s 240 fnt83 670 8779(i)m 240 fnt78 +817 8771(\255)m 240 fnt83 1038 8779(l)m 240 fnt78 1116 8771(\))m +1254(+)s 1455(\()s 1539(2)s 240 fnt83 1665 8779(i)m +240 fnt78 1812 8771(\255)m 240 fnt83 2033 8779(r)m 240 fnt78 +2143 8771(\))m 2293(\243)s 2503(5)s 240 fnt83 2622 8779(i)m +240 fnt82 0 8226(with)m 482(the)s 240 fnt78 842 8220(\255)m +240 fnt82 1051 8226(\(i.e.)m 1466(max\))s 2006(operations)s 3053(arising)s +3756(from)s 4280(mark)s 4832(alignment.)s 5952(Eliminating)s 7133(them)s +7671(gi)s 6(v)k 3(es)k 240 fnt78 480 7674(1)m +240 fnt83 586 7682(i)m 240 fnt78 721 7674(+)m 922(2)s +240 fnt83 1048 7682(i)m 240 fnt78 1207 7674(\243)m 1417(5)s +240 fnt83 1536 7682(i)m 583 7387(l)m 240 fnt78 721 7379(+)m +922(2)s 240 fnt83 1048 7387(i)m 240 fnt78 1207 7379(\243)m +1417(5)s 240 fnt83 1536 7387(i)m 240 fnt78 571 7091(1)m +240 fnt83 677 7099(i)m 240 fnt78 812 7091(+)m 240 fnt83 +1013 7099(r)m 240 fnt78 1207 7091(\243)m 1417(5)s 240 fnt83 +1536 7099(i)m 674 6804(l)m 240 fnt78 812 6796(+)m 240 fnt83 +1013 6804(r)m 240 fnt78 1207 6796(\243)m 1417(5)s 240 fnt83 +1536 6804(i)m 240 fnt82 0 6293(and)m 428(since)s 1000(we)s +1359(assume)s 2144(that)s 220 fnt35 2587 6290(a)m 240 fnt82 +2788 6293(\207ts)m 3156(into)s 3606(the)s 3978(a)s 4(v)k 6(ailable)k +4911(space,)s 5573(the)s 5946(\207rst)s 6402(inequality)s 7436(may)s +7927(be)s 8234(dropped,)s 0 6005(lea)m 4(ving)k 240 fnt83 +851 5454(l)m 240 fnt78 1013 5446(\243)m 1223(3)s 240 fnt83 +1340 5454(i)m 480 5159(l)m 240 fnt78 618 5151(+)m 240 fnt83 +819 5159(r)m 240 fnt78 1013 5151(\243)m 1223(5)s 240 fnt83 +1342 5159(i)m 819 4871(r)m 240 fnt78 1013 4863(\243)m 1223(4)s +240 fnt83 1348 4871(i)m 240 fnt82 0 4362(Object)m 220 fnt35 +697 4359(b)m 240 fnt82 871 4362(may)m 1337(ha)s 4(v)k 3(e)k +1838(width)s 240 fnt83 2440 4364(l)m 240 fnt78 2518 4356(,)m +240 fnt83 2625 4364(r)m 240 fnt82 2783 4362(for)m 3121(an)s 3(y)k +240 fnt83 3518 4364(l)m 240 fnt82 3644 4362(and)m 240 fnt83 +4048 4364(r)m 240 fnt82 4206 4362(satisfying)m 5188(these)s 5735(inequalities,)s +6943(and)s 7347(no)s 7640(others.)s 480 3988(Here)m 1000(is)s +1210(another)s 1987(e)s 3(xample:)k 220 fnt35 480 3487(5i @High { a /2ix b })m +240 fnt82 0 2986(Assuming)m 1024(that)s 220 fnt35 1442 2983(a)m +240 fnt82 1619 2986(has)m 1989(height)s 240 fnt78 2647 2980(1)m +240 fnt83 2753 2988(i)m 240 fnt78 2828 2980(,)m 2935(1)s +240 fnt83 3041 2988(i)m 240 fnt82 3104 2986(,)m 3211(the)s +3559(height)s 240 fnt83 4217 2988(l)m 240 fnt78 4295 2980(,)m +240 fnt83 4402 2988(r)m 240 fnt82 4560 2986(of)m 220 fnt35 +4831 2983(b)m 240 fnt82 5005 2986(must)m 5530(satisfy)s 240 fnt78 +480 2428(1)m 240 fnt83 586 2436(i)m 240 fnt78 721 2428(+)m +922(\()s 1006(\()s 1090(1)s 240 fnt83 1196 2436(i)m +240 fnt78 1331 2428(+)m 240 fnt83 1532 2436(l)m 240 fnt78 +1610 2428(\))m 1760(\255)s 1981(2)s 240 fnt83 2107 2436(i)m +240 fnt78 2182 2428(\))m 2320(+)s 240 fnt83 2521 2436(r)m +240 fnt78 2703 2428(\243)m 2913(5)s 240 fnt83 3032 2436(i)m +240 fnt82 0 1883(This)m 478(time)s 960(the)s 240 fnt78 +1325 1877(\255)m 240 fnt82 1539 1883(operation)m 2501(arises)s 3098(from)s +3624(the)s 3975(mark-to-mark)s 5364(g)s 1(ap)k 5765(mode,)s +6406(which)s 7050(will)s 7479(widen)s 8123(the)s 240 fnt78 +8474 1877(2)m 240 fnt83 8602 1885(i)m 240 fnt82 8728 1883(g)m 1(ap)k +0 1595(if)m 217(necessary)s 1200(to)s 1439(pre)s 6(v)k 3(ent)k +220 fnt35 2207 1592(a)m 240 fnt82 2384 1595(and)m 220 fnt35 +2788 1592(b)m 240 fnt82 2962 1595(from)m 3486(o)s 3(v)k 3(erlapping.)k +4787(This)s 5263(inequality)s 6273(can)s 6662(be)s 6944(re)s 6(written)k +7856(as)s 240 fnt83 851 1044(l)m 240 fnt78 1013 1036(\243)m +288 fnt78 1223 1024(\245)m 240 fnt83 480 753(l)m 240 fnt78 +618 745(+)m 240 fnt83 819 753(r)m 240 fnt78 1013 745(\243)m +1223(3)s 240 fnt83 1340 753(i)m 819 465(r)m 240 fnt78 +1013 457(\243)m 1223(2)s 240 fnt83 1349 465(i)m +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 31 32 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Symbol +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4297 13844(-)m 4425(31)s 4700(-)s 0 13253(In)m 263(general,)s +1080(Lout)s 1599(is)s 1816(designed)s 2732(so)s 3005(that)s +3430(the)s 3785(a)s 4(v)k 6(ailable)k 4700(width)s +5309(or)s 5575(height)s 6240(at)s 6479(an)s 3(y)k +6883(point)s 7442(can)s 7838(be)s 8128(e)s 3(xpressed)k +0 12965(by)m 294(three)s 827(inequalities)s 1979(of)s 2250(the)s +2598(form)s 240 fnt83 851 12414(l)m 240 fnt78 1013 12406(\243)m +240 fnt83 1223 12414(x)m 480 12123(l)m 240 fnt78 618 12115(+)m +240 fnt83 819 12123(r)m 240 fnt78 1013 12115(\243)m 240 fnt83 +1223 12123(y)m 819 11808(r)m 240 fnt78 1013 11800(\243)m 240 fnt83 +1223 11808(z)m 240 fnt82 0 11287(where)m 240 fnt83 641 11289(x)m +240 fnt82 747 11287(,)m 240 fnt83 855 11289(y)m 240 fnt82 +1018 11287(and)m 240 fnt83 1423 11289(z)m 240 fnt82 1575 11287(may)m +2042(be)s 288 fnt78 2325 11269(\245)m 240 fnt82 2523 11287(.)m +2688(W)s 19(e)k 3058(abbre)s 6(viate)k 4104(these)s +4652(three)s 5186(inequalities)s 6339(to)s 240 fnt83 6579 11289(l)m +240 fnt78 6658 11281(,)m 240 fnt83 6768 11289(r)m 240 fnt78 +6953 11281(\243)m 240 fnt83 7166 11289(x)m 240 fnt78 7285 11281(,)m +240 fnt83 7395 11289(y)m 240 fnt78 7510 11281(,)m 240 fnt83 +7620 11289(z)m 240 fnt82 7711 11287(,)m 7819(and)s 8224(we)s +8560(call)s 240 fnt83 8960 11289(x)m 240 fnt78 0 10993(,)m +240 fnt83 107 11001(y)m 240 fnt78 221 10993(,)m 240 fnt83 +328 11001(z)m 240 fnt82 479 10999(a)m 240 fnt83 645 11001(size)m +1056(constr)s 3(aint)k 240 fnt82 2027 10999(.)m 480 10625(The)m +920(tw)s 2(o)k 1343(e)s 3(xamples)k 2307(abo)s 3(v)k 3(e)k +2942(sho)s 6(wed)k 3739(ho)s 6(w)k 4213(to)s +4465(propag)s 1(ate)k 5475(the)s 5836(size)s 6276(constraint)s +288 fnt78 7291 10607(\245)m 240 fnt78 7514 10619(,)m 7659(5)s +240 fnt83 7791 10627(i)m 240 fnt78 7879 10619(,)m 288 fnt78 +8025 10607(\245)m 240 fnt82 8296 10625(for)m 220 fnt35 8647 10622(a / b)m +240 fnt82 0 10337(do)m 6(wn)k 586(one)s 991(le)s 6(v)k 3(el)k +1504(to)s 1746(the)s 2097(child)s 220 fnt35 2636 10334(b)m +240 fnt82 2750 10337(.)m 2917(Basser)s 3617(Lout)s 4132(contains)s +4982(a)s 5151(complete)s 6086(set)s 6414(of)s 6688(general)s +7449(rules)s 7967(for)s 8308(all)s 8604(node)s 0 10049(types,)m +627(too)s 1002(complicated)s 2244(to)s 2499(gi)s 6(v)k 3(e)k +2974(here.)s 3565(Instead,)s 4378(we)s 4729(gi)s 6(v)k 3(e)k +5203(just)s 5624(one)s 6042(e)s 3(xample)k 6921(of)s +7208(ho)s 6(w)k 7685(these)s 8248(rules)s 8779(are)s +0 9761(deri)m 6(v)k 3(ed,)k 815(using)s 1387(the)s +1735(object)s 240 fnt83 480 9265(x)m 168 fnt78 586 9172(1)m +220 fnt35 772 9260(/)m 240 fnt83 956 9265(x)m 168 fnt78 +1062 9172(2)m 220 fnt35 1262 9260(/)m 240 fnt83 1446 9265(.)m +1552(.)s 1658(.)s 220 fnt35 1812 9260(/)m 240 fnt83 +1996 9265(x)m 168 fnt83 2102 9178(n)m 240 fnt82 0 8719(where)m +240 fnt83 640 8721(x)m 168 fnt83 746 8634(j)m 240 fnt82 +852 8719(has)m 1222(width)s 240 fnt83 1824 8721(l)m 168 fnt83 +1890 8634(j)m 240 fnt78 1948 8713(,)m 240 fnt83 2055 8721(r)m +168 fnt83 2127 8634(j)m 240 fnt82 2233 8719(for)m 2571(all)s +240 fnt83 2864 8721(j)m 240 fnt82 2930 8719(.)m 480 8345(Suppose)m +1345(the)s 1689(whole)s 2326(object)s 2966(has)s 3333(width)s +3931(constraint)s 240 fnt83 4929 8347(X)m 240 fnt78 5097 8339(,)m +240 fnt83 5204 8347(Y)m 240 fnt78 5367 8339(,)m 240 fnt83 +5474 8347(Z)m 240 fnt82 5619 8345(,)m 5722(and)s 6123(we)s +6454(require)s 7182(the)s 7526(width)s 8124(constraint)s 0 8057(of)m +240 fnt83 271 8059(x)m 168 fnt83 377 7972(i)m 240 fnt82 +421 8057(.)m 586(Let)s 240 fnt83 965 8059(L)m 240 fnt78 +1185 8051(=)m 240 fnt82 1401 8057(max)m 168 fnt83 1808 7972(j)m +240 fnt83 1917 8059(l)m 168 fnt83 1983 7972(j)m 240 fnt82 +2090 8057(and)m 240 fnt83 2495 8059(R)m 240 fnt78 2723 8051(=)m +240 fnt82 2939 8057(max)m 168 fnt83 3346 7972(j)m 240 fnt83 +3455 8059(r)m 168 fnt83 3527 7972(j)m 240 fnt82 3573 8057(,)m +3681(so)s 3948(that)s 240 fnt83 4367 8059(L)m 240 fnt78 +4512 8051(,)m 240 fnt83 4619 8059(R)m 240 fnt82 4821 8057(is)m +5032(the)s 5381(width)s 5984(of)s 6256(the)s 6605(whole)s +7247(object.)s 7996(W)s 19(e)k 8366(assume)s 240 fnt83 +0 7746(L)m 240 fnt78 145 7738(,)m 240 fnt83 252 7746(R)m +240 fnt78 477 7738(\243)m 240 fnt83 687 7746(X)m 240 fnt78 +855 7738(,)m 240 fnt83 962 7746(Y)m 240 fnt78 1125 7738(,)m +240 fnt83 1232 7746(Z)m 240 fnt82 1377 7744(.)m 1541(Then)s +240 fnt83 2090 7746(x)m 168 fnt83 2196 7659(i)m 240 fnt82 +2300 7744(can)m 2689(be)s 2971(enlar)s 4(ged)k 3848(to)s +4087(an)s 3(y)k 4484(size)s 240 fnt83 4911 7746(l)m +168 fnt83 4977 7659(i)m 240 fnt78 5081 7738(,)m 240 fnt83 +5188 7746(r)m 168 fnt83 5260 7659(i)m 240 fnt82 5364 7744(satisfying)m +240 fnt78 480 7151(\()m 240 fnt83 564 7159(l)m 168 fnt83 +630 7072(i)m 240 fnt78 758 7151(\255)m 240 fnt83 979 7159(L)m +240 fnt78 1124 7151(\))m 1202(,)s 1309(\()s 240 fnt83 +1393 7159(r)m 168 fnt83 1465 7072(i)m 240 fnt78 1593 7151(\255)m +240 fnt83 1814 7159(R)m 240 fnt78 1967 7151(\))m 2117(\243)s +240 fnt83 2327 7159(X)m 240 fnt78 2495 7151(,)m 240 fnt83 +2602 7159(Y)m 240 fnt78 2765 7151(,)m 240 fnt83 2872 7159(Z)m +240 fnt82 0 6619(which)m 642(e)s 3(xpands)k 1475(to)s +1714(eight)s 2252(inequalities:)s 240 fnt83 917 6068(l)m 168 fnt83 +983 5981(i)m 240 fnt78 1123 6060(\243)m 240 fnt83 1333 6068(X)m +894 5704(L)m 240 fnt78 1123 5696(\243)m 240 fnt83 1333 5704(X)m +528 5413(l)m 168 fnt83 594 5326(i)m 240 fnt78 710 5405(+)m +240 fnt83 911 5413(r)m 168 fnt83 983 5326(i)m 240 fnt78 +1123 5405(\243)m 240 fnt83 1333 5413(Y)m 503 5041(l)m 168 fnt83 +569 4954(i)m 240 fnt78 685 5033(+)m 240 fnt83 886 5041(R)m +240 fnt78 1123 5033(\243)m 240 fnt83 1333 5041(Y)m 505 4677(L)m +240 fnt78 710 4669(+)m 240 fnt83 911 4677(r)m 168 fnt83 +983 4590(i)m 240 fnt78 1123 4669(\243)m 240 fnt83 1333 4677(Y)m +480 4313(L)m 240 fnt78 685 4305(+)m 240 fnt83 886 4313(R)m +240 fnt78 1123 4305(\243)m 240 fnt83 1333 4313(Y)m 911 4030(r)m +168 fnt83 983 3943(i)m 240 fnt78 1123 4022(\243)m 240 fnt83 +1333 4030(Z)m 886 3666(R)m 240 fnt78 1123 3658(\243)m 240 fnt83 +1333 3666(Z)m 240 fnt82 0 3159(Three)m 613(are)s 960(already)s +1717(kno)s 6(wn,)k 2471(and)s 2875(slightly)s 3646(rearranging)s +4800(the)s 5148(others)s 5783(gi)s 6(v)k 3(es)k +240 fnt83 869 2608(l)m 168 fnt83 935 2521(i)m 240 fnt78 +1075 2600(\243)m 240 fnt83 1285 2608(X)m 869 2236(l)m 168 fnt83 +935 2149(i)m 240 fnt78 1075 2228(\243)m 240 fnt83 1285 2236(Y)m +240 fnt78 1508 2228(-)m 240 fnt83 1708 2236(R)m 480 1864(l)m +168 fnt83 546 1777(i)m 240 fnt78 662 1856(+)m 240 fnt83 +863 1864(r)m 168 fnt83 935 1777(i)m 240 fnt78 1075 1856(\243)m +240 fnt83 1285 1864(Y)m 863 1500(r)m 168 fnt83 935 1413(i)m +240 fnt78 1075 1492(\243)m 240 fnt83 1285 1500(Z)m 863 1136(r)m +168 fnt83 935 1049(i)m 240 fnt78 1075 1128(\243)m 240 fnt83 +1285 1136(Y)m 240 fnt78 1508 1128(-)m 240 fnt83 1708 1136(L)m + +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 32 33 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Symbol +%%+ font Times-Bold +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Symbol +/fnt78 { /Symbol LoutFont } def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(32)s 4710(-)s 0 13253(Therefore)m 997(the)s +1345(width)s 1947(constraint)s 2949(of)s 240 fnt83 3220 13255(x)m +168 fnt83 3326 13168(i)m 240 fnt82 3430 13253(is)m 480 12715(min)m +240 fnt78 861 12709(\()m 240 fnt83 945 12717(X)m 240 fnt78 +1113 12709(,)m 240 fnt83 1220 12717(Y)m 240 fnt78 1443 12709(-)m +240 fnt83 1643 12717(R)m 240 fnt78 1796 12709(\))m 1874(,)s +240 fnt83 1981 12717(Y)m 240 fnt78 2144 12709(,)m 240 fnt82 +2251 12715(min)m 240 fnt78 2632 12709(\()m 240 fnt83 2716 12717(Z)m +240 fnt78 2873 12709(,)m 240 fnt83 2980 12717(Y)m 240 fnt78 +3203 12709(-)m 240 fnt83 3403 12717(L)m 240 fnt78 3548 12709(\))m +240 fnt82 0 12213(The)m 445(size)s 890(constraint)s 1909(of)s +2198(an)s 3(y)k 2613(node)s 3152(can)s 3559(be)s +3858(found)s 4493(by)s 4805(climbing)s 5725(the)s 6091(tree)s +6521(to)s 6778(a)s 240 fnt83 6962 12215(WIDE)m 240 fnt82 +7641 12213(or)m 240 fnt83 7918 12215(HIGH)m 240 fnt82 8604 12213(node)m +0 11925(where)m 636(the)s 980(constraint)s 1978(is)s 2184(tri)s 6(vial,)k +2850(then)s 3315(propag)s 1(ating)k 4506(it)s 4694(back)s +5203(do)s 6(wn)k 5783(to)s 6018(the)s 6362(node,)s +6931(and)s 7331(this)s 7723(is)s 7929(the)s 8272(function)s +0 11637(of)m 271(procedure)s 240 fnt83 1283 11639(Constr)m 3(ained)k +240 fnt82 2530 11637(in)m 2773(Basser)s 3470(Lout.)s 480 11263(After)m +1043(some)s 1604(components)s 2813(ha)s 4(v)k 3(e)k +3314(been)s 3824(promoted)s 4799(into)s 5225(a)s 5391(tar)s 4(get,)k +6038(the)s 6386(sizes)s 6902(stored)s 7544(in)s 7788(its)s +8064(parent)s 8722(and)s 0 10975(higher)m 665(ancestors)s 1598(must)s +2117(be)s 2392(adjusted)s 3241(to)s 3473(re\210ect)s 4122(the)s +4464(increased)s 5417(size.)s 5946(This)s 6415(is)s 6618(done)s +7134(by)s 7421(yet)s 7767(another)s 8537(set)s 8855(of)s +0 10687(recursi)m 6(v)k 3(e)k 925(rules,)s 1500(upw)s 2(ard-mo)k 3(ving)k +3081(this)s 3481(time,)s 4016(which)s 4662(cease)s 5239(as)s +5492(soon)s 6006(as)s 6260(some)s 6825(ancestor')s 13(s)k +7835(size)s 8266(does)s 8760(not)s 0 10399(change.)m 830(These)s +1445(rules)s 1948(are)s 2283(embodied)s 3273(in)s 3504(procedure)s +240 fnt83 4504 10401(AdjustSize)m 240 fnt82 5541 10399(of)m 5800(Basser)s +6485(Lout.)s 7089(The)s 7505(adjustment)s 8601(must)s 0 10111(be)m +282(done)s 804(before)s 1470(relinquishing)s 2785(control)s 3517(to)s +3756(an)s 3(y)k 4153(other)s 4704(g)s 1(alle)k 3(y)k 15(,)k +5376(b)s 4(ut)k 5738(not)s 6104(after)s 6600(e)s 6(v)k 3(ery)k +7176(component.)s 240 fnt84 0 9462(5.4.)m 471(The)s 926(limited)s +1696(lookahead)s 2802(pr)s 4(oblem)k 240 fnt82 480 8985(Basser)m +1189(Lout)s 1714(assumes)s 2575(that)s 3006(there)s 3552(will)s +3991(be)s 4286(enough)s 5062(internal)s 5859(memory)s 6723(to)s +6975(hold)s 7472(the)s 7833(symbol)s 8606(table)s 0 8697(plus)m +461(a)s 638(fe)s 6(w)k 1055(pages,)s 1719(b)s 4(ut)k +2092(not)s 2469(an)s 2764(entire)s 3374(document.)s 4493(This)s +4980(section)s 5726(describes)s 6677(the)s 7036(consequent)s 8185(problems)s +0 8409(and)m 441(ho)s 6(w)k 940(the)s 3(y)k +1441(were)s 1999(solv)s 3(ed.)k 2763(Other)s 3405(interpreters,)s +4636(notably)s 5446(interacti)s 6(v)k 3(e)k 6538(editors)s +7277(running)s 8113(on)s 8448(virtual)s 0 8121(memory)m 851(systems,)s +1715(w)s 2(ould)k 2370(not)s 2736(necessarily)s 3851(need)s +4361(this)s 4757(assumption.)s 480 7747(Although)m 1434(Basser)s 2122(Lout)s +2625(can)s 3005(read)s 3466(and)s 3861(format)s 4548(an)s 3(y)k +4936(le)s 3(g)k 1(al)k 5442(input,)s 6033(its)s +6300(memory)s 7142(consumption)s 8427(will)s 8844(be)s 0 7459(optimized)m +1004(when)s 1570(the)s 1908(b)s 4(ulk)k 2381(of)s +2642(the)s 2980(document)s 3974(resides)s 4677(in)s 4910(g)s 1(alle)k 3(ys)k +5624(whose)s 6282(tar)s 4(gets)k 6955(can)s 7334(be)s +7606(identi\207ed)s 8557(at)s 8778(the)s 0 7171(moment)m 843(the)s 3(y)k +1304(are)s 1650(encountered.)s 2981(Let)s 3358(us)s 3620(tak)s 2(e)k +4071(the)s 4417(typical)s 5121(e)s 3(xample)k 5982(of)s +6252(a)s 6416(root)s 6860(g)s 1(alle)k 3(y)k +7492(which)s 8133(is)s 8341(a)s 8506(list)s 8855(of)s +0 6883(pages,)m 652(a)s 220 fnt35 818 6880(@BodyT)m 26(e)k 6(xt)k +240 fnt82 1991 6883(g)m 1(alle)k 3(y)k 2625(tar)s 4(geted)k +3448(into)s 3872(the)s 4220(pages,)s 220 fnt35 4872 6880(@Chapter)m +240 fnt82 5934 6883(g)m 1(alle)k 3(ys)k 6658(tar)s 4(geted)k +7481(into)s 220 fnt35 7905 6880(@BodyT)m 26(e)k 6(xt)k +240 fnt82 9019 6883(,)m 0 6595(and)m 220 fnt35 404 6592(@Section)m +240 fnt82 1404 6595(g)m 1(alle)k 3(ys)k 2128(tar)s 4(geted)k +2951(into)s 3376(the)s 220 fnt35 3724 6592(@Chapter)m 240 fnt82 +4787 6595(g)m 1(alle)k 3(ys:)k 220 fnt35 480 6094(@P)m 8(ageList)k +480 5806(//)m 480 5518(@BodyT)m 26(e)k 6(xt)k 480 5230(//)m +480 4942(@Chapter {)m 480 4654( @Section { ...)m 13( })k 480 4366( @Section { ...)m 13( })k +480 4078( ...)m 480 3790( @Section { ...)m 13( })k 480 3502(})m 480 3214(@Chapter {)m +480 2926( ...)m 480 2638(})m 240 fnt82 0 2144(Basser)m 702(Lout)s +1220(is)s 1436(able)s 1896(to)s 2141(read)s 2616(and)s +3026(process)s 3800(such)s 4302(g)s 1(alle)k 3(ys)k +5032(one)s 5440(paragraph)s 6459(at)s 6697(a)s 6869(time)s +7355(\(strictly)s 15(,)k 8194(from)s 8724(one)s 220 fnt35 +0 1853(//)m 240 fnt82 185 1856(at)m 417(the)s 765(outer)s +1316(le)s 6(v)k 3(el)k 1826(of)s 2097(a)s +2263(g)s 1(alle)k 3(y)k 2897(to)s 3136(the)s +3484(ne)s 3(xt\),)k 4079(as)s 4329(we)s 4664(no)s 6(w)k +5125(describe.)s 480 1482(When)m 1147(the)s 1534(parser)s 2215(encounters)s +3341(the)s 3727(be)s 3(ginning)k 4774(of)s 5083(a)s +5288(g)s 1(alle)k 3(y)k 15(,)k 5998(lik)s 2(e)k +220 fnt35 6449 1479(@Chapter)m 240 fnt82 7550 1482(or)m 220 fnt35 +7848 1479(@Section)m 240 fnt82 8788 1482(,)m 8934(it)s 0 1194(initiates)m +831(a)s 1023(ne)s 6(w)k 1495(g)s 1(alle)k 3(y)k +2155(process.)s 3061(The)s 3515(special)s 4258(recepti)s 6(v)k 3(e)k +5206(symbol)s 220 fnt35 5991 1191(@Input)m 240 fnt82 6784 1194(is)m +7019(substituted)s 8139(for)s 8502(the)s 8876(as)s 0 906(yet)m +357(unread)s 1071(right)s 1588(parameter)s 2607(of)s 2884(the)s +3237(g)s 1(alle)k 3(y)k 15(.)k 3972(As)s +4294(each)s 4795(paragraph)s 5813(of)s 6090(the)s 6443(right)s +6960(parameter)s 7979(is)s 8195(read,)s 8718(it)s 8916(is)s +0 618(deleted)m 763(from)s 1302(the)s 1665(parse)s 2240(tree)s +2668(and)s 3087(injected)s 3916(into)s 4356(the)s 4719(g)s 1(alle)k 3(y')k 13(s)k +220 fnt35 5524 615(@Input)m 240 fnt82 6231 618(.)m 6410(The)s +6853(g)s 1(alle)k 3(y)k 7502(is)s 7727(then)s +8212(resumed.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 33 34 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4293 13844(-)m 4421(33)s 4705(-)s 0 13253(The)m 429(parser)s +1074(thus)s 1526(acts)s 1950(as)s 2202(an)s 2487(e)s 3(xtra)k +3022(concurrent)s 4106(process;)s 4937(it)s 5131(has)s 5503(lo)s 6(w)k +5912(priority)s 15(,)k 6721(so)s 6989(that)s 7409(input)s +7963(is)s 8175(read)s 8646(only)s 0 12965(when)m 597(there)s +1151(is)s 1382(nothing)s 2188(else)s 2636(to)s 2897(do.)s +3322(Since)s 3930(g)s 1(alle)k 3(ys)k 4675(may)s +5162(be)s 5465(nested,)s 6205(a)s 6392(stack)s 6965(of)s +220 fnt35 7257 12962(@Input)m 240 fnt82 8045 12965(symbols)m 8916(is)s +0 12677(needed,)m 781(each)s 1271(with)s 1749(its)s 2020(o)s 6(wn)k +2480(en)s 9(vironment)k 3735(and)s 4135(style.)s 4745(If)s +4971(a)s 5132(g)s 1(alle)k 3(y)k 5762(is)s +5967(encountered)s 7190(for)s 7523(which)s 8161(a)s 8322(tar)s 4(get)k +8916(is)s 0 12389(not)m 370(immediately)s 1622(identi\207able)s 2757(\(a)s +3006(footnote,)s 3914(for)s 4257(e)s 3(xample\),)k 5254(it)s +5450(is)s 5664(read)s 6137(in)s 6385(its)s 6665(entirety)s +7452(and)s 7860(hung)s 8397(in)s 8645(pure)s 0 12101(parse)m +551(tree)s 954(form)s 1468(from)s 1983(an)s 240 fnt83 +2256 12103(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k +240 fnt82 3811 12101(inde)m 3(x)k 4386(in)s 4619(the)s +4957(usual)s 5508(w)s 2(ay)k 15(,)k 5987(with)s +6459(an)s 6733(en)s 9(vironment)k 7983(b)s 4(ut)k +8335(without)s 0 11813(a)m 166(style.)s 781(It)s 986(will)s +1412(be)s 1694(\210ushed)s 2444(later)s 2927(when)s 3503(its)s +3779(component)s 4903(is)s 5113(promoted.)s 480 11439(In)m 735(addition)s +1575(to)s 1813(producing)s 2836(a)s 3001(steady)s 3665(\210o)s 6(w)k +4138(of)s 4407(components)s 5614(from)s 6137(input,)s 6735(we)s +7069(must)s 7593(also)s 8030(ensure)s 8708(that)s 0 11151(recepti)m 6(v)k 3(e)k +928(symbols)s 1783(do)s 2083(not)s 2455(unduly)s 3182(block)s +3781(their)s 4285(promotion.)s 5452(The)s 220 fnt35 5886 11148(@F)m 6(ootSect)k +240 fnt82 7044 11151(symbol)m 7810(at)s 8049(the)s 8403(foot)s +8855(of)s 0 10863(each)m 495(page)s 1003(is)s 1213(a)s +1379(typical)s 2084(e)s 3(xample:)k 3057(until)s 3550(it)s +3742(is)s 3952(deleted)s 4700(the)s 5048(page)s 5556(cannot)s +6254(be)s 6536(printed.)s 480 10489(Recepti)m 6(v)k 3(e)k +1501(symbols)s 2368(are)s 2733(e)s 3(xpanded)k 3724(only)s +4222(on)s 4537(demand,)s 5421(so)s 220 fnt35 5705 10486(@F)m 6(ootSect)k +240 fnt82 6874 10489(can)m 7281(be)s 7581(deleted)s 8347(as)s +8616(soon)s 0 10201(as)m 250(we)s 585(can)s 974(pro)s 3(v)k 3(e)k +1570(that)s 1988(it)s 2180(is)s 2390(not)s 2757(w)s 2(anted.)k +3610(The)s 4038(symbol)s 4799(table)s 5319(can)s 5708(tell)s +6067(us)s 6332(that)s 6750(only)s 220 fnt35 7230 10198(@F)m 6(ootNote)k +240 fnt82 8402 10201(g)m 1(alle)k 3(ys)k 0 9913(\(with)m +220 fnt35 555 9910(@F)m 6(ootPlace&&f)k 6(ollo)k 3(wing)k +240 fnt82 2935 9913(tar)m 4(gets\))k 3688(w)s 2(ant)k +4205(it,)s 4438(so)s 4697(it)s 4883(might)s 5494(be)s +5770(possible)s 6604(to)s 6836(deduce)s 7564(that)s 220 fnt35 +7975 9910(@F)m 6(ootSect)k 240 fnt82 0 9625(may)m 466(be)s +748(deleted)s 1496(as)s 1746(soon)s 2256(as)s 2506(body)s +3040(te)s 3(xt)k 3455(enters)s 4076(the)s 4424(follo)s 6(wing)k +5401(page.)s 480 9251(The)m 904(author)s 1571(w)s 2(as)k +1987(unable)s 2677(to)s 2912(mak)s 2(e)k 3479(this)s +3871(w)s 2(ork,)k 4463(so)s 4725(Basser)s 5418(Lout)s +5925(requires)s 6741(the)s 7085(user)s 7538(to)s 7773(identify)s +8565(those)s 0 8963(g)m 1(alle)k 3(ys)k 715(which)s +1348(will)s 1764(carry)s 2299(the)s 2637(b)s 4(ulk)k +3111(of)s 3372(the)s 3711(document)s 4705(\()s 220 fnt35 +4778 8960(@Chapter)m 240 fnt82 5781 8963(,)m 220 fnt35 5879 8960(@Section)m +240 fnt82 6819 8963(,)m 220 fnt35 6916 8960(@BodyT)m 26(e)k 6(xt)k +240 fnt82 8030 8963(\))m 8149(as)s 240 fnt83 8389 8965(for)m 8(cing)k +0 8677(galle)m 7(ys)k 240 fnt82 665 8675(,)m 792(by)s +1107(writing)s 220 fnt35 1871 8672(f)m 6(orce into)k 240 fnt82 +2841 8675(instead)m 3596(of)s 220 fnt35 3888 8672(into)m 240 fnt82 +4315 8675(in)m 4579(their)s 5097(de\207nitions.)s 6291(As)s 6629(described)s +7624(in)s 7888(the)s 8257(pre)s 6(vious)k 0 8387(section,)m +790(when)s 1373(a)s 1546(forcing)s 2296(g)s 1(alle)k 3(y)k +2937(attaches)s 3763(to)s 4009(a)s 4182(tar)s 4(get,)k +4835(all)s 5135(recepti)s 6(v)k 3(e)k 6063(symbols)s +6919(preceding)s 7922(the)s 8277(tar)s 4(get)k 8883(in)s +0 8099(its)m 278(g)s 1(alle)k 3(y)k 914(are)s +1263(deleted,)s 2062(remo)s 3(ving)k 3031(all)s 3326(impediments)s +4614(to)s 4855(\210ushing.)s 5793(F)s 3(or)k 6184(e)s 3(xample,)k +7100(when)s 7678(a)s 7846(forcing)s 8592(body)s 0 7811(te)m 3(xt)k +421(g)s 1(alle)k 3(y)k 1062(enters)s 1690(a)s +1863(ne)s 6(w)k 2317(page,)s 2882(the)s 220 fnt35 +3237 7808(@F)m 6(ootSect)k 240 fnt82 4395 7811(symbol)m 5162(on)s +5466(the)s 5820(preceding)s 6823(page)s 7338(will)s 7771(be)s +8060(deleted.)s 8921(It)s 0 7523(seems)m 629(lik)s 2(ely)k +1219(that)s 1631(a)s 1791(system)s 2509(which)s 3145(could)s +3729(af)s 6(ford)k 4358(to)s 4591(w)s 2(ait)k +5054(until)s 5541(all)s 5828(input)s 6374(w)s 2(as)k +6789(read)s 7252(before)s 7912(deleting)s 8729(an)s 3(y)k +0 7235(recepti)m 6(v)k 3(e)k 922(symbols)s 1771(w)s 2(ould)k +2426(not)s 2792(need)s 3302(forcing)s 4045(g)s 1(alle)k 3(ys.)k +480 6861(Galle)m 3(ys)k 1258(whose)s 1925(tar)s 4(gets)k +2607(are)s 2953(a)s 3118(long)s 3597(w)s 2(ay)k +4047(from)s 4570(their)s 5066(in)s 9(v)k 4(ocation)k +6119(points)s 6755(can)s 7143(be)s 7424(a)s 7589(problem.)s +8549(If)s 8778(the)s 0 6573(direction)m 917(is)s 220 fnt35 +1139 6570(f)m 6(ollo)k 3(wing)k 240 fnt82 1969 6573(,)m +2087(such)s 2595(g)s 1(alle)k 3(ys)k 3330(are)s +3689(held)s 4170(in)s 4425(internal)s 5221(memory)s 6083(for)s +6433(a)s 6610(long)s 7101(time,)s 7643(unless)s 8304(the)s 3(y)k +8779(are)s 0 6285(to)m 248(be)s 539(sorted.)s 1296(If)s +1535(the)s 1892(direction)s 2807(is)s 220 fnt35 3026 6282(preceding)m +240 fnt82 3977 6285(,)m 4093(then)s 4571(either)s 5183(the)s +5540(entire)s 6148(interv)s 3(ening)k 7296(document)s 8309(must)s +8844(be)s 0 5997(held)m 466(in)s 704(memory)s 1551(\(pre)s 6(v)k 3(ented)k +2617(by)s 2907(the)s 3250(tar)s 4(get)k 3844(from)s +4364(\210ushing\),)s 5317(or)s 5572(else)s 5994(some)s 6551(forcing)s +7289(g)s 1(alle)k 3(y)k 7918(prematurely)s 0 5709(deletes)m +714(the)s 1062(tar)s 4(get,)k 1708(lea)s 4(ving)k +2461(the)s 2809(g)s 1(alle)k 3(y)k 3443(bereft.)s +480 5335(The)m 929(typical)s 1655(e)s 3(xample)k 2539(of)s +2832(the)s 3201(latter)s 3771(case)s 4260(occurs)s 4956(when)s +5553(the)s 5922(g)s 1(alle)k 3(y)k 6578(is)s +6809(an)s 7113(entry)s 7680(in)s 7944(the)s 8313(table)s +8855(of)s 0 5047(contents,)m 907(launched)s 1832(backw)s 2(ards)k +2907(from)s 3435(the)s 3786(be)s 3(ginning)k 4797(of)s +5071(a)s 5241(chapter)s 6007(or)s 6269(section.)s 7113(Its)s +7406(tar)s 4(get)k 8008(in)s 8254(the)s 8606(table)s +0 4759(of)m 286(contents)s 1150(will)s 1592(ha)s 4(v)k 3(e)k +2108(been)s 2633(deleted)s 3397(long)s 3891(before,)s 4624(to)s +4879(permit)s 5578(the)s 5941(rest)s 6361(of)s 6648(the)s +7011(document)s 8031(to)s 8286(print,)s 8860(so)s 0 4471(the)m +349(g)s 1(alle)k 3(y)k 985(ultimately)s 2009(emer)s 4(ges)k +2854(as)s 3106(an)s 3391(unattached)s 4487(g)s 1(alle)k 3(y)k +5122(promoted)s 6099(out)s 6467(of)s 6740(the)s 7090(root)s +7537(g)s 1(alle)k 3(y)k 15(.)k 8268(All)s +8630(such)s 0 4183(g)m 1(alle)k 3(ys)k 717(are)s +1056(written)s 1781(to)s 2013(an)s 2288(auxiliary)s 3183(\207le,)s +3588(inde)s 3(x)k 3(ed)k 4390(by)s 4676(the)s +5016(missing)s 5806(tar)s 4(get.)k 6501(On)s 6843(the)s +7184(ne)s 3(xt)k 7645(run,)s 8063(just)s 8460(before)s +0 3895(that)m 418(tar)s 4(get)k 1017(is)s 1227(deleted,)s +2024(the)s 2372(auxiliary)s 3275(\207le)s 3636(is)s 3846(check)s 2(ed)k +4686(and)s 5090(an)s 3(y)k 5487(g)s 1(alle)k 3(ys)k +6211(for)s 6549(it)s 6741(are)s 7088(read)s 7557(in)s +7800(and)s 8204(\210ushed.)s 240 fnt84 0 3246(5.5.)m 471(Horizontal)s +1628(galleys)s 240 fnt82 480 2769(There)m 1108(is)s 1333(a)s +1514(strong)s 2180(analogy)s 3007(between)s 3876(breaking)s 4781(a)s +4962(column)s 5752(of)s 6038(te)s 3(xt)k 6468(into)s +6908(page-sized)s 8003(pieces,)s 8722(and)s 0 2481(breaking)m 912(a)s +1101(paragraph)s 2137(into)s 2585(line-sized)s 3594(pieces.)s 4378(In)s +4657(f)s 2(act,)k 5142(the)s 5513(tw)s 2(o)k +5946(dif)s 6(fer)k 6552(only)s 7055(in)s 7321(direction:)s +8359(v)s 3(ertical)k 0 2193(for)m 343(body)s 883(te)s 3(xt,)k +1351(horizontal)s 2381(for)s 2724(paragraphs.)s 3943(In)s 4205(this)s +4607(section)s 5347(we)s 5687(de\207ne)s 240 fnt83 6334 2195(horizontal)m +7384(galle)s 7(ys)k 240 fnt82 8049 2193(,)m 8162(and)s +8572(sho)s 6(w)k 0 1905(ho)m 6(w)k 493(the)s 3(y)k +989(pro)s 3(vide)k 1806(an)s 2122(unlimited)s 3129(number)s +3953(of)s 4257(paragraph)s 5302(breaking)s 6225(styles,)s 6909(as)s +7192(well)s 7691(as)s 7974(solv)s 3(e)k 8565(some)s +0 1617(other)m 587(problems.)s 1677(Re)s 3(grettably)k 15(,)k +2917(lack)s 3412(of)s 3719(time)s 4235(has)s 4641(pre)s 6(v)k 3(ented)k +5669(their)s 6202(incorporation)s 7583(into)s 8044(the)s 8429(Basser)s +0 1329(Lout)m 512(interpreter)s 13(.)k 480 955(Imagine)m 1337(a)s +1521(g)s 1(alle)k 3(y)k 2173(whose)s 2859(components)s +4085(are)s 4450(separated)s 5428(by)s 5740(horizontal)s 6782(concatenation)s +8186(operators)s 0 667(instead)m 725(of)s 986(v)s 3(ertical)k +1742(ones,)s 2278(perhaps)s 3062(indicated)s 3986(by)s 4269(a)s +220 fnt35 4425 664(hor)m -3(iz)k 3(ontally)k 5582(into)s +240 fnt82 5977 667(clause.)m 6728(Then)s 7266(all)s 7549(object)s +8182(breaking,)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 34 35 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13844(-)m 4416(34)s 4710(-)s 0 13253(including)m 957(paragraph)s +1970(breaking,)s 2914(could)s 3504(be)s 3786(replaced)s 4653(by)s +4947(g)s 1(alle)k 3(y)k 5581(component)s 6705(promotion)s +7759(lik)s 2(e)k 8171(this:)s 220 fnt35 480 12752(def @P)m 8(ar)k 2(ag)k 2(r)k 2(aph r)k -3(ight x)k +480 12464({)m 480 12176( def @LinePlace { @Galle)m 4(y })k 480 11600( def @LineList)m 480 11312( {)m +480 11024( @HExpand @LinePlace)m 480 10736( //1vx @LineList)m 480 10448( })m 480 9872( def @P)m 8(ar hor)k -3(iz)k 3(ontally into { @LinePlace&&preceding })k +480 9584( r)m -3(ight x)k 480 9296( { x })m 480 8720( @LineList // @P)m 8(ar { 0.2i @Wide {} &0i x &1r)k -8(t })k +480 8432(})m 240 fnt82 0 7938(The)m 220 fnt35 431 7935(@HExpand)m +240 fnt82 1607 7938(operator)m 9(,)k 2504(which)s 3149(is)s +3362(a)s 3531(primiti)s 6(v)k 3(e)k 4456(of)s +4730(Basser)s 5430(Lout,)s 5992(horizontally)s 7204(e)s 3(xpands)k +8040(the)s 8391(g)s 1(aps)k 8883(in)s 0 7650(its)m +290(right)s 816(parameter)s 1844(until)s 2352(the)s 2715(result)s +3319(\207lls)s 3743(the)s 4105(a)s 4(v)k 6(ailable)k +5028(space,)s 5681(thus)s 6145(implementing)s 7541(line)s 7970(adjustment,)s +0 7362(e)m 3(xcept)k 689(when)s 1274(the)s 1631(parameter)s +2654(contains)s 3511(tab)s 4(ulation)k 4529(g)s 1(aps)k +5027(lik)s 2(e)k 220 fnt35 5447 7359(&1r)m -8(t)k +240 fnt82 5853 7362(,)m 5969(which)s 6620(cause)s 7216(the)s +7573(parameter)s 8596(to)s 8844(be)s 0 7074(already)m 757(e)s 3(xpanded.)k +1836(The)s 2264(result)s 2854(of)s 220 fnt35 480 6573(@P)m 8(ar)k 2(ag)k 2(r)k 2(aph { A shor)k -8(t par)k 2(ag)k 2(r)k 2(aph of te)k 6(xt.)k 13( })k +240 fnt82 0 6074(w)m 2(ould)k 655(then)s 1124(be)s +1406(something)s 2456(lik)s 2(e)k 768 5571(A)m 1073(short)s +1687(paragraph)s 480 5283(of)m 751(te)s 3(xt.)k 0 4830(depending)m +1061(on)s 1368(the)s 1726(a)s 4(v)k 6(ailable)k +2645(horizontal)s 3679(space.)s 4384(An)s 4744(unlimited)s 5729(range)s +6326(of)s 6607(paragraph)s 7630(breaking)s 8531(styles)s 0 4542(could)m +590(be)s 872(de\207ned,)s 1684(including)s 2641(ragged)s 3350(right,)s +3908(ragged)s 4617(left,)s 5041(break-and-center)s 9(,)k 6757(and)s +7161(so)s 7427(on.)s 480 4168(In)m 765(Basser)s 1492(Lout,)s +2081(indented)s 2992(paragraphs)s 4122(are)s 4499(produced)s 5477(by)s +5801(preceding)s 6827(them)s 7394(with)s 7906(a)s 8102(horizontal)s +0 3880(concatenation)m 1380(operator)s 9(,)k 2269(for)s 2602(e)s 3(xample)k +220 fnt35 3459 3877(|0.5i)m 240 fnt82 3855 3880(.)m 4014(This)s +4485(has)s 4849(the)s 5192(unfortunate)s 6345(ef)s 6(fect)k +6935(of)s 7201(making)s 7967(an)s 8244(indented)s 0 3592(paragraph)m +1007(into)s 1426(a)s 1586(single)s 2207(component)s 3325(of)s +3590(the)s 3932(enclosing)s 4895(g)s 1(alle)k 3(y)k 15(,)k +5561(so)s 5821(that)s 6233(it)s 6419(will)s 6839(al)s 2(w)k 2(ays)k +7544(be)s 7820(k)s 2(ept)k 8283(together)s 0 3304(on)m +297(one)s 699(page.)s 1315(Horizontal)s 2392(g)s 1(alle)k 3(ys)k +3116(solv)s 3(e)k 3674(this)s 4070(problem)s 4927(with)s +5409(a)s 5575(simple)s 6268(change)s 7002(to)s 220 fnt35 +7241 3301(@LineList)m 240 fnt82 8215 3304(:)m 220 fnt35 480 2803(def @LineList)m +480 2515({)m 480 2227( |0.5i @HExpand @LinePlace)m 480 1939( //1vx @LineList)m 480 1651(})m 240 fnt82 +0 1157(sho)m 6(wing)k 860(the)s 1210(\210e)s 3(xibility)k +2192(that)s 2611(comes)s 3275(from)s 3801(bringing)s 4666(the)s +5016(full)s 5404(po)s 6(wer)k 6057(of)s 6330(the)s +6680(Lout)s 7193(language)s 8115(to)s 8356(bear)s 8829(on)s +0 869(paragraph)m 1013(layout.)s 1775(It)s 1980(is)s 2190(easy)s +2669(to)s 2908(mak)s 2(e)k 3480(pro)s 3(vision)k +4438(for)s 4776(a)s 4942(tag)s 5287(on)s 5584(the)s +5932(\207rst)s 6363(line.)s 480 495(Although)m 1451(Basser)s 2158(Lout)s +2679(permits)s 3456(recepti)s 6(v)k 3(e)k 4387(symbols)s +5246(within)s 5923(paragraphs,)s 7089(the)s 3(y)k 7561(are)s +7918(of)s 8198(little)s 8700(use,)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 35 36 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Helvetica +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4292 13841(-)m 4420(35)s 4706(-)s 0 13250(because)m 835(their)s +1355(a)s 4(v)k 6(ailable)k 2286(width)s 2911(is)s +3144(calculated)s 4193(after)s 4711(paragraph)s 5747(breaking,)s 6714(and)s +7141(the)s 7512(incoming)s 8492(g)s 1(alle)k 3(y)k +0 12962(cannot)m 736(spread)s 1456(o)s 3(v)k 3(er)k +1973(more)s 2558(than)s 3065(one)s 3505(line.)s 4066(W)s 9(ith)k +4630(horizontal)s 5692(g)s 1(alle)k 3(ys,)k 6510(such)s +7044(symbols)s 7931(w)s 2(ould)k 8625(ha)s 4(v)k 3(e)k +0 12674(in\207nite)m 733(a)s 4(v)k 6(ailable)k 1641(width,)s +2293(and)s 2697(we)s 3032(could)s 3622(easily)s 4233(produce)s +5060(a)s 5226(\207lled)s 5775(paragraph)s 6788(of)s 7059(footnotes)s +8000(lik)s 2(e)k 8412(this:)s 200 fnt82 480 12199(1)m +240 fnt82 559 12104(See)m 987(Jones)s 1597(and)s 2028(Saunders)s +2983(\(1982\).)s 200 fnt82 3932 12199(2)m 240 fnt82 4027 12104(Or)m +4366(so)s 4659(Jacobsen)s 480 11804(\(1973\))m 1167(asserts.)s 200 fnt82 +2087 11899(3)m 240 fnt83 2174 11806(ibid)m 240 fnt82 2552 11804(,)m +2659(p.)s 2883(327.)s 0 11301(based)m 603(on)s 900(an)s +1183(in\207nite)s 1916(horizontal)s 2940(sequence)s 3873(of)s 220 fnt35 +4144 11298(@F)m 6(ootPlace)k 240 fnt82 5400 11301(symbols)m 6249(inside)s +6876(a)s 7042(horizontal)s 8066(g)s 1(alle)k 3(y)k 15(.)k +480 10927(When)m 1133(body)s 1692(te)s 3(xt)k 2132(is)s +2367(placed)s 3074(on)s 3395(pages,)s 4072(the)s 4445(length)s +5125(of)s 5421(each)s 5940(column)s 6740(v)s 6(aries)k +7380(depending)s 8456(on)s 8778(the)s 0 10639(a)m 4(v)k 6(ailable)k +914(v)s 3(ertical)k 1687(space.)s 2389(Horizontal)s 3472(g)s 1(alle)k 3(ys)k +4203(could)s 4799(analogously)s 6017(produce)s 6850(lines)s 7359(of)s +7636(v)s 6(arying)k 8421(length,)s 0 10351(and)m 404(so)s +670(could)s 1260(\207ll)s 1580(non-rectangular)s 3153(shapes.)s 480 9977(An)m +835(important)s 1829(theoretical)s 2896(bene\207t)s 3612(of)s 3888(horizontal)s +4918(g)s 1(alle)k 3(ys)k 5647(is)s 5862(that)s +6285(the)s 3(y)k 6753(w)s 2(ould)k 7413(permit)s +8102(horizontal)s 0 9689(and)m 403(v)s 3(ertical)k 1168(to)s +1405(be)s 1685(treated)s 2390(in)s 2631(a)s 2795(perfectly)s +3695(symmetrical)s 4928(w)s 2(ay)k 15(,)k 5415(whereas)s +6247(at)s 6477(present)s 7225(paragraph)s 8236(breaking)s 0 9401(is)m +243(horizontal)s 1300(only)s 15(,)k 1851(and)s 2288(g)s 1(alle)k 3(y)k +2955(breaking)s 3878(is)s 4121(v)s 3(ertical)k 4921(only)s 15(.)k +5529(This)s 6038(must)s 6596(simplify)s 7479(the)s 7860(treatment)s +8855(of)s 0 9113(non-European)m 1432(languages)s 2459(which)s 3121(\207ll)s +3460(in)s 3722(unusual)s 4542(directions,)s 5610(although)s 6525(it)s +6736(is)s 6965(not)s 7351(itself)s 7918(suf\207cient)s 8887(to)s +0 8825(implement)m 1082(them.)s 480 8451(There)m 1132(are)s 1519(a)s +1725(fe)s 6(w)k 2170(minor)s 2841(problems)s 3822(with)s +4343(horizontal)s 5407(g)s 1(alle)k 3(ys.)k 6284(First,)s +6867(the)s 7255(syntactic)s 8197(o)s 3(v)k 3(erhead)k +0 8163(of)m 319(enclosing)s 1337(each)s 1880(paragraph)s 2941(in)s +220 fnt35 3233 8160(@P)m 8(ar)k 2(ag)k 2(r)k 2(aph { ...)k 13( })k +240 fnt82 5064 8163(or)m 5371(whate)s 6(v)k 3(er)k +6346(is)s 6604(unacceptable.)s 8065(Permitting)s 0 7875(user)m 4(-de\207ned)k +1234(operators)s 2172(to)s 2409(ha)s 4(v)k 3(e)k +2908(lo)s 6(wer)k 3504(precedence)s 4633(than)s 5100(the)s +5446(white)s 6031(space)s 6616(between)s 7468(tw)s 2(o)k +7876(w)s 2(ords)k 8508(might)s 0 7587(help)m 450(here.)s +1009(Second,)s 1805(the)s 2137(b)s 4(uilt-in)k 2877(paragraph)s +3874(break)s 2(er)k 4632(includes)s 5464(h)s 1(yphenation,)k +6738(and)s 7126(it)s 7302(permits)s 8053(line)s 8451(breaks)s +0 7299(in)m 246(the)s 598(input)s 1153(to)s 1396(determine)s +2410(line)s 2828(breaks)s 3506(in)s 3753(the)s 4105(output,)s +4827(if)s 5048(desired.)s 5905(These)s 6536(features)s 7345(must)s +7874(someho)s 6(w)k 8844(be)s 0 7011(preserv)m 3(ed.)k +1081(Finally)s 15(,)k 1841(we)s 2167(ha)s 4(v)k 3(e)k +2659(e)s 3(xplained)k 3634(ho)s 6(w)k 4086(the)s +4425(Basser)s 5113(Lout)s 5616(interpreter)s 6659(assigns)s 7392(equal)s +7956(width)s 8549(to)s 8778(the)s 0 6723(wider)m 607(columns)s +1473(of)s 1748(tables)s 2359(\(Section)s 3216(2.5\).)s 3763(The)s +4194(equi)s 6(v)k 6(alent)k 5242(situation)s 6126(in)s +6372(v)s 3(ertical)k 7143(g)s 1(alle)k 3(ys)k +7871(occurs)s 8550(when)s 0 6435(tw)m 2(o)k 416(recepti)s 6(v)k 3(e)k +1345(symbols)s 2201(compete)s 3074(for)s 3419(v)s 3(ertical)k +4193(space)s 4786(\(e.g.)s 220 fnt35 5262 6432(@T)m 26(e)k 6(xtPlace)k +240 fnt82 6487 6435(and)m 220 fnt35 6898 6432(@F)m 6(ootSect)k +240 fnt82 7989 6435(\),)m 8182(and)s 8593(there)s 0 6147(it)m +187(is)s 392(con)s 9(v)k 3(entional)k 1666(to)s +1900(grant)s 2446(as)s 2691(much)s 3274(as)s 3519(required)s +4368(to)s 4602(the)s 4945(\207rst)s 5371(arri)s 6(v)k 6(al.)k +6140(It)s 6339(is)s 6544(not)s 6905(clear)s 7423(to)s +7657(the)s 8000(author)s 8665(ho)s 6(w)k 0 5859(these)m +547(dif)s 6(ferent)k 1422(approaches)s 2549(can)s 2938(be)s +3220(reconciled.)s 240 fnt84 0 5066(6.)m 291(Cr)s 4(oss)k +926(r)s 4(efer)k 4(ences)k 240 fnt82 480 4634(Cross)m +1064(references,)s 2138(such)s 2622(as)s 2859(`see)s 3286(page)s +3782(57')s 4121(and)s 4512(`see)s 4940(Figure)s 5607(5,)s 16(')k +5871(are)s 6205(a)s 6358(useful)s 6985(b)s 4(ut)k +7334(highly)s 7987(error)s 4(-prone)k 0 4346(feature)m 716(of)s +985(documents.)s 2184(Scribe)s 2848([7])s 3163(introduced)s 4242(a)s +4406(method)s 5180(of)s 5449(k)s 2(eeping)k 6256(them)s +6792(up)s 7083(to)s 7320(date)s 7772(automatically)s 0 4058(as)m +245(the)s 587(document)s 1585(changes:)s 2517(the)s 2859(user)s +3311(gi)s 6(v)k 3(es)k 3852(each)s 4342(referenced)s +5401(entity)s 5993(a)s 6153(tag,)s 6547(and)s 6945(operators)s +7879(are)s 8220(pro)s 3(vided)k 0 3770(that)m 418(return)s +1045(the)s 1393(page)s 1901(or)s 2160(sequence)s 3093(number)s +3884(of)s 4155(the)s 4503(entity)s 5101(with)s 5583(a)s +5749(gi)s 6(v)k 3(en)k 6329(tag.)s 480 3396(A)m +712(cross)s 1256(reference)s 2201(tak)s 2(es)k 2743(an)s +3028(object)s 3674(\(such)s 4251(as)s 4503(a)s 4671(page)s +5181(number\))s 6042(from)s 6568(one)s 6972(point)s 7526(in)s +7771(the)s 8122(document)s 0 3108(and)m 435(copies)s 1128(it)s +1351(to)s 1621(another)s 9(,)k 2467(and)s 2902(this)s +3329(generalization)s 4770(suggests)s 5663(other)s 6245(applications.)s 7595(F)s 3(or)k +8015(e)s 3(xample,)k 8960(a)s 0 2820(running)m 831(header)s +1562(is)s 1806(copied)s 2536(from)s 3094(the)s 3475(title)s +3935(of)s 4240(a)s 4440(nearby)s 5179(chapter)s 9(,)k +6013(and)s 6451(a)s 6651(reference)s 7628(is)s 7872(copied)s +8602(from)s 0 2532(a)m 207(bibliographic)s 1576(database.)s 2604(Making)s +3443(the)s 3832(unity)s 4419(of)s 4731(these)s 5319(applications)s +6566(manifest)s 7489(is)s 7740(an)s 8065(interesting)s 0 2244(language)m +920(design)s 1602(problem.)s 240 fnt84 0 1595(6.1.)m 471(The)s +926(cr)s 4(oss)k 1494(r)s 4(efer)k 4(ence)k +2496(abstraction)s 240 fnt82 480 1164(In)m 736(de)s 6(v)k 3(eloping)k +1844(the)s 2192(cross)s 2734(reference)s 3677(abstraction,)s 4832(it)s +5024(seemed)s 5799(best)s 6244(to)s 6483(be)s 3(gin)k +7069(with)s 7551(the)s 7899(database)s 8779(ap)s 8998(-)s +0 876(plication,)m 943(since)s 1490(it)s 1682(is)s 1892(the)s +2240(simplest.)s 3200(Database)s 4132(relations)s 5005(are)s 5352(naturally)s +6255(mapped)s 7071(into)s 7496(Lout)s 8008(de\207nitions:)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 36 37 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4288 13842(-)m 4416(36)s 4709(-)s 220 fnt35 480 13253(def @Ref)m 6(erence)k +480 12965( named @T)m 26(ag {})k 480 12677( named @A)m 6(uthor {})k 480 12389( named @Title {})m +480 12101( named @Jour)m -5(nal {})k 480 11813({})m 240 fnt82 0 11319(The)m +434(set)s 766(of)s 1043(all)s 1343(in)s 9(v)k 4(ocations)k +2490(of)s 220 fnt35 2768 11316(@Ref)m 6(erence)k 240 fnt82 +4055 11319(is)m 4272(a)s 4444(relation)s 5237(whose)s 5911(attrib)s 4(utes)k +6853(are)s 7206(the)s 7561(parameters,)s 8722(and)s 0 11031(whose)m +659(tuples)s 1271(are)s 1608(the)s 1946(in)s 9(v)k 4(ocations.)k +3191(T)s 19(o)k 3481(complete)s 4403(the)s 4741(correspondence,)s +6339(we)s 6665(need)s 7165(only)s 7635(declare)s 8370(that)s +8778(the)s 220 fnt35 0 10740(@T)m 26(ag)k 240 fnt82 +623 10743(parameter)m 1637(is)s 1847(special,)s 2617(serving)s 3374(as)s +3624(the)s 3972(k)s 2(e)k 3(y)k 4367(attrib)s 4(ute.)k +480 10369(F)m 3(ollo)k 6(wing)k 1508(the)s 1856(database)s +2735(model,)s 3440(we)s 3775(ne)s 3(xt)k 4244(need)s +4755(a)s 4921(notation)s 5762(for)s 6100(retrie)s 6(ving)k +7075(the)s 7423(in)s 9(v)k 4(ocation)k 8477(with)s +8960(a)s 0 10081(gi)m 6(v)k 3(en)k 580(tag:)s +220 fnt35 480 9580(@Ref)m 6(erence&&kingston91)k 240 fnt82 0 9081(This)m +240 fnt83 534 9083(cr)m 10(oss)k 1143(r)s 8(efer)k 8(ence)k +240 fnt82 2141 9081(is)m 2410(lik)s 2(e)k 2881(an)s +3223(arro)s 6(w)k 3887(pointing)s 4796(to)s 5094(the)s +5501(in)s 9(v)k 4(ocation.)k 6721(T)s 19(o)k +7080(access)s 7800(its)s 8135(attrib)s 4(utes,)k 0 8793(we)m +335(write)s 220 fnt35 480 8341(@Ref)m 6(erence&&kingston91 @Open { @A)k 6(uthor)k 11(, @Title })k +240 fnt82 0 7842(The)m 220 fnt35 484 7839(@Open)m 240 fnt82 +1347 7842(operator)m 2260(e)s 6(v)k 6(aluates)k 3245(its)s +3578(right)s 4146(parameter)s 5217(in)s 5517(an)s 5857(en)s 9(vironment)k +7174(which)s 7873(includes)s 8778(the)s 0 7554(e)m 3(xported)k +892(parameters)s 1990(of)s 2261(its)s 2537(left.)s 480 7180(An)m +829(in)s 9(v)k 4(ocation)k 1882(is)s 2091(chosen)s +2812(to)s 3050(be)s 3331(a)s 3496(running)s 4293(header)s +4989(because)s 5801(of)s 6071(its)s 6346(proximity)s 7342(to)s +7580(the)s 7927(place)s 8486(where)s 0 6892(it)m 223(is)s +465(used,)s 1043(rather)s 1691(than)s 2192(by)s 2517(its)s +2825(tag.)s 3313(Such)s 3881(proximity)s 4910(is)s 5151(naturally)s +6086(e)s 3(xpressed)k 7116(by)s 7442(tw)s 2(o)k +7884(special)s 8634(tags,)s 220 fnt35 0 6601(preceding)m 240 fnt82 +1049 6604(and)m 220 fnt35 1491 6601(f)m 6(ollo)k 3(wing)k +240 fnt82 2321 6604(;)m 2471(for)s 2848(e)s 3(xample,)k +220 fnt35 3800 6601(@Sym&&f)m 6(ollo)k 3(wing)k 240 fnt82 +5682 6604(will)m 6146(point)s 6737(to)s 7014(the)s 7400(closest)s +8149(follo)s 6(wing)k 0 6316(in)m 9(v)k 4(ocation)k +1083(of)s 220 fnt35 1383 6313(@Sym)m 240 fnt82 2121 6316(in)m +2393(the)s 2771(\207nal)s 3280(printed)s 4045(document.)s 5182(This)s +5688(is)s 5927(much)s 6546(simpler)s 7351(conceptually)s 8657(than)s +0 6028(reference)m 937(to)s 1169(the)s 1511(internal)s 2288(state)s +2775(of)s 3039(the)s 3381(document)s 4378(formatter)s 5319(at)s +5544(a)s 5704(critical)s 6413(moment,)s 7298(the)s 7639(usual)s +8192(approach)s 0 5740(to)m 239(running)s 1037(headers.)s 480 5366(It)m +691(turns)s 1227(out)s 1600(that)s 2025(the)s 2380(abo)s 3(v)k 3(e)k +3009(design)s 3698(solv)s 3(es)k 4350(all)s 4650(the)s +5005(cross)s 5554(referencing)s 6701(problems)s 7649(encountered)s 8883(in)s +0 5078(practice)m 825(e)s 3(xcept)k 1521(one,)s 1988(which)s +2645(may)s 3126(be)s 3422(typi\207ed)s 4226(by)s 4535(the)s +4897(problem)s 5769(of)s 6054(\207nding)s 6801(the)s 7164(number)s +7969(of)s 8255(the)s 8618(page)s 0 4790(on)m 303(which)s +952(the)s 1306(chapter)s 2076(whose)s 2750(tag)s 3102(is)s +220 fnt35 3318 4787(intro)m 240 fnt82 3804 4790(be)m 3(gins.)k +4596(T)s 19(w)k 2(o)k 5074(cross)s 5622(referencing)s +6769(steps)s 7304(are)s 7658(needed,)s 8449(\207rst)s 8887(to)s +220 fnt35 0 4499(@Chapter&&intro)m 240 fnt82 1714 4502(,)m 1821(then)s +2290(from)s 2814(there)s 3347(to)s 220 fnt35 3586 4499(@P)m 8(age&&preceding)k +240 fnt82 5556 4502(,)m 5663(where)s 6303(the)s 6651(page)s +7159(number)s 7950(is)s 8160(kno)s 6(wn.)k 480 4128(Gi)m 6(v)k 3(en)k +1113(our)s 1492(success)s 2260(so)s 2526(f)s 2(ar)k 9(,)k +2886(this)s 3282(last)s 3673(problem)s 4530(pro)s 3(v)k 3(es)k +5213(to)s 5452(be)s 5734(surprisingly)s 6930(dif\207cult.)s 7850(W)s 19(e)k +8219(\207rst)s 8650(try)s 220 fnt35 480 3627(@Chapter&&intro @Open {)m 480 3339( @P)m 8(age&&preceding @Open { @P)k 8(ageNum })k +480 3051(})m 240 fnt82 0 2557(b)m 4(ut)k 363(this)s +761(f)s 2(ails)k 1222(because)s 220 fnt35 2037 2554(@P)m 8(age&&preceding)k +240 fnt82 4069 2557(is)m 4281(e)s 6(v)k 6(aluated)k +5245(in)s 5490(the)s 5840(present)s 6592(conte)s 3(xt,)k +7402(not)s 7770(in)s 8015(the)s 8365(conte)s 3(xt)k +0 2269(of)m 220 fnt35 271 2266(@Chapter&&intro)m 240 fnt82 2045 2269(as)m +2295(required.)s 3255(So)s 3561(our)s 3940(ne)s 3(xt)k +4409(attempt)s 5185(is)s 220 fnt35 480 1768(def @Chapter)m 480 1480( named @P)m 8(ageNum { @P)k 8(age&&preceding @Open { @P)k 8(ageNum } })k +480 1192( ...)m 240 fnt82 0 741(with)m 482(the)s 220 fnt35 +830 738(@P)m 8(age&&preceding)k 240 fnt82 2860 741(cross)m 3402(reference)s +4345(attached)s 5199(to)s 5438(the)s 5786(chapter;)s 6601(we)s +6936(write)s 220 fnt35 480 240(@Chapter&&intro @Open { @P)m 8(ageNum })k +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 37 38 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Bold +%%+ font Times-Italic +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4291 13844(-)m 4419(37)s 4707(-)s 0 13253(This)m 604(also)s +1170(f)s 2(ails,)k 1813(because)s 2754(parameters)s 3980(are)s +4456(e)s 6(v)k 6(aluated)k 5546(after)s 6170(substitution,)s +7521(so)s 7915(once)s 8552(ag)s 1(ain)k 220 fnt35 +0 12962(@P)m 8(age&&preceding)k 240 fnt82 2015 12965(is)m 2209(e)s 6(v)k 6(aluated)k +3156(in)s 3383(the)s 3716(wrong)s 4365(conte)s 3(xt.)k +5215(W)s 19(e)k 5568(could)s 6143(of)s 6398(course)s +7063(de\207ne)s 7688(a)s 7839(ne)s 6(w)k 8270(operator)s +0 12677(speci\207cally)m 1142(for)s 1480(this)s 1876(case:)s 220 fnt35 +480 12176(@P)m 8(age&&{ @Preceding @Chapter&&intro })k 240 fnt82 0 11677(or)m 267(some)s +836(such.)s 1448(This)s 1932(is)s 2151(free)s 2585(of)s +2864(the)s 3221(anno)s 2(ying)k 4172(conte)s 3(xt-sensiti)k 6(vity)k 15(,)k +6029(b)s 4(ut)k 6399(it)s 6599(seems)s 7243(quite)s +7785(comple)s 3(x,)k 8722(and)s 0 11389(the)m 348(e)s 3(xpected)k +1253(cross)s 1795(reference)s 220 fnt35 2738 11386(@P)m 8(age&&preceding)k +240 fnt82 4768 11389(does)m 5258(not)s 5624(appear)s 13(.)k +480 11015(The)m 939(author)s 1642(w)s 2(as)k 2095(lost)s +2532(in)s 2806(these)s 3385(obscurities)s 4503(for)s 4873(some)s +5465(time,)s 6028(and)s 6464(ultimately)s 7518(rescued)s 8338(himself)s +0 10727(by)m 306(looking)s 1103(ahead)s 1731(to)s 1982(the)s +2342(implementation)s 3912(of)s 4195(the)s 220 fnt35 4555 10724(preceding)m +240 fnt82 5578 10727(and)m 220 fnt35 5994 10724(f)m 6(ollo)k 3(wing)k +240 fnt82 6897 10727(tags,)m 7401(to)s 7652(see)s 8025(if)s +8254(a)s 8433(simple)s 0 10439(e)m 3(xtension)k 971(of)s +1242(it)s 1434(w)s 2(ould)k 2089(solv)s 3(e)k +2647(the)s 2995(problem.)s 3956(This)s 4432(led)s 4782(to)s +5021(the)s 220 fnt35 5369 10436(@T)m 26(agged)k 240 fnt82 +6358 10439(operator:)m 220 fnt35 480 9938(@P)m 8(age&&preceding @T)k 26(agged intro)k +240 fnt82 0 9439(placed)m 686(at)s 922(the)s 1274(be)s 3(ginning)k +2286(of)s 2562(the)s 2914(body)s 3452(of)s 3727(the)s +4079(chapter)s 4847(will)s 5277(attach)s 220 fnt35 5908 9436(intro)m +240 fnt82 6391 9439(as)m 6645(an)s 6933(e)s 3(xtra)k +7471(tag)s 7820(to)s 8063(the)s 8416(closest)s 0 9151(preceding)m +996(in)s 9(v)k 4(ocation)k 2050(of)s 220 fnt35 +2321 9148(@P)m 8(age)k 240 fnt82 3040 9151(,)m 3147(so)s +3413(that)s 220 fnt35 480 8650(@P)m 8(age&&intro @Open { @P)k 8(ageNum })k +240 fnt82 0 8151(yields)m 635(the)s 996(desired)s 1758(page)s +2279(number)s 13(.)k 3174(There)s 3801(is)s 4024(something)s +5087(lo)s 6(w-le)k 6(v)k 3(el)k 6043(and)s +6460(ad)s 6757(hoc)s 7170(about)s 7775(the)s 220 fnt35 +8137 8148(@T)m 26(agged)k 240 fnt82 0 7863(operator)m 9(,)k +894(b)s 4(ut)k 1256(the)s 1604(tw)s 2(o)k +2014(cross)s 2556(references)s 3587(do)s 3880(appear)s 4577(naturally)s 15(,)k +5518(and)s 5922(it)s 6114(w)s 2(orks.)k 240 fnt84 +0 7214(6.2.)m 471(Implementation)s 2159(of)s 2431(cr)s 4(oss)k +2999(r)s 4(efer)k 4(ences)k 240 fnt82 480 6737(Before)m +1185(an)s 1466(object)s 2109(can)s 2496(be)s 2777(sized)s +3324(and)s 3727(printed,)s 4509(the)s 4855(v)s 6(alues)k +5510(of)s 5779(an)s 3(y)k 6175(cross)s 6715(references)s +7745(within)s 8411(it)s 8601(must)s 0 6449(be)m 279(kno)s 6(wn.)k +1086(If)s 1312(the)s 3(y)k 1772(refer)s 2277(to)s +2512(in)s 9(v)k 4(ocations)k 3650(that)s 4064(ha)s 4(v)k 3(e)k +4561(not)s 4924(yet)s 5272(been)s 5777(read,)s 6292(there)s +6821(is)s 7027(a)s 7190(problem.)s 8147(Scribe)s 8809([7])s +0 6161(solv)m 3(es)k 649(it)s 844(by)s 1141(capitalizing)s +2311(on)s 2611(the)s 2962(f)s 2(act)k 3381(that)s +3802(documents)s 4893(are)s 5243(formatted)s 6232(repeatedly)s 7284(during)s +7965(the)s 8317(drafting)s 0 5873(process.)m 868(All)s 1214(tagged)s +1897(in)s 9(v)k 4(ocations)k 3024(are)s 3358(copied)s +4040(to)s 4266(an)s 4535(auxiliary)s 5425(\207le)s 5772(during)s +6437(the)s 6771(\207rst)s 7189(run,)s 7601(and)s 7992(inde)s 3(x)k 3(ed)k +8788(for)s 0 5585(quick)m 593(retrie)s 6(v)k 6(al)k +1429(on)s 1725(the)s 2072(second.)s 2901(A)s 3130(ne)s 6(w)k +3576(auxiliary)s 4478(\207le)s 4839(is)s 5048(written)s 5780(during)s +6457(the)s 6805(second)s 7527(run,)s 7952(for)s 8289(retrie)s 6(v)k 6(al)k +0 5297(on)m 301(the)s 654(third,)s 1217(and)s 1625(so)s +1896(on.)s 2305(Cross)s 2906(references)s 3941(al)s 2(w)k 2(ays)k +4657(lag)s 5007(one)s 5413(run)s 5794(behind)s 6509(the)s +6862(rest)s 7270(of)s 7546(the)s 7899(document;)s 8960(a)s +0 5009(perfect)m 711(cop)s 2(y)k 1217(may)s 1671(be)s +1942(produced)s 2879(by)s 3161(formatting)s 4210(the)s 4547(same)s +5082(v)s 3(ersion)k 5828(twice,)s 6440(e)s 3(xcept)k +7110(in)s 7341(a)s 7495(fe)s 6(w)k 7889(pathological)s +0 4721(cases)m 555(that)s 973(f)s 2(ail)k 1343(to)s +1582(con)s 9(v)k 3(er)k 4(ge.)k 480 4347(Cross)m +1123(referencing)s 2310(in)s 2600(Lout)s 3159(is)s 3416(implemented)s +4769(on)s 5113(top)s 5519(of)s 5837(a)s 6050(simple)s +6790(database)s 7716(system.)s 8591(Each)s 0 4059(database)m 879(is)s +1089(either)s 1692(writable)s 2530(or)s 2790(readable)s 3655(b)s 4(ut)k +4017(not)s 4383(both)s 4867(at)s 5099(once,)s 5658(and)s +6062(holds)s 6633(a)s 6799(set)s 7124(of)s 7395(k)s 2(e)k 3(y-v)k 6(alue)k +8384(entries:)s 0 3771(the)m 348(k)s 2(e)k 3(ys)k +833(are)s 1180(ASCII)s 1861(strings,)s 2605(and)s 3009(the)s +3358(v)s 6(alues)k 4014(are)s 4361(Lout)s 4873(objects,)s +5658(possibly)s 6510(with)s 6992(en)s 9(vironments,)k 8393(written)s +0 3483(in)m 290(Lout)s 850(source.)s 1685(Operations)s 2833(are)s +3227(pro)s 3(vided)k 4181(for)s 4566(writing)s 5357(an)s +5687(entry)s 15(,)k 6318(con)s 9(v)k 3(erting)k +7429(from)s 8001(writable)s 8887(to)s 0 3195(readable,)m 916(retrie)s 6(v)k 6(al)k +1753(by)s 2047(k)s 2(e)k 3(y)k 15(,)k +2480(and)s 2884(sequential)s 3908(retrie)s 6(v)k 6(al)k +4745(in)s 4988(k)s 2(e)k 3(y)k 5383(order)s 13(.)k +480 2821(The)m 905(implementation,)s 2509(which)s 3148(is)s 3354(quite)s +3885(unsophisticated,)s 5477(emplo)s 2(ys)k 6334(one)s 6732(or)s +6988(more)s 7532(ASCII)s 240 fnt83 8208 2823(database)m 0 2535(\207les)m +240 fnt82 380 2533(,)m 485(containing)s 1545(the)s 1891(v)s 6(alues,)k +2600(and)s 3001(one)s 3401(ASCII)s 240 fnt83 4078 2535(inde)m 4(x)k +4650(\207le)s 240 fnt82 4992 2533(per)m 5354(database,)s 6282(containing)s +7342(the)s 7688(k)s 2(e)k 3(ys.)k 8283(T)s 19(o)k +8580(write)s 0 2245(an)m 283(entry)s 15(,)k 866(the)s +1214(v)s 6(alue)k 1782(is)s 1992(\207rst)s 2423(appended)s +3399(to)s 3638(a)s 3804(database)s 4683(\207le,)s 5095(then)s +5564(a)s 5730(line)s 6144(lik)s 2(e)k 220 fnt35 +480 1744(@Chapter&&intro ch1.ld 57)m 240 fnt82 0 1248(is)m 204(appended)s 1174(to)s +1406(the)s 1748(inde)s 3(x)k 2326(\207le,)s 2731(gi)s 6(ving)k +3384(the)s 3725(\207le)s 4080(and)s 4478(of)s 6(fset)k +5068(where)s 5702(the)s 6043(v)s 6(alue)k 6605(is)s +6809(stored.)s 7550(T)s 19(o)k 7844(con)s 9(v)k 3(ert)k +8602(from)s 0 960(writable)m 831(to)s 1062(readable,)s 1971(the)s +2311(inde)s 3(x)k 2887(\207le)s 3241(is)s 3443(sorted.)s +4183(Then)s 4725(retrie)s 6(v)k 6(al)k 5554(by)s +5840(k)s 2(e)k 3(y)k 6228(requires)s 7040(a)s +7198(binary)s 7856(search)s 8515(of)s 8778(the)s 0 672(inde)m 3(x)k +584(\207le)s 945(and)s 1349(one)s 1751(seek)s 2237(into)s +2662(a)s 2828(database)s 3707(\207le,)s 4119(and)s 4523(sequential)s +5547(retrie)s 6(v)k 6(al)k 6384(by)s 6678(k)s 2(e)k 3(y)k +7073(is)s 7283(tri)s 6(vial.)k 480 298(This)m 945(database)s +1813(system)s 2526(is)s 2725(used)s 3211(in)s 3443(se)s 6(v)k 3(eral)k +4154(w)s 2(ays.)k 4797(F)s 3(or)k 5175(an)s +5447(e)s 3(xternal)k 6257(database,)s 7176(say)s 7538(of)s +7798(bibliographic)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 38 39 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Helvetica +%%+ font Times-Italic +%%+ font Times-Bold +/pgsave save def +%%IncludeResource: font Helvetica +/Helveticafnt35 vec2 /Helvetica LoutRecode +/fnt35 { /Helveticafnt35 LoutFont } def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4291 13844(-)m 4419(38)s 4706(-)s 0 13253(references,)m 1093(the)s +1447(user)s 1912(creates)s 2631(the)s 2985(database)s 3871(\207le)s +4238(of)s 4516(v)s 6(alues)k 5178(\(without)s 6054(en)s 9(vironments\),)k +7540(Lout)s 8058(creates)s 8778(the)s 0 12965(inde)m 3(x)k +587(\207le)s 951(whene)s 6(v)k 3(er)k 1935(it)s +2130(cannot)s 2831(\207nd)s 3265(one,)s 3721(and)s 4128(retrie)s 6(v)k 6(als)k +5057(by)s 5354(k)s 2(e)k 3(y)k 5752(proceed)s +6570(as)s 6823(usual.)s 7495(Cross)s 8095(references)s 0 12677(with)m +476(tags)s 906(other)s 1451(than)s 220 fnt35 1913 12674(preceding)m +240 fnt82 2918 12677(and)m 220 fnt35 3316 12674(f)m 6(ollo)k 3(wing)k +240 fnt82 4200 12677(are)m 4540(treated)s 5241(as)s 5485(described)s +6453(abo)s 3(v)k 3(e,)k 7119(by)s 7407(writing)s +8144(all)s 8430(tagged)s 0 12389(in)m 9(v)k 4(ocations)k +1131(\(with)s 1681(en)s 9(vironments\))k 3092(to)s 3320(a)s +3475(single)s 4092(database,)s 5011(which)s 5643(is)s 5842(con)s 9(v)k 3(erted)k +6820(to)s 7049(readable)s 7903(at)s 8125(the)s 8462(end)s +8855(of)s 0 12101(the)m 334(run)s 695(for)s 1018(retrie)s 6(v)k 6(als)k +1930(on)s 2212(the)s 2545(ne)s 3(xt)k 3000(run.)s +3468(Sorted)s 4135(g)s 1(alle)k 3(ys,)k 4900(such)s +5382(as)s 5617(inde)s 3(x)k 6186(entries,)s 6915(are)s +7247(written)s 7965(out)s 8316(inde)s 3(x)k 3(ed)k +0 11813(by)m 307(tar)s 4(get)k 920(and)s 1337(k)s 2(e)k 3(y)k +1746(and)s 2163(retrie)s 6(v)k 3(ed)k 3074(sequentially)s +4297(on)s 4607(the)s 4969(ne)s 3(xt)k 5451(run.)s +5948(Unsorted)s 6896(g)s 1(alle)k 3(ys)k 7634(with)s +8130(preceding)s 0 11525(tar)m 4(gets)k 684(which)s 1327(pop)s +1741(of)s 6(f)k 2086(the)s 2435(top)s 2795(of)s +3067(the)s 3416(root)s 3863(g)s 1(alle)k 3(y)k +4498(without)s 5290(\207nding)s 6023(a)s 6190(tar)s 4(get,)k +6837(such)s 7334(as)s 7585(entries)s 8273(in)s 8518(tables)s +0 11237(of)m 274(contents,)s 1181(are)s 1532(treated)s 2242(similarly)s 15(,)k +3186(e)s 3(xcept)k 3870(that)s 4291(the)s 3(y)k +4758(are)s 5108(inde)s 3(x)k 3(ed)k 5922(by)s +6219(tar)s 4(get)k 6821(and)s 7229(a)s 7398(sequence)s +8335(number)s 0 10949(that)m 418(preserv)s 3(es)k 1368(their)s +1865(relati)s 6(v)k 3(e)k 2627(order)s 3191(during)s +3869(the)s 4217(sort.)s 480 10575(When)m 1107(Lout)s 1617(processes)s +2581(a)s 2745(multi-\207le)s 3687(document,)s 4735(one)s 5135(cross)s +5674(reference)s 6615(database)s 7492(\207le)s 7850(is)s 8058(written)s +8788(for)s 0 10287(each)m 504(input)s 1065(\207le,)s 1486(b)s 4(ut)k +1858(the)s 3(y)k 2330(share)s 2899(a)s 3074(common)s +3979(inde)s 3(x)k 4572(\207le.)s 5050(At)s 5358(end)s +5772(of)s 6052(run,)s 6487(the)s 6844(ne)s 6(w)k +7301(inde)s 3(x)k 7894(\207le)s 8264(is)s 8484(sorted)s +0 9999(and)m 404(mer)s 4(ged)k 1176(with)s 1658(the)s +2007(old)s 2371(one)s 2774(in)s 3017(such)s 3514(a)s +3680(w)s 2(ay)k 4132(as)s 4383(to)s 4622(preserv)s 3(e)k +5485(entries)s 6172(relating)s 6955(to)s 7194(\207les)s 7644(not)s +8010(read)s 8480(on)s 8778(the)s 0 9711(current)m 737(run.)s +1221(This)s 1699(pro)s 3(vides)k 2572(some)s 3135(support)s +3914(for)s 4254(piecemeal)s 5278(formatting,)s 6395(b)s 4(ut)k +6758(e)s 6(v)k 3(entually)k 7801(the)s 8150(\207les)s +8601(must)s 0 9423(all)m 293(be)s 575(formatted)s 1561(together)s 13(.)k +480 9049(When)m 1120(a)s 220 fnt35 1297 9046(preceding)m 240 fnt82 +2319 9049(or)m 220 fnt35 2590 9046(f)m 6(ollo)k 3(wing)k +240 fnt82 3491 9049(cross)m 4044(reference)s 4998(is)s 5220(found,)s +5897(it)s 6100(is)s 6321(attached)s 7187(to)s 7437(a)s +7614(g)s 1(alle)k 3(y)k 8259(inde)s 3(x)k +8855(of)s 0 8761(type)m 240 fnt83 474 8763(CR)m 9(OSS_PREC)k +240 fnt82 1973 8761(or)m 240 fnt83 2238 8763(CR)m 9(OSS_FOLL)k +240 fnt82 3653 8761(,)m 3766(together)s 4615(with)s 5103(an)s +5392(automatically)s 6752(generated)s 7745(tag)s 8097(composed)s 0 8473(of)m +258(the)s 593(current)s 1316(\207le)s 1663(name)s 2224(and)s +2615(a)s 2767(sequence)s 3687(number)s 13(.)k 4556(When)s +5172(a)s 5324(tagged)s 6007(in)s 9(v)k 4(ocation)k +7048(is)s 7244(found,)s 7897(it)s 8076(is)s 8272(attached)s +0 8185(to)m 237(a)s 240 fnt83 401 8187(CR)m 9(OSS_T)k 12(ARG)k +240 fnt82 1875 8185(inde)m 3(x.)k 2565(These)s 3190(g)s 1(alle)k 3(y)k +3822(inde)s 3(x)k 3(es)k 4595(are)s 4940(carried)s +5658(along)s 6241(through)s 7040(the)s 7386(dynamic)s 8261(tree,)s +8722(and)s 0 7897(e)m 6(v)k 3(entually)k 1049(pop)s +1470(of)s 6(f)k 1822(the)s 2178(top)s 2545(of)s +2824(the)s 3180(root)s 3633(g)s 1(alle)k 3(y)k 15(,)k +4313(at)s 4553(which)s 5203(point)s 5763(it)s 5963(is)s +6181(easy)s 6668(to)s 6915(determine)s 7934(which)s 8584(cross)s +0 7609(references)m 1029(refer)s 1536(to)s 1773(which)s 2413(in)s 9(v)k 4(ocations,)k +3608(since)s 4153(the)s 4499(inde)s 3(x)k 3(es)k +5273(are)s 5618(no)s 6(w)k 6077(in)s 6318(\207nal)s +6796(printed)s 7529(document)s 8531(order)s 13(.)k 0 7321(Each)m +541(referenced)s 1613(in)s 9(v)k 4(ocation)k 2674(is)s +2891(then)s 3367(written)s 4107(to)s 4353(the)s 4708(cross)s +5257(reference)s 6207(database,)s 7144(multiply)s 8015(inde)s 3(x)k 3(ed)k +8832(by)s 0 7033(the)m 344(generated)s 1327(tags)s 1758(of)s +2025(the)s 2369(associated)s 3404(cross)s 3942(references.)s 5082(On)s +5427(the)s 5771(ne)s 3(xt)k 6236(run,)s 6657(when)s +7229(the)s 7573(same)s 220 fnt35 8115 7030(preceding)m 240 fnt82 +0 6745(and)m 220 fnt35 408 6742(f)m 6(ollo)k 3(wing)k +240 fnt82 1302 6745(cross)m 1848(references)s 2883(are)s 3234(found,)s +3904(chances)s 4716(are)s 5067(good)s 5609(that)s 6031(the)s +6383(same)s 6934(tags)s 7374(will)s 7804(be)s 8090(generated,)s +0 6457(and)m 404(the)s 752(appropriate)s 1896(v)s 6(alues)k +2552(can)s 2941(be)s 3223(retrie)s 6(v)k 3(ed)k +4120(from)s 4644(the)s 4992(database)s 5871(immediately)s 15(.)k +480 6083(This)m 982(approach)s 1942(w)s 2(as)k 2389(the)s +2763(genesis)s 3544(of)s 3842(the)s 220 fnt35 4216 6080(@T)m 26(agged)k +240 fnt82 5231 6083(operator)m 9(,)k 6151(whose)s 6845(implementation)s +8428(is)s 8665(no)s 6(w)k 0 5795(immediate:)m 1106(for)s +1436(each)s 220 fnt35 1923 5792(@T)m 26(agged)k 240 fnt82 +2903 5795(operator)m 3751(we)s 4078(produce)s 4897(one)s 240 fnt83 +5290 5797(CR)m 9(OSS_PREC)k 240 fnt82 6775 5795(or)m 240 fnt83 +7026 5797(CR)m 9(OSS_FOLL)k 240 fnt82 8492 5795(g)m 1(alle)k 3(y)k +0 5507(inde)m 3(x,)k 645(replacing)s 1596(the)s 1953(generated)s +2949(tag)s 3304(with)s 3795(the)s 4152(right)s 4672(parameter)s +5696(of)s 5976(the)s 220 fnt35 6333 5504(@T)m 26(agged)k +240 fnt82 7331 5507(operator)m 13(.)k 8288(Nothing)s 0 5219(more)m +547(is)s 757(required.)s 240 fnt84 0 4426(7.)m 291(Conclusion)s +240 fnt82 480 3994(Since)m 1054(its)s 1316(public)s 1953(release)s +2657(in)s 2886(October)s 3702(1991,)s 4275(the)s 4609(Basser)s +5292(Lout)s 5790(interpreter)s 6829(has)s 7185(been)s 7680(ported)s +8335(without)s 0 3706(incident)m 819(to)s 1047(a)s 1202(wide)s +1712(v)s 6(ariety)k 2412(of)s 2672(Unix)s 3195(systems)s +3992(and)s 4385(hardw)s 2(are.)k 5425(It)s 5619(w)s 2(as)k +6029(tested)s 6633(e)s 3(xtensi)k 6(v)k 3(ely)k +7753(before)s 8408(release)s 0 3418(on)m 293(its)s 565(o)s 6(wn)k +1025(documentation,)s 2549(and)s 2949(the)s 3293(fe)s 6(w)k +3695(minor)s 4321(b)s 4(ugs)k 4817(which)s 5455(ha)s 4(v)k 3(e)k +5952(emer)s 4(ged)k 6824(since)s 7367(then)s 7832(ha)s 4(v)k 3(e)k +8329(all)s 8617(been)s 0 3130(\207x)m 3(ed)k 534(in)s +777(the)s 1125(second)s 1848(release,)s 2617(scheduled)s 3632(to)s +3871(appear)s 4568(in)s 4811(mid-1992.)s 480 2756(Se)m 6(v)k 3(en)k +1105(substantial)s 2173(packages)s 3093(of)s 3355(de\207nitions)s 4407(are)s +4746(distrib)s 4(uted)k 5813(with)s 6286(Basser)s 6975(Lout.)s +7582(The)s 8001(Document)s 8998(-)s 0 2468(Layout)m 748(package,)s +1649(and)s 2063(its)s 2349(v)s 6(ariants)k 3160(ReportLayout)s +4560(and)s 4974(BookLayout,)s 6289(pro)s 3(vide)k 7083(the)s +7441(standard)s 8320(features)s 0 2180(that)m 411(all)s 696(documents)s +1776(require:)s 2610(pages,)s 3254(columns,)s 4165(paragraphs,)s 5313(headings,)s +6263(footnotes,)s 7252(\210oating)s 8028(\207gures)s 8722(and)s 0 1892(tables,)m +683(chapters)s 1550(and)s 1973(sections,)s 2870(displays)s 3724(and)s +4148(lists,)s 4658(access)s 5339(to)s 5597(bibliographic)s 6945(databases,)s +7987(cross)s 8549(refer)s 8998(-)s 0 1604(ences,)m 623(and)s +1012(so)s 1263(on)s 1545([11].)s 2092(The)s 2505(BookLayout)s +3748(package)s 4572(has)s 4927(e)s 3(xtra)k 5446(features)s +6237(needed)s 6958(by)s 7237(books,)s 7902(including)s 8843(an)s +0 1316(automatically)m 1355(generated)s 2343(table)s 2864(of)s 3136(contents,)s +4041(Roman)s 4791(page)s 5300(numbers)s 6176(for)s 6515(the)s +6864(pref)s 2(atory)k 7792(material,)s 8682(run)s 8998(-)s +0 1028(ning)m 468(page)s 965(headers,)s 1790(odd)s 2197(and)s +2589(e)s 6(v)k 3(en)k 3078(page)s 3574(layouts,)s +4361(and)s 4754(a)s 4908(sorted)s 5539(inde)s 3(x.)k +6220(The)s 6637(Eq)s 6949(package)s 7778(formats)s 8546(equa)s +8998(-)s 0 740(tions,)m 572(and)s 976(P)s 3(as)k +1356(formats)s 2136(P)s 3(ascal)k 2798(programs)s 3752([10];)s +4262(T)s 19(ab)k 4668(formats)s 5448(tables)s 6056([12];)s +6566(and)s 6970(Fig)s 7342(dra)s 3(ws)k 7961(\207gures)s +8663([6].)s 480 366(The)m 899(non-e)s 3(xpert)k 1983(user)s +2431(who)s 2888(uses)s 3341(these)s 3879(packages)s 4797(percei)s 6(v)k 3(es)k +5732(a)s 5889(system)s 6603(of)s 6865(a)s 7021(standard)s +7880(quite)s 8404(similar)s 0 78(to)m 246(other)s 804(fully)s +1317(de)s 6(v)k 3(eloped)k 2357(batch)s 2940(formatters,)s +4034(although)s 4936(the)s 5292(interf)s 2(ace)k 6187(is)s +6405(considerably)s 7688(more)s 8243(coherent)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 39 40 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +%%+ font Times-Bold +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +1 LoutMargSet +grestore +4289 13844(-)m 4417(39)s 4708(-)s 0 13251(than,)m 525(say)s 15(,)k +942(the)s 1297(trof)s 6(f)k 1792(f)s 2(amily')k 13(s)k +2630([8].)s 3078(The)s 3512(e)s 3(xpert)k 4173(user)s +4637(percei)s 6(v)k 3(es)k 5588(a)s 5760(system)s +6490(which)s 7139(is)s 7355(radically)s 8251(dif)s 6(ferent)k +0 12963(from)m 547(pre)s 6(vious)k 1440(ones,)s 2009(in)s +2276(which)s 2941(a)s 3131(great)s 3691(deal)s 4168(can)s +4580(be)s 4886(achie)s 6(v)k 3(ed)k 5808(v)s 3(ery)k +6308(quickly)s 15(.)k 7198(T)s 19(o)k 7522(tak)s 2(e)k +7997(an)s 8304(e)s 3(xtreme)k 0 12675(e)m 3(xample,)k +936(P)s 3(as)k 1338(w)s 2(as)k 1781(designed,)s +2761(implemented,)s 4138(tested,)s 4825(and)s 5251(documented)s 6501(in)s +6766(one)s 7190(afternoon.)s 8292(Eq)s 8639(took)s 0 12387(about)m +587(a)s 747(week,)s 1353(b)s 4(ut)k 1709(most)s +2229(of)s 2494(that)s 2906(time)s 3380(w)s 2(as)k +3796(spent)s 4355(in)s 4592(marshalling)s 5767(the)s 6110(v)s 6(ast)k +6543(repertoire)s 7520(of)s 7785(mathematical)s 0 12099(symbols,)m 934(and)s +1367(\207ne-tuning)s 2499(the)s 2876(spacing.)s 3800(Most)s 4381(of)s +4681(the)s 5059(ef)s 6(fort)k 5671(seems)s 6335(to)s +6603(go)s 6925(into)s 7379(designing)s 8392(a)s 8588(good)s +0 11811(interf)m 2(ace;)k 944(most)s 1469(symbols)s 2318(are)s +2665(implemented)s 3971(in)s 4214(just)s 4619(one)s 5021(or)s +5280(a)s 5446(fe)s 6(w)k 5852(lines)s 6354(of)s +6625(Lout.)s 480 11437(A)m 698(group)s 1297(of)s 1556(about)s +2135(20)s 2418(satis\207ed)s 3246(non-e)s 3(xpert)k 4327(users)s +4856(has)s 5214(gro)s 6(wn)k 5864(up)s 6145(within)s +6800(the)s 7136(author')s 13(s)k 7944(department,)s 0 11149(mainly)m +703(Honours)s 1563(students)s 2383(with)s 2849(no)s 3127(in)s 9(v)k 3(estment)k +4208(in)s 4436(older)s 4971(systems)s 5764(to)s 5987(hold)s +6456(them)s 6978(back.)s 7579(Basser)s 8260(Lout)s 8756(has)s +0 10861(been)m 511(adv)s 3(ertised)k 1550(on)s 1849(the)s +2199(Internet)s 3003(ne)s 6(ws)k 3542(as)s 3794(a)s 4(v)k 6(ailable)k +4704(via)s 5058(anon)s 3(ymous)k 240 fnt83 6213 10863(ftp)m +240 fnt82 6458 10861(,)m 6567(so)s 6835(the)s 7185(e)s 3(xtent)k +7828(of)s 8101(its)s 8379(outside)s 0 10573(user)m 469(community)s +1624(is)s 1845(hard)s 2339(to)s 2589(g)s 1(auge.)k +3335(About)s 4005(50)s 4311(people)s 5016(ha)s 4(v)k 3(e)k +5528(mailed)s 6247(comments)s 7292(or)s 7562(questions)s 8528(to)s +8778(the)s 0 10285(author;)m 733(man)s 3(y)k 1327(of)s +1608(these)s 2166(people)s 2871(ha)s 4(v)k 3(e)k +3382(ported)s 4062(the)s 4420(program,)s 5348(written)s 6092(small)s +6674(de\207nitions,)s 7802(and)s 8217(modi\207ed)s 0 9997(the)m 348(standard)s +1216(packages.)s 480 9623(Future)m 1160(w)s 2(ork)k 1711(could)s +2301(usefully)s 3125(be)s 3(gin)k 3711(with)s 4194(the)s +4542(impro)s 3(v)k 3(ements)k 5955(suggested)s 6957(in)s +7200(this)s 7596(paper:)s 8294(o)s 3(v)k 3(erlap)k +8998(-)s 0 9335(ping)m 489(spanning)s 1418(columns,)s 2346(better)s +2960(semantics)s 3964(for)s 4312(a)s 4(v)k 6(ailable)k +5231(space,)s 5880(and)s 6294(especially)s 7314(horizontal)s 8349(g)s 1(alle)k 3(ys.)k +0 9047(Support)m 814(for)s 1147(non-)s 1575(European)s 2544(languages)s +3547(is)s 3752(also)s 4185(needed.)s 5022(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k +5977(the)s 6320(main)s 6850(task)s 7291(is)s 7496(the)s +7839(de)s 6(v)k 3(elopment)k 0 8759(of)m 271(an)s +553(interacti)s 6(v)k 3(e)k 1607(document)s 2610(editor)s +3227(based)s 3829(on)s 4126(Lout.)s 4741(A)s 4971(structure)s +5861(editor)s 6478(similar)s 7199(to)s 7438(Lilac)s 7980([13],)s +8484(which)s 0 8471(already)m 753(has)s 1119(objects)s 1843(and)s +2243(user)s 4(-)k 2705(de\207ned)s 3463(symbols,)s 4364(is)s +4570(en)s 9(visaged;)k 5626(since)s 6168(cross)s 6706(references)s +7733(are)s 8076(easy)s 8550(when)s 0 8183(the)m 343(whole)s +979(document)s 1978(is)s 2182(a)s 4(v)k 6(ailable,)k +3136(the)s 3479(only)s 3954(major)s 4565(ne)s 6(w)k +5007(problem)s 5859(is)s 6064(the)s 6406(treatment)s 7362(of)s +7628(g)s 1(alle)k 3(ys,)k 8402(includ)s 8998(-)s +0 7895(ing)m 359(the)s 707(e)s 3(xpansion)k 1732(and)s +2136(retraction)s 3107(of)s 3378(recepti)s 6(v)k 3(e)k +4300(symbols.)s 240 fnt84 0 7146(Note.)m 240 fnt82 657 7147(Since)m +1253(the)s 1610(abo)s 3(v)k 3(e)k 2240(w)s 2(as)k +2670(written)s 3412(the)s 3768(author)s 4448(has)s 4827(completed)s +5889(a)s 6064(re)s 6(vised)k 6815(v)s 3(ersion)k +7581(of)s 7861(Basser)s 8567(Lout,)s 0 6859(in)m 243(which)s +885(the)s 1233(problem)s 2090(concerning)s 3206(a)s 4(v)k 6(ailable)k +4114(space)s 4701(mentioned)s 5769(in)s 6012(Section)s 6786(2.5)s +7132(has)s 7502(been)s 8011(resolv)s 3(ed.)k 240 fnt84 +0 6110(Ackno)m 2(wledgment.)k 240 fnt82 2027 6111(The)m 2534(author)s +3283(gratefully)s 4344(ackno)s 6(wledges)k 5824(man)s 3(y)k +6485(v)s 6(aluable)k 7424(discussions)s 8644(with)s 0 5823(Douglas)m +862(W)s 22(.)k 1183(Jones,)s 1835(especially)s 2857(during)s +3548(the)s 3909(de)s 6(v)k 3(elopment)k 5209(of)s +5493(the)s 5854(g)s 1(alle)k 3(y)k 6501(abstraction;)s +7674(and)s 8091(also)s 8543(man)s 3(y)k 0 5535(helpful)m +732(comments)s 1766(on)s 2063(presentation)s 3288(by)s 3582(the)s +3930(anon)s 3(ymous)k 5083(referee.)s 240 fnt84 0 4742(Refer)m 4(ences)k +240 fnt82 0 4288(1.)m 480(Kingston,)s 1501(Jef)s 6(fre)k 3(y)k +2244(H..)s 2677(Document)s 3770(F)s 3(ormatting)k 4918(with)s +5436(Lout)s 5888(.)s 6088(T)s 16(ech.)k 6690(Rep.)s +7216(408)s 7659(\(1991\))s 8286(,)s 8429(Basser)s 480 4000(Department)m +1668(of)s 1939(Computer)s 2956(Science,)s 3806(The)s 4234(Uni)s 6(v)k 3(ersity)k +5288(of)s 5559(Sydne)s 3(y)k 15(,)k 6367(Australia)s +7242(.)s 0 3497(2.)m 480(Kingston,)s 1492(Jef)s 6(fre)k 3(y)k +2227(H..)s 2652(A)s 2910(ne)s 6(w)k 3385(approach)s +4347(to)s 4613(document)s 5645(formatting)s 6646(.)s 6838(T)s 16(ech.)k +7432(Rep.)s 7950(412)s 8392(\(1991\))s 9019(,)s 480 3209(Basser)m +1177(Department)s 2365(of)s 2636(Computer)s 3653(Science,)s 4503(The)s +4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k +7064(Australia)s 7939(.)s 0 2706(3.)m 480(Kingston,)s 1491(Jef)s 6(fre)k 3(y)k +2224(H..)s 2647(The)s 3101(Basser)s 3824(Lout)s 4362(Document)s +5445(F)s 3(ormatter)k 6383(,)s 6516(1991)s 6971(.)s +7161(Computer)s 8204(program;)s 480 2418(V)m 26(ersion)k 1287(2)s +1480(publicly)s 2337(a)s 4(v)k 6(ailable)k 3264(in)s +3526(the)s 240 fnt83 3893 2420(pub)m 240 fnt82 4326 2418(subdirectory)m +5595(of)s 5885(the)s 6252(home)s 6859(directory)s 7794(of)s +240 fnt83 8084 2420(ftp)m 240 fnt82 8408 2418(to)m 8667(host)s +240 fnt83 480 2132(ftp.cs.su.oz.au)m 240 fnt82 1924 2130(with)m 2439(login)s +3021(name)s 240 fnt83 3628 2132(anonymous)m 240 fnt82 4808 2130(and)m +5246(no)s 5572(passw)s 2(ord.)k 6671(Distrib)s 4(ution)k +7912(via)s 8297(email)s 8916(is)s 480 1842(a)m 4(v)k 6(ailable)k +1388(for)s 1726(non-)s 240 fnt83 2154 1844(ftp)m 240 fnt82 +2459 1842(sites.)m 3047(All)s 3407(enquiries)s 4334(to)s 4573(jef)s 6(f@cs.su.oz.au.)k +0 1339(4.)m 480(Furuta,)s 1211(Richard,)s 2075(Sco\207eld,)s 2965(Jef)s 6(fre)k 3(y)k 15(,)k +3710(and)s 4113(Sha)s 3(w)k 15(,)k 4734(Alan.)s +5363(Document)s 6419(formatting)s 7480(systems:)s 8402(surv)s 3(e)k 3(y)k 15(,)k +480 1051(concepts,)m 1424(and)s 1828(issues)s 2390(.)s 240 fnt83 +2554 1053(Computing)m 3673(Surve)s 7(ys)k 240 fnt84 4465 1050(14)m +240 fnt82 4699 1051(,)m 4806(417\211472)s 5700(\(1982\))s 6327(.)s +0 546(5.)m 480(K)s 6(ernighan,)k 1645(Brian)s 2287(W)s 22(.)k +2649(and)s 3107(Cherry)s 15(,)k 3917(Lorinda)s 4789(L..)s +5213(A)s 5497(system)s 6275(for)s 6667(typesetting)s 7824(mathematics)s +9022(.)s 240 fnt83 480 260(Communications)m 2158(of)s 2439(the)s +2784(A)s 7(CM)k 240 fnt84 3351 257(18)m 240 fnt82 +3585 258(,)m 3692(182\211193)s 4576(\(1975\))s 5203(.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Page: 40 41 +%%BeginPageSetup +%%PageResources: font Times-Roman +%%+ font Times-Italic +/pgsave save def +0.0500 dup scale 10 setlinewidth +%%EndPageSetup +gsave +0 0 translate +240 fnt82 0.0 0.0 0.0 setrgbcolor 11900 16840 0 16840 240 288 60 LoutGraphic +gsave +LoutPageSet +grestore +gsave +0 16840 translate +0.0000 rotate +9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2 +0 LoutMargSet +grestore +4287 13844(-)m 4415(40)s 4710(-)s 0 13252(6.)m 480(Kingston,)s +1488(Jef)s 6(fre)k 3(y)k 2218(H..)s 2638(Fig)s +3033(\211)s 3236(a)s 3425(Lout)s 3961(package)s 4824(for)s +5185(dra)s 3(wing)k 6042(\207gures)s 6684(.)s 6871(T)s 16(ech.)k +7460(Rep.)s 7973(411)s 8392(\(1991\))s 9019(,)s 480 12964(Basser)m +1177(Department)s 2365(of)s 2636(Computer)s 3653(Science,)s 4503(The)s +4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k +7064(Australia)s 7939(.)s 0 12459(7.)m 480(Reid,)s 1042(Brian)s +1633(K..)s 2033(A)s 2266(High-)s 2813(Le)s 6(v)k 3(el)k +3406(Approach)s 4410(to)s 4652(Computer)s 5672(Document)s 6732(Production)s +7779(.)s 7946(In)s 240 fnt83 8205 12461(Pr)m 10(oceed)k +240 fnt82 8998 12459(-)m 240 fnt83 480 12173(ings)m 935(of)s +1217(the)s 1564(7th)s 1926(Symposium)s 3074(on)s 3370(the)s +3716(Principles)s 4755(of)s 5037(Pr)s 10(o)k 2(gr)k 3(amming)k +6421(Langua)s 2(g)k 2(es)k 7526(\(POPL\),)s 8376(Las)s +8779(V)s 26(e)k 240 fnt82 8998 12171(-)m 240 fnt83 +480 11885(gas)m 868(NV)s 240 fnt82 1192 11883(,)m 1299(pages)s +1895(24\21131)s 2470(,)s 2577(1980)s 3052(.)s 0 11378(8.)m +480(Joseph)s 1207(F)s 19(.)k 1443(Ossanna.)s 2436(Nrof)s 6(f/T)k 8(rof)k 6(f)k +3605(User')s 13(s)k 4284(Manual)s 5010(.)s 5193(T)s 16(ech.)k +5777(Rep.)s 6285(54)s 6597(\(1976\))s 7224(,)s 7349(Bell)s +7821(Laboratories)s 9019(,)s 480 11090(Murray)m 1251(Hill,)s 1729(NJ)s +2051(07974)s 2645(.)s 0 10585(9.)m 480(Knuth,)s 1186(Donald)s +1949(E..)s 240 fnt83 2319 10587(The)m 2731(T)s 2882 10539(E)m +3033 10587(XBook)m 240 fnt82 3675 10585(.)m 3839(Addison-W)s 19(esle)k 3(y)k +5419(,)s 5526(1984)s 6000(.)s 0 10082(10.)m 480(Kingston,)s +1485(Jef)s 6(fre)k 3(y)k 2212(H..)s 2629(Eq)s +2973(\211)s 3173(a)s 3359(Lout)s 3892(package)s 4752(for)s +5110(typesetting)s 6232(mathematics)s 7430(.)s 7614(T)s 16(ech.)k +8200(Rep.)s 8711(410)s 480 9794(\(1991\))m 1107(,)s 1248(Basser)s +1980(Department)s 3203(of)s 3509(Computer)s 4561(Science,)s 5446(The)s +5909(Uni)s 6(v)k 3(ersity)k 6998(of)s 7304(Sydne)s 3(y)k 15(,)k +8147(Australia)s 9022(.)s 480 9506(\(Contains)m 1461(an)s 1744(appendix)s +2677(describing)s 3726(the)s 4074(P)s 3(as)k 4454(P)s 3(ascal)k +5116(formatter)s 13(.\))k 0 9003(11.)m 480(Kingston,)s 1478(Jef)s 6(fre)k 3(y)k +2198(H..)s 2608(A)s 2851(be)s 3(ginners')k 3903(guide)s +4504(to)s 4756(Lout)s 5208(.)s 5385(T)s 16(ech.)k +5964(Rep.)s 6467(409)s 6891(\(1991\))s 7518(,)s 7638(Basser)s +8348(Depart)s 8998(-)s 480 8715(ment)m 1018(of)s 1289(Computer)s +2306(Science,)s 3156(The)s 3584(Uni)s 6(v)k 3(ersity)k +4638(of)s 4909(Sydne)s 3(y)k 15(,)k 5717(Australia)s +6592(.)s 0 8212(12.)m 480(Kingston,)s 1475(Jef)s 6(fre)k 3(y)k +2193(H..)s 2600(T)s 19(ab)k 3017(\211)s 3207(a)s +3384(Lout)s 3907(package)s 4757(for)s 5106(formatting)s 6177(tables)s +6725(.)s 6900(T)s 16(ech.)k 7476(Rep.)s 7977(413)s +8392(\(1991\))s 9019(,)s 480 7924(Basser)m 1177(Department)s 2365(of)s +2636(Computer)s 3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k +5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s +7939(.)s 0 7421(13.)m 480(Brooks,)s 1279(K)s 6(enneth)k +2141(P)s 26(..)k 2472(Lilac:)s 3068(a)s 3234(tw)s 2(o-vie)k 6(w)k +4183(document)s 5187(editor)s 5744(.)s 240 fnt83 5908 7423(IEEE)m +6490(Computer)s 240 fnt82 7453 7421(,)m 7560(7\21119)s 8091(\(1991\))s +8718(.)s +grestore + +grestore + +grestore + +pgsave restore +showpage + +%%Trailer +%%DocumentNeededResources: font Helvetica +%%+ font Symbol +%%+ font Times-Roman +%%+ font Times-Italic +%%+ font Times-Bold +%%DocumentSuppliedResources: procset LoutStartUp +%%+ procset LoutTabPrependGraphic +%%+ procset LoutFigPrependGraphic +%%+ procset LoutBasicSetup +%%+ encoding vec2 +%%Pages: 41 +%%EOF diff --git a/doc/design/s1_0 b/doc/design/s1_0 new file mode 100644 index 0000000..ca487ba --- /dev/null +++ b/doc/design/s1_0 @@ -0,0 +1,45 @@ +@Section + @Title { Introduction } +@Begin +@PP +Lout [1, 2] is a high-level language +for document formatting, designed and implemented by the author. The +implementation, known as Basser Lout, is a fully operational production +version written in C for the Unix operating system, +@FootNote { Unix is a trademark of "AT&T" Bell Laboratories. } +which translates Lout source code into PostScript, +@FootNote { PostScript is a trademark of Adobe Systems, Incorporated. } +a device-independent graphics rendering language accepted by many +high-resolution output devices, including most laser printers. Basser +Lout is available free of charge [3]. It includes +installation instructions, C source, seven standard packages, and complete +documentation in the form of six technical reports and a manual page. +@PP +The Lout project arose out of the author's desire to bring to document +formatting languages the elegance of expression found in programming +languages like Algol-60 and Pascal. This emphasis on expressiveness +has produced an order of magnitude reduction in the cost of developing +document formatting applications. For example, an equation formatting +application, which may be difficult or impossible to add to other +systems, can be written in Lout in a few days. +@PP +When expert users can implement such applications quickly, non-experts +benefit. Although Lout itself provides only a small kernel of carefully +chosen primitives, packages written in Lout and distributed with Basser +Lout provide an unprecedented array of advanced features in a form +accessible to non-expert users. The features include rotation and scaling, +fonts, paragraph and page breaking, displays and lists, floating figures +and tables, footnotes, chapters and sections (automatically numbered), +running page headers and footers, odd-even page layouts, automatically +generated tables of contents, sorted indexes and reference lists, +bibliographic and other databases (including databases of formats for +printing references), equations, tables, diagrams, formatting of +Pascal programs, and automatically maintained cross references. +@PP +This paper charts the evolution of Lout from conception in mid-1984 to the +public release of Basser Lout in October 1991. Lout is organized around +four key concepts -- objects, definitions, galleys, and cross references -- +and they were developed in the order listed, so this paper will treat each +in turn, discussing its design, implementation, problems, and +prospects for further improvement. +@End @Section diff --git a/doc/design/s2_0 b/doc/design/s2_0 new file mode 100644 index 0000000..ef4bea7 --- /dev/null +++ b/doc/design/s2_0 @@ -0,0 +1,14 @@ +@Section + @Title { Objects } +@Begin +@PP +The essence of any move to a higher level is the introduction of some +abstraction which serves to organize the low-level operations, +resulting in a more succinct expression of their +common combinations at the cost of some loss of detailed control. The +early part of the Lout project was spent in the development of such an +abstraction for the building blocks of documents, one which could +explain, not just the simple phenomena of words, lines, and paragraphs, +but also the alignment of columns in tables, and the complex nested +structures of equations. +@BeginSubSections diff --git a/doc/design/s2_1 b/doc/design/s2_1 new file mode 100644 index 0000000..4ee4c31 --- /dev/null +++ b/doc/design/s2_1 @@ -0,0 +1,87 @@ +@SubSection + @Tag { genesis } + @Title { The genesis of the object abstraction } +@Begin +@PP +When one examines previous document formatting systems [4] +looking for ideas for abstractions, as the author did in 1984, the Eqn +formatting language [5] stands out like a beacon. In +Eqn, a mathematical formula such as +@ID @Eq { { x sup 2 + 1 } over 4 } +is produced by typing +@ID @Code "{ x sup 2 + 1 } over 4" +in the input file; @Code sup and @Code over are binary operators, and +braces are used for grouping. This is document formatting at a very +high level, close to the language of mathematics itself, with all +reference to font changes and spacing suppressed. +@PP +Eqn provides a single data type (let us call it the {@I expression}), +built up recursively in context-free style: where one expression may appear, +any expression may appear. This approach is common in algebra and +programming languages, where its simplicity and expressiveness have long +been appreciated; but Eqn was the first language to demonstrate its +utility in document formatting. +@PP +Each expression is treated by Eqn as a rectangle with a +{@I {horizontal axis}}, used for alignment with adjacent expressions: +@ID @ShowMarks marks { horizontal } @Eq { { x sup 2 + 1 } over 4 } +The size and rendering of the expression on the printed page are +known only to the implementation, never explicitly calculated or +accessed by the user. This prohibition is +crucial to the maintenance of the context-free property in practice. In +Lout, for example, equations, figures, tables, and arbitrary objects may +be mixed together freely. This would be impossible if size information +was hidden from the implementation in user calculations. +@PP +The object abstraction of Lout is a direct descendant of the Eqn +expression. It employs the same context-free recursive style of construction, +and each object is treated by Lout as a rectangle: +@ID @Fig { +@ShowMarks { 1c @Wide ^| 2c @Wide 0.45c @High ^/ 0.35c @High } +} +The horizontal axis, called a @I { row mark } in Lout, has a +vertical analogue called a {@I {column mark}}, creating a valuable +symmetry between horizontal and vertical. Multiple column and row marks +are permitted: +@ID @OneRow @Fig { +A:: @Box margin { 0c } paint { grey } { 1.2c @Wide 0.8c @High } +|1c +B:: @Box margin { 0c } paint { grey } { 1c @Wide 0.8c @High } +/0.5c +C:: @Box margin { 0c } paint { grey } { 0.7c @Wide 0.8c @High } +|1c +D:: @Box margin { 0c } paint { grey } { 1.3c @Wide 0.8c @High } +// @Line linestyle { dashed } + from { A@W -- { 0.3 cm 0 } } + to { B@W ++ { 1.6 cm 0 } } +// @Line linestyle { dashed } + from { C@W -- { 0.3 cm 0 } } + to { D@W ++ { 1.6 cm 0 } } +// @Line linestyle { dashed } + from { A@NW ++ { 0 0.3 cm } } + to { C@SW -- { 0 0.3 cm } } +// @Line linestyle { dashed } + from { B@NW ++ { 0.3 cm 0.3 cm } } + to { D@SW ++ { 0.3 cm -0.3 cm } } +} +so that objects are able to represent tables. +@PP +This abstraction has some limitations, the most obvious being the restriction +of size calculations to rectangular bounding boxes. Non-rectangular and +disconnected shapes arise naturally in figures and in the characters of +fonts; the extension to them is conceptually straightforward and might +help to explain some fine points of layout such as kerning. However, +there are implementation and language design problems, particularly +when filling non-rectangular shapes with text, and so the author chose +to keep to Eqn's rectangles. +@PP +A more fundamental limitation of the object abstraction arises from the +inability of recursive data types to describe cross-linked structures, +which seem to require some means of naming the multiply referenced +parts. Lout is obliged to introduce additional abstractions to cope +with cross linking: galleys for inserting text into pages +(Section {@NumberOf galleys}), cross references (Section {@NumberOf cross}), +and labelled points in figure drawing [6]. An +abstraction closer to hypertext might form a more unified basis for +these features. +@End @SubSection diff --git a/doc/design/s2_2 b/doc/design/s2_2 new file mode 100644 index 0000000..f4a3818 --- /dev/null +++ b/doc/design/s2_2 @@ -0,0 +1,79 @@ +@SubSection + @Tag { lexical } + @Title { Grammatical and lexical structure } +@Begin +@PP +If objects are to be constructed like mathematical expressions, the +natural notation is a functional language based on operators, as in +Eqn. The grammar of Lout objects is accordingly +@ID @OneRow @Eq { +matrix { +object +nextcol +--> above --> above --> above --> above --> above --> above --> above --> +nextcol +{ object ``` infixop ``` object } +labove gap { "1fx" } +{ prefixop ``` object } +labove gap { "1fx" } +{ object ``` postfixop } +labove gap { "1fx" } +{ noparsop } +labove gap { "1fx" } +{ literalword } +labove gap { "1fx" } +{ @Code "{" ``` object ``` @Code "}" } +labove gap { "1fx" } +{ object ``` object } +labove gap { "1fx" } +} +} +where {@Eq {infixop}}, {@Eq {prefixop}}, {@Eq {postfixop}}, and +{@Eq {noparsop}} are identifiers naming operators which take 0, 1 +or 2 parameters, as shown, and @Eq {literalword} is a sequence of +non-space characters, or an arbitrary sequence of characters +enclosed in double quotes. Ambiguities are resolved by precedence +and associativity. +@PP +The last production allows a meaning for expressions such as +{@Code "{}"}, in which an object is missing. The value of this +@I {empty object} is a rectangle of size 0 by 0, with one column +mark and one row mark, that prints as nothing. +@PP +The second-last production generates sequences of arbitrary objects +separated by white space, called {@I paragraphs}. Ignoring +paragraph breaking for now, the natural meaning is that the two +objects should appear side by side, and Lout's parser accordingly +interpolates an infix horizontal concatenation operator (see below) +between them. This operator is associative, so the grammatical +ambiguity does no harm. However, the Algol-60 rule that white space +should be significant only as a separator is necessarily broken by +Lout in just this one place. +@PP +Algol-like languages distinguish literal strings from identifiers by +enclosing them in quotes, but literals are far too frequent in document +formatting for this to be viable. The conventional solution is to +begin identifiers with a special character, and Lout follows Scribe +[7] in using "`@'" rather than the "`\\'" of troff +[8] and @TeX [9]. +@PP +However, Lout takes the unusual step of making an initial "`@'" +optional. The designers of Eqn apparently considered such +characters disfiguring in fine-grained input like equations, and +this author agrees. The implementation is straightforward: "`@'" is +classed as just another letter, and every word is searched for in +the symbol table. If it is found, it is an identifier, otherwise it +is a literal. A warning message is printed when a literal beginning +with "`@'" is found, since it is probably a mis-spelt identifier. No +such safety net is possible for identifiers without "`@'". +@PP +Equation formatting also demands symbols made from punctuation +characters, such as @Code "+" and {@Code "<="}. It is traditional to +allow such symbols to be juxtaposed, which means that the input +@ID @Code "<=++" +for example must be interpreted within the lexical analyser by searching +the symbol table for its prefixes in the order {@Code "<=++"}, +{@Code "<=+"}, {@Code "<="}. Although this takes quadratic time, in +practice such sequences are too short to make a more sophisticated +linear method like tries worthwhile. +@End @SubSection diff --git a/doc/design/s2_3 b/doc/design/s2_3 new file mode 100644 index 0000000..341ea74 --- /dev/null +++ b/doc/design/s2_3 @@ -0,0 +1,326 @@ +@SubSection + @Tag { objects } + @Title { Basic structural operators } +@Begin +@PP +A programming language may be considered complete when it attains the +power of a Turing machine, but no such criterion seems relevant to +document formatting. Instead, as the language develops and new +applications are attempted, deficiencies are exposed and the operator set is +revised to overcome them. +@PP +Lout has a repertoire of 23 primitive operators +(Figure {@NumberOf primitives}), + +@Figure + @Caption { The 23 primitive operators of Lout, in order of +increasing precedence. } + @Tag { primitives } +@Tab + vmargin { 0.5vx } + @Fmta { @Col @I A ! @Col B } +{ +@Rowa + A { object {@Code "/"}gap object } + B { Vertical concatenation with mark alignment } +@Rowa + A { object {@Code "//"}gap object } + B { Vertical concatenation with left justification } +@Rowa + A { object {@Code "|"}gap object } + B { Horizontal concatenation with mark alignment } +@Rowa + A { object {@Code "||"}gap object } + B { Horizontal concatenation with top-justification } +@Rowa + A { object {@Code "&"}gap object } + B { Horizontal concatenation within paragraphs } +@Rowa + A { {@Code "@OneCol"} object } + B { Hide all but one column mark of @I object } +@Rowa + A { {@Code "@OneRow"} object } + B { Hide all but one row mark of @I object } +@Rowa + A { font @Code "@Font" object } + B { Render @I object in nominated font } +@Rowa + A { breakstyle @Code "@Break" object} + B { Break paragraphs of @I object in nominated style } +@Rowa + A { spacestyle @Code "@Space" object } + B { Render spaces between words in nominated style } +@Rowa + A { length {@Code "@Wide"} object } + B { Render @I object to width @I length } +@Rowa + A { length {@Code "@High"} object } + B { Render @I object to height @I length } +@Rowa + A { {@Code "@HExpand"} object} + B { Expand horizontal gaps to fill available space } +@Rowa + A { {@Code "@VExpand"} object} + B { Expand vertical gaps to fill available space } +@Rowa + A { {@Code "@HScale"} object } + B { Horizontal geometrical scaling to fill available space } +@Rowa + A { {@Code "@VScale"} object } + B { Vertical geometrical scaling to fill available space } +@Rowa + A { angle {@Code "@Rotate"} object } + B { Rotate @I object by @I angle } +@Rowa + A { PostScript {@Code "@Graphic"} object } + B { Escape to graphics language } +@Rowa + A { @Code "@Next" object } + B { Add 1 to an object denoting a number } +@Rowa + A { object @Code "@Case" alternatives } + B { Select from a set of alternative objects } +@Rowa + A { identifier @Code "&&" object } + B { Cross reference } +@Rowa + A { cross-reference @Code "@Open" object } + B { Retrieve value from cross reference } +@Rowa + A { cross-reference @Code "@Tagged" object} + B { Attach cross referencing tag to object } +} + +which has proven adequate for a wide variety of features, including equations, +tables, and page layout, and so seems to be reasonably complete in this +pragmatic sense. In this section we introduce the eight concatenation and +mark-hiding operators. To them falls the basic task of assembling complex +objects from simple ones, and they were the first +to be designed and implemented. +@PP +Many of the operators of Eqn can be viewed as building small tables. A +built-up fraction, for example, has one column and three rows +(numerator, line, and denominator). Numerous investigations of this +kind convinced the author that operators capable of assembling the rows +and columns of tables would suffice for building all kinds of objects. +@PP +The simplest objects are empty objects and literal words like +{@Code metempsychosis}, which have one column mark and one row mark: +@ID { +@ShowMarks metempsychosis +} +To place two arbitrary objects side by side, we use the infix +operator {@Code "|"}, denoting horizontal concatenation. For +example, +@ID { +@Code "USA |0.2i Australia" +} +produces the object +@ID { +@ShowMarks USA |0.2i @ShowMarks Australia +} +The row marks are merged into one, fixing the vertical position of +the objects relative to each other; their horizontal separation is +determined by the @I gap attached to the operator, in this case 0.2 +inches. We think of the gap as part of the operator, although +strictly it is a third parameter. It may be omitted, defaulting to +{@Code "0i"}. +@PP +@I {Vertical concatenation} & , denoted by the infix operator {@Code "/"}, +is the same apart from the change of direction: +@ID { +@Code "Australia /0.1i USA" +} +produces the object +@ID { +@ShowMarks Australia /0.1i +@ShowMarks USA +} +with column marks merged and a 0.1 inch gap. +@PP +Consider now what happens when horizontal and vertical are combined: +@ID @OneRow @Code { + |1m "{" USA |1m "|0.2i" |1m Australia "}" +/1vx "/0.1i" | "{" Washington | "|" | Canberra "}" +} +The two parameters of @Code "/" now have two column marks each, and +they will be merged with the corresponding marks in the other +parameter, yielding the object + +@ID @OneRow { + @BackEnd @Case { + PostScript @Yield { + @ShowMarks USA & + { 0 ymark moveto xsize 10 pt add ymark lineto [ 3 pt ] 0 setdash stroke } + @Graphic {1c @Wide } + |0.2i @ShowMarks Australia +/0.1i @ShowMarks Washington | @ShowMarks Canberra + } + PDF @Yield { + @ShowMarks USA & + { [ __mul(3, __pt) ] 0 d 0 __ymark m __add(__xsize, __mul(10, __pt)) __ymark l S } + @Graphic {1c @Wide } + |0.2i @ShowMarks Australia +/0.1i @ShowMarks Washington | @ShowMarks Canberra + } + } +} +The @Code "0.2i" gap separates columns, not individual items in +columns, so a gap attached to the second @Code "|" would serve no +purpose; any such gap is ignored. If the number of marks to be merged +differs, empty columns are added at the right to equalize the number. The +four marks protruding from the result are all available for merging +with neighbouring marks by other concatenation operators. The precedence +of @Code "|" is higher than the precedence of {@Code "/"}, so the braces +could be omitted. +@PP +When lines of text are concatenated, it is conventional to measure +their separation from baseline to baseline (mark to mark in Lout), +rather than from edge to edge as above. This idea of different +reference points for measurement evolved over the years into a +system of six @I {gap modes} (Figure {@NumberOf gapmodes}), expressed +by appending a letter to the length. For example, @Code "|0.2i" is +an abbreviation for {@Code "|0.2ie"}, meaning 0.2 inches measured +from edge to edge; @Code "|0.3ix" +produces a 0.3 inch gap measured from mark to mark and widened if +necessary to prevent overstriking; and @Code "|2.5it" places its right +parameter 2.5 inches from the current left margin, irrespective of +the position of the left parameter. There is also a choice of +eleven units of measurement (inches, centimetres, multiples of the +current font size, etc.), the most interesting being +the @Code r unit: one @Code r is the column width minus the width of +the following object, so that @Code "|1rt" produces sufficient space +to right justify the following object, and @Code "|0.5rt" to center +it. These features implement spacings needed in practice rather +than suggested by theory. They work with all five concatenation +operators, horizontal and vertical. + +@Figure + @Tag { gapmodes } + @Caption { The six gap modes (@I length is any length). Hyphenation +mode has an extra property not shown here. } +@Fig { +{ /2.5vx Edge-to-edge |0.3i {@Code "|"} &1p {@I length} &1p {@Code e} + /4.2vx Hyphenation |0.3i {@Code "|"} &1p {@I length} &1p {@Code h} + /4.2vx Overstrike |0.3i {@Code "|"} &1p {@I length} &1p {@Code o} + /4.2vx Mark-to-mark |0.3i {@Code "|"} &1p {@I length} &1p {@Code x} + /4.2vx Kerning |0.3i {@Code "|"} &1p {@I length} &1p {@Code k} + /4.2vx Tabulation |0.3i {@Code "|"} &1p {@I length} &1p {@Code t} +} +||0.5i +@Box margin { 0c } 6c @Wide 14.5c @High 9p @Font +{ + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 2.2c @Wide 1.4c @High } @Put { @DoubleArrow 1.8c } + @At { 2.2c @Wide 1.6c @High } @Put { 1.8c @Wide { &0.5rt @I length } } + } + //4vx + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 2.2c @Wide 1.4c @High } @Put { @DoubleArrow 1.8c } + @At { 2.2c @Wide 1.6c @High } @Put { 1.8c @Wide { &0.5rt @I length } } + } + //4vx + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 1.2c @Wide 1.5c @High } @Put { @DoubleArrow 3.3c } + @At { 1.2c @Wide 1.7c @High } @Put { 3.3c @Wide { &0.5rt @I length } } + } + //4vx + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 1.2c @Wide 1.5c @High } @Put { @DoubleArrow 3.3c } + @At { 1.2c @Wide 1.7c @High } + @Put 3.3c @Wide { |0.5rt @Eq { max(length, a+b) } } + @At { 1.2c @Wide 0.4c @High } @Put { @DoubleArrow 1.0c } + @At { 1.2c @Wide 0.2c @High } @Put { 1.0c @Wide { &0.5rt @I a } } + @At { 4c @Wide 0.4c @High } @Put { @DoubleArrow 0.5c } + @At { 4c @Wide 0.2c @High } @Put { 0.5c @Wide { &0.5rt @I b } } + } + //4.5vx + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 1.2c @Wide 1.5c @High } @Put { @DoubleArrow 3.3c } + @At { 1.2c @Wide 1.7c @High } + @Put { 3.3c @Wide { |0.5rt @Eq { max(length, a, b) } } } + @At { 1.2c @Wide 0.4c @High } @Put { @DoubleArrow 1.0c } + @At { 1.2c @Wide 0.2c @High } @Put { 1.0c @Wide { &0.5rt @I a } } + @At { 4c @Wide 0.4c @High } @Put { @DoubleArrow 0.5c } + @At { 4c @Wide 0.2c @High } @Put { 0.5c @Wide { &0.5rt @I b } } + } + //4vx + @OneRow { + @At { 1c @Wide 0.5c @High } @Put { @LBox 0.2co } + @At { 4c @Wide 0.5c @High } @Put { @LBox 0.5co } + @At { 0.0c @Wide 1.6c @High } @Put { @DoubleArrow 4.0c } + @At { 2.8c @Wide 1.8c @High } @Put { @I length } + } + //5vx + @DoubleArrow 6c + //0.1c |0.5rt @I { current bound } +} +} + +@PP +When we construct a built-up fraction, the result has three row marks, but +only the second should be visible outside the object: +@ID @Eq { @ShowMarks { X over Y } } +This is a common problem, and accordingly a @Code "@OneRow" operator was +introduced for hiding all but one of the row marks of its +parameter. Normally, the first mark is the survivor, but a later mark can +be chosen by prefixing @Code "^" to the preceding concatenation operator: +@ID @Code "@OneRow { X ^/2p @HLine /2p Y }" +has the desired result, where {@Code "2p"} is two points and @Code "@HLine" +is an easy combination of Lout's graphics operators. A similar operator, +{@Code "@OneCol"}, hides column marks. +@PP +A variant of @Code "/" called @Code "//" is provided which performs +vertical concatenation but ignores all column marks and simply +left-justifies its two parameters: +@ID @OneRow @Code { +"Heading //0.1i" +"A |0.2i B /0.1i" +"C | D" +} +has result +@ID { Heading //0.1i A |0.2i B /0.1i C | D } +showing that spanning columns in tables motivate the inclusion of this +operator. There is an analogous @Code "||" operator. The author +would have preferred to leave out these operators, since they +complicate the implementation, and it is interesting to examine the +prospects of doing so. +@PP +The @Code "//" operator is formally redundant, because in general +the expression @Code "x // y" can be replaced by +@ID @OneRow @Code { +"@OneCol { | x } /" +"@OneCol { | y }" +} +for any objects {@Code x} and {@Code y}. By concatenating an empty +object at the left of @Code x and hiding all but that empty object's +column mark, we effectively shift {@Code x}'s column mark to its left +edge. The same goes for {@Code y}, so the @Code "/" operator has just +one column mark to merge, at the extreme left, and its effect is +indistinguishable from {@Code "//"}. +@PP +Unfortunately, if @Code y consists of two rows separated by {@Code "/"}, +as in the example above, both rows must be placed inside the +{@Code "@OneCol"}, and the table cannot be entered in the simple +row-by-row manner that non-expert users naturally expect. Another +advantage of @Code "//" is that its left parameter can be printed +before its right parameter is known; this is important when the left +parameter is an entire page. +@PP +The fifth and final concatenation operator, {@Code "&"}, is an explicit +version of the horizontal concatenation operator interpolated when +objects are separated by white space. It is formally identical to +@Code "|" except for taking higher precedence and being subject to +replacement by @Code "//1vx" during paragraph breaking +(Section {@NumberOf style}). +@End @SubSection diff --git a/doc/design/s2_4 b/doc/design/s2_4 new file mode 100644 index 0000000..38d25e7 --- /dev/null +++ b/doc/design/s2_4 @@ -0,0 +1,345 @@ +@SubSection + @Tag { objects.impl } + @Title { Implementation of objects and concatenation } +@Begin +@PP +In this section we discuss the implementation of objects and concatenation, +and especially mark alignment. The first step is to use an operator +precedence parser to convert input such as +@ID @Code "a |0.5i b /0.2i c | d" +into parse trees such as +@ID @Eq { +@Fig { +@Tree { +@Node @FCircle fraction +@FirstSub { + @Node @FCircle bar + @FirstSub { @Node @FCircle a } + @NextSub { @Node @FEllipse 0.5i } + @NextSub { @Node @FCircle b } +} +@NextSub { @Node @FEllipse 0.2i } +@NextSub { + @Node @FCircle bar + @FirstSub { @Node @FCircle c } + @NextSub { @Node @FCircle } + @NextSub { @Node @FCircle d } +} +} +} +} +Missing objects are replaced by empty objects, and sequences of +concatenation operators are consolidated: +@ID @Eq { +@Fig { +@Tree { +@Node @FCircle bar +@FirstSub { @Node @FCircle a } +@NextSub { @Node @FEllipse 0.2i } +@NextSub { + @Node @FCircle bar + @FirstSub { @Node @FCircle c } + @NextSub { @Node @FEllipse 0.3i } + @NextSub { @Node @FCircle d } +} +} +} +&2m ==> &2m +@Fig { +@Tree { +@Node @FCircle bar +@FirstSub { @Node @FCircle a } +@NextSub { @Node @FEllipse 0.2i } +@NextSub { @Node @FCircle c } +@NextSub { @Node @FEllipse 0.3i } +@NextSub { @Node @FCircle d } +} +} +} +to make manifest their associativity and reduce the depth of the tree +for efficiency later. +@PP +The required semantic information is the size of each subobject, +consisting of four integers: width to left and right of the +distinguished column mark, and height above and below the distinguished +row mark. These numbers are always non-negative in Basser Lout, but +this restriction is unnecessary and should be dropped. +@PP +For the leaves, which are simple words, the numbers are obtained from +font tables. For the higher levels we apply recursive rules. Suppose +that @Eq { hgap(x, g, y) } returns the desired distance between the +column marks of objects @Eq { x } and @Eq { y } when they are separated by +gap @Eq { g }: @Eq { right(x) + length(g) + left(y) } when the gap mode is +edge-to-edge, the larger of @Eq { length(g) } and +@Eq { right(x) + left(y) } when the mode is mark-to-mark, and so on. Given +an object +@ID @Eq { +X = x sub 1 ````` bar g sub 1 ````` ... ````` { "-2p" @Font "^"}bar g sub i-1 +````` x sub i ````` ... ````` bar g sub n-1 ````` x sub n +} +we may calculate its size as follows: +@ID @Eq { +left(X) ^= left( x sub 1 ) + hgap( x sub 1 , g sub 1 , x sub 2 ) ++ ... + hgap( x sub i-1 , g sub i-1 , x sub i ) +/1.4vx +right(X) ^= hgap( x sub i , g sub i , x sub i+1 ) ++ ... + hgap( x sub n-1 , g sub n-1 , x sub n ) + right( x sub n ) +/1.4vx +"above"(X) ^= "above"(x sub 1 ) up ... up "above"(x sub n ) +/1.4vx +"below"(X) ^= "below"(x sub 1 ) up ... up "below"(x sub n ) +} +where @Eq { non up } returns the larger of its two parameters. Similar +formulas are easily derived for the other operators. +@PP +For purposes of exposition we will now make the simplifying +assumptions that all gaps are {@Code "0i"}, all column marks lie at +the left edge, and all row marks lie at the top edge. Then the size +of each object can be expressed by just two numbers, width and +height, and the four formulas reduce to +@ID @Eq { +width( x sub 1 rel bar ... rel bar x sub n ) ^= +width( x sub 1 ) + ... + width( x sub n ) +/1.4vx +height( x sub 1 rel bar ... rel bar x sub n ) ^= +height( x sub 1 ) up ... up height( x sub n ) +} +The corresponding formulas for vertical concatenation are +@ID @Eq { +width( x sub 1 rel "/" ... rel "/" x sub n ) ^= +width( x sub 1 ) up ... up width( x sub n ) +/1.4vx +height( x sub 1 rel "/" ... rel "/" x sub n ) ^= +height( x sub 1 ) + ... + height( x sub n ) +} +According to these formulas, the height of +@ID @Eq { @Fig { @Tree { +@Node @FCircle fraction +@LeftSub { + @Node @FCircle bar + @LeftSub { @Node @FCircle a } + @RightSub { @Node @FCircle b } +} +@RightSub { + @Node @FCircle bar + @LeftSub { @Node @FCircle c } + @RightSub { @Node @FCircle d } +} +}}} +is +@ID @Eq { +[ height(a) up height(b)] + [ height(c) up height(d)] +} +which is correct, but for width they yield +@ID @Eq { +[ width(a) + width(b)] up [ width(c) + width(d)] +} +which is not, since it does not take the merging of column marks into +account. The asymmetry between horizontal and vertical has come +about because the row entries, such as @Eq {a} and {@Eq {b}}, are +adjacent in the tree, but the column entries, such as @Eq {a} and +{@Eq {c}}, are not. It would be possible to solve this cross-linking +problem by augmenting the size information stored in each node to +record the number of marks and the size of each, but the author has +preferred the following method which makes structural changes to the +tree instead. +@PP +If @Eq { a } and @Eq { c } share a column mark, they each might as well +have width { @Eq {width(a) up width(c) }}, since all width calculations +apply to entire columns. Accordingly, we introduce a new operator, +@Eq {COL}, defined by +@ID @Eq { width( x sub 1 bin COL ... bin COL x sub n ) = +width( x sub 1 ) up ... up width( x sub n ) +} +and replace both @Eq { a } and @Eq { c } by {@Eq { a bin COL c }}. To +prevent @Eq { COL } operators from disturbing height calculations, we +define a binary operator called @Eq { SPLIT } by +@ID @Eq { width( x bin SPLIT y) ^= width(x) +/1.4vx +height( x bin SPLIT y) ^= height(y) } +which switches height and width calculations onto different +subtrees. Then the transformation +@ID @Eq { +@Fig { @Tree { + @Node @FCircle a +}} +&2m ==> &2m +@Fig { @Tree { + @Node @FEllipse SPLIT + @LeftSub { + @Node @FEllipse COL + @LeftSub { @Node @FCircle a } + @RightSub { @Node @FCircle c } + } + @RightSub { @Node @FCircle a } +}} +} +# where @Eq { S } denotes a @Eq { SPLIT } node and @Eq { C } denotes a +# @Eq { COL } node, +widens @Eq { a } to @Eq {width(a) up width(c) } without affecting its height; +it is applied to every object that shares its column mark with at least +one other object. A similar transformation involving a @Eq { ROW } operator +deals with shared row marks. The effect on our little table is to replace +@ID @Eq { @Fig { @Tree { +@Node @FCircle fraction +@LeftSub { + @Node @FCircle bar + @LeftSub { @Node @FCircle a } + @RightSub { @Node @FCircle b } +} +@RightSub { + @Node @FCircle bar + @LeftSub { @Node @FCircle c } + @RightSub { @Node @FCircle d } +} +}}} +by +@ID @Eq { @Fig maxlabels { "70" } { @Tree hmargin { "0.1c" } { +@Node @FCircle fraction +@FirstSub { + @Node @FCircle bar + @FirstSub { + @Node @FEllipse SPLIT + @FirstSub { + @Node @FEllipse COL + @FirstSub { @Node @FCircle a } + @NextSub { @Node @FCircle c } + } + @NextSub { + @Node @FEllipse ROW + @FirstSub { @Node @FCircle a } + @NextSub { @Node @FCircle b } + } + } + @NextSub { + @Node @FEllipse SPLIT + @FirstSub { + @Node @FEllipse COL + @FirstSub { @Node @FCircle b } + @NextSub { @Node @FCircle d } + } + @NextSub { + @Node @FEllipse ROW + @FirstSub { @Node @FCircle a } + @NextSub { @Node @FCircle b } + } + } +} +@NextSub { + @Node @FCircle bar + @FirstSub { + @Node @FEllipse SPLIT + @FirstSub { + @Node @FEllipse COL + @FirstSub { @Node @FCircle a } + @NextSub { @Node @FCircle c } + } + @NextSub { + @Node @FEllipse ROW + @FirstSub { @Node @FCircle c } + @NextSub { @Node @FCircle d } + } + } + @NextSub { + @Node @FEllipse SPLIT + @FirstSub { + @Node @FEllipse COL + @FirstSub { @Node @FCircle b } + @NextSub { @Node @FCircle d } + } + @NextSub { + @Node @FEllipse ROW + @FirstSub { @Node @FCircle c } + @NextSub { @Node @FCircle d } + } + } +} +}}} +In fact, common subexpressions are identified (trivially) and the result +is a directed acyclic graph; each affected leaf has two parents, one for +width and one for height; and each @Eq { COL } or @Eq { ROW } node has +one parent and one child for each object lying on the corresponding +mark. The data structure roughly doubles in size, and this occurs only +rarely in practice. +@PP +This method can cope with any legal input, including +@ID @OneRow @Code { +"{ a // c | d } | { b / e }" +"/ { f / i } | { g | h // j }" +} +which produces overlapping spanning columns: +@ID @I @Fig { + @FBox margin { 0.2c } width { 1.6c } 1.2f @Font a | + @FBox margin { 0.2c } width { 0.6c } 1.2f @Font b | +// @FBox margin { 0.2c } width { 0.6c } 1.2f @Font c | + @FBox margin { 0.2c } width { 0.6c } 1.2f @Font d | + @FBox margin { 0.2c } width { 0.6c } 1.2f @Font e | +// @FBox margin { 0.2c } width { 0.6c } 1.2f @Font f | + @FBox margin { 0.2c } width { 0.6c } 1.2f @Font g | + @FBox margin { 0.2c } width { 0.6c } 1.2f @Font h | +// @FBox margin { 0.2c } width { 0.6c } 1.2f @Font i | + @FBox margin { 0.2c } width { 1.6c } 1.2f @Font j | +} +The boxes have been added to clarify the structure. The width of this +object is formally +@ID @Eq { ((width(a) up (x + y)) + z) up (x + ((y + z) up width(j))) } +where +@IL +@ListItem @Eq { x = width(c) up width(`f`) up width(i) } +@ListItem @Eq { y = width(d`) up width(g) } +@ListItem @Eq { z = width(b) up width(e) up width(h) } +@EL +It seems clear that @Eq { y } at least must appear twice in any +expression for the width of this object made out of simple addition +and maxing operations, showing that an ordinary tree +structure is insufficient for overlapping spanning columns. The Basser +Lout interpreter actually rejects such structures, owing to the author's +doubts about the implementability of @I Constrained and @I AdjustSize +(Section {@NumberOf constraints}) on them; but with hindsight this caution +was unnecessary. +@PP +The directed acyclic graph is ordered in the sense that the order of +the edges entering and leaving each node matters. The structure is +highly dynamic, and traversals both with and against the arrows are +required. After a few ad-hoc attempts to extend the usual tree +representation had failed, the author developed a representation based +on doubly linked lists of records denoting links, whose flexibility more +than compensated for the somewhat excessive memory consumption. For example, +@ID @Eq { @Fig { + A:: @FCircle a |2c |2c B:: @FCircle b +/1.5c C:: @FCircle c | D:: @FCircle d +// A @JoinFigures arrow { forward } C +// A @JoinFigures arrow { forward } D +// B @JoinFigures arrow { forward } D +}} +is represented by +@CD @Eq { @Fig maxlabels { "300" } { +A:: @DagBox mid { @BlackDot } base { a } |2c |2c |2c |2c +B:: @DagBox mid { @BlackDot } base { b } +/1c L:: @DagBox top { @BlackDot } mid { @BlackDot } base { LK } +| M:: @DagBox top { @BlackDot } mid { @BlackDot } base { LK } +| | N:: @DagBox top { @BlackDot } mid { @BlackDot } base { LK } +/1c +C:: @DagBox top { @BlackDot } base { c } | | +D:: @DagBox top { @BlackDot } base { d } +// @TVShape nw { A@MID@CTR } ne { A@MID@CTR } sw {L@MID@CTR } se { M@MID@CTR } +// @TVShape nw { L@TOP@CTR } ne { L@TOP@CTR } sw {C@TOP@CTR } se { C@TOP@CTR } +// @TVShape nw { M@TOP@CTR } ne { N@TOP@CTR } sw {D@TOP@CTR } se { D@TOP@CTR } +// @TVShape nw { B@MID@CTR } ne { B@MID@CTR } sw {N@MID@CTR } se { N@MID@CTR } +}} +where @Eq { LK } tags a record representing a link. The first list +in any node contains all the incoming links, the second contains the +outgoing ones. The node serves as the header for both lists. The +required operations reduce to simple appends, deletes, and traversals +of doubly linked lists, all having small constant cost. There is a +highly tuned memory allocator, and care is taken to dispose of each node +when the last incoming link is deleted, so that there is no need for +garbage collection. +@PP +In normal use the number of nodes at higher levels of the dag is small +in comparison with the leaves and their incoming links, so we may +estimate the space complexity at about 60 bytes per input word (20 bytes +per link, 40 per leaf node). Careful optimization could easily halve +this, but since memory is reclaimed after printing each page there is +little need. +@End @SubSection diff --git a/doc/design/s2_5 b/doc/design/s2_5 new file mode 100644 index 0000000..87d826b --- /dev/null +++ b/doc/design/s2_5 @@ -0,0 +1,90 @@ +@SubSection + @Tag { style } + @Title { Context-sensitive attributes of objects } +@Begin +@PP +Although we are free to place any object in any context, the context +must influence the appearance of the object, since otherwise +@ID @Code "A short paragraph of text." +could not appear in a variety of fonts, column widths, etc. This +influence cannot take the purely static form that block-structured +languages use to associate values with identifiers, for then an operator +could not influence the appearance of its parameters; and a state +variable solution is not compatible with the overall functional design. +@PP +The information needed from the context seems quite limited, comprising +the font family, face, and size to use, the style of paragraph breaking +required, how much space to substitute between the words of paragraphs, +and how much horizontal and vertical space is available to receive the +object. These four items constitute the so-called `style information' +of Lout. As graphics rendering hardware improves, the style information +will probably grow to include colour and texture information. +@PP +The way to deal with fonts at least is very clear: +@ID @Code "{ Times Slope 12p } @Font { Hello, world }" +should have result +@ID { { Times Slope 12p } @Font { Hello, world } } +Lout also provides @Code "@Break" and @Code "@Space" symbols for +controlling the paragraph breaking and space styles mentioned +above. These work in the same way, returning their right +parameters in the style of their left. The implementation is very +simple: one merely broadcasts the style information down into the parse +tree of the right parameter. A font, for example, is converted to an +8-bit internal name and stored in each leaf, while a breaking style is +stored in the root node of each paragraph. +@PP +The same language design can be used for available width and height, +only here the implementation is much more demanding: +@ID @Code { +"2i @Wide {" +"(1) |0.1i An example" +"containing a small" +"paragraph of filled text." +"}" +} +is guaranteed to be two inches wide: +@ID { +2i @Wide { +(1) |0.1i An example +containing a small +paragraph of filled text. +} +} +One must calculate that 1.9 inches minus the width of @Code "(1)" is +available +to the paragraph, and break it accordingly; Basser Lout does this in two +stages. In the first, upward-moving stage, widths are calculated using the +formulae of Section {@NumberOf objects}, which assume that available +space is infinite. If the upward movement reaches a @Eq { WIDE } +node, corresponding to a @Code "@Wide" operator, and +the calculated width exceeds that allowed, a second, downward-moving stage +is initiated which attempts to reduce the width by finding and breaking +paragraphs. This second stage is quite routine except at @Code "|" nodes, +whose children are the columns of a table. It is necessary to apportion +the available width (minus inter-column gaps) among the columns. Basser +Lout leaves narrow columns unbroken and breaks the remaining columns to +equal width, using up all of the available space. +@PP +The size of an object is not clearly determined when the upward-moving +size is less than the downward-moving available space, and the object +contains constructs that depend on available space (e.g. right +justification). For example, in +@ID @Code "2i @Wide { Heading // a |1rt b }" +it seems natural to assign a width of two inches to the subobject +@Code "a |1rt b" because of the right justification, but it would be +equally plausible if the width of @Code Heading was assigned to the +subobject instead. The author is conscious of having failed to resolve +this matter properly; an extra operator for controlling available space +is probably necessary. +@PP +The actual paragraph breaking is just a simple transformation on the +parse tree; the real issue is how to describe the various styles: ragged +right, adjusted, outdented, and so on. Their diversity suggests that +they should somehow be defined using more basic features; but then there +are algorithms for high-quality paragraph breaking, which presumably +must be built-in. This dilemma was not clearly grasped by the author in +1985, and he included a built-in paragraph breaker, with the @Code +"@Break" operator selecting from a fixed set of styles. A much better +solution based on galleys will be given in Section {@NumberOf horizontal}, +but, regrettably, it is not implemented. +@End @SubSection diff --git a/doc/design/s2_9 b/doc/design/s2_9 new file mode 100644 index 0000000..648a1b6 --- /dev/null +++ b/doc/design/s2_9 @@ -0,0 +1,2 @@ +@EndSubSections +@End @Section diff --git a/doc/design/s3_0 b/doc/design/s3_0 new file mode 100644 index 0000000..3f42ff5 --- /dev/null +++ b/doc/design/s3_0 @@ -0,0 +1,10 @@ +@Section + @Title { Definitions } +@Begin +@PP +The need to provide a means of packaging useful pieces of code for easy +repeated use was recognised in the very earliest programming +languages. This need is even more acute in document formatting, if that +is possible, because the majority of users are not programmers and do +not understand the code they invoke. +@BeginSubSections diff --git a/doc/design/s3_1 b/doc/design/s3_1 new file mode 100644 index 0000000..2fb44c6 --- /dev/null +++ b/doc/design/s3_1 @@ -0,0 +1,76 @@ +@SubSection + @Tag { operators } + @Title { Operators } +@Begin +@PP +It is evident from the example of Eqn that user-defined operators are +needed that mimic the primitive ones in taking objects as parameters +and returning objects as results. For example, to define a superscript +operator so that +@ID @Code "2 sup n" +appears as {@Eq {2 sup @R n}}, the following operator definition may +be used: +@ID @OneRow @Code { +"def sup" +" precedence 50" +" associativity right" +" left x" +" right y" +"{" +" @OneRow { | {-2p @Font y} ^/0.5fk x }" +"}" +} +The @Code "sup" operator has precedence 50, is right associative, takes +two objects as parameters passed on the left and right, and returns the +object between braces as result. This object has the structure +@ID @I +2p @Font { +| @ShowMarks @Code y / @ShowMarks @Code x +} +but with the first row mark hidden by the @Code "@OneRow" operator, +and @Code y two points smaller than it would otherwise have been. The +length @Code "0.5f" specifies half the current font size; Figure +{@NumberOf gapmodes} describes the @Code k gap mode. In the Eq equation +formatting package [10] the equation as a whole is +set in italic font, and @Code 2 is an identifier whose body contains +a font change back to Roman. The digits @Code 0 to @Code 9 are classed +as punctuation characters, permitting @Code 234 for example to be +interpreted as a sequence of three identifiers. +@PP +These definitions are easily implemented by a standard symbol table +and an operator precedence parser. Algol block structure with the +usual scope rules was adopted as a matter of course. +@PP +Operators are limited to at most two parameters, left and +right, and the parameters cannot be given default values. @I Named +parameters solve both problems: +@ID @OneRow @Code { +"def @Preface" +" named @Tag {}" +" named @Title { Preface }" +" right @Body" +"{" +" Bold @Font @Title" +" //0.3v @Body" +"}" +} +The default value appears just after the parameter's declaration, +between braces. Invocations have a natural syntax: +@ID @OneRow @Code { +"@Preface" +" @Title { About this book }" +"{" +" Few observers would have supposed in 1984, that ..." +"}" +} +with the actual named parameters following directly after the +operator, before any right parameter. In this example, @Code "@Tag" +will receive its default value, and a less expert user could safely +omit the @Code "@Title" parameter as well. +@PP +Lout permits named parameters to have parameters, a feature with +applications to bibliographic databases, running headers, and other +places where a format has to be supplied before content is +known. One could go further and provide a complete lambda calculus, +with functions as first-class objects, provided care was taken not +to intimidate the non-expert user. +@End @SubSection diff --git a/doc/design/s3_2 b/doc/design/s3_2 new file mode 100644 index 0000000..0c5fd70 --- /dev/null +++ b/doc/design/s3_2 @@ -0,0 +1,113 @@ +@SubSection + @Tag { recursion } + @Title { Recursion and page layout } +@Begin +@PP +Design and implementation should proceed together in exploratory projects, +since otherwise the design too easily becomes unrealistic. Sometimes the +implementation does more than its designer intended. The author wrote the +following purely as a testing scaffold: +@ID @OneRow @Code { +"def @Page right x" +"{" +" 8i @Wide 11i @High" +" {" +" //1i ||1i x ||1i" +" //1i" +" }" +"}" +} +Only afterwards did he realize its significance: the concept of a page +had been defined outside the implementation, removing the need for +commands for setting page width and height, margins, and so on. +@PP +Defining a sequence of pages is harder, since their number is not known +in advance. A simple version of this same problem is afforded by the +leaders found in tables of contents: +@ID { +4i @Wide { Chapter 7 @Leaders 53 } +} +This seemed to require recursion, specifically the definition +@ID @Code { +"def @Leaders { .. @Leaders }" +} +Note that both @Code ".." and @Code "@Leaders" are objects, so the two +spaces separating them are significant. No base case is given, and indeed +we have no boolean or conditional operators with which to express it; +but we can adopt the implicit base `if space is not sufficient, delete +{@Code "@Leaders"} and any preceding space'. Then the expression +@ID @Code "4i @Wide { Chapter 7 @Leaders 53 }" +will produce the object shown above. It is hard to see how this base +could be made explicit, without violating the general principle of +keeping all size information internal. In the implementation, +@Code "@Leaders" remains unexpanded while sizes are being +calculated; then it is treated similarly to a receptive symbol, with +its body as an incoming galley (Section {@NumberOf flushing}). +@PP +With this settled, it is now clear how to define a document which is a +numbered sequence of pages. Let @Code "@Next" be a prefix operator +which returns its parameter plus one. Then +@ID @OneRow @Code { +"def @PageList" +" right @PageNum" +"{" +" @Page {" +" |0.5rt - @PageNum -" +" //1v @TextPlace" +" //1rt @FootSect" +" }" +" //" +" @PageList @Next @PageNum" +"}" +} +when invoked in the expression {@Code "@PageList 1"}, has for its result +the potentially infinite object +@ID @OneRow { +@LittlePage { +|0.5rt - 1 - +//1.2vx @Code "@TextPlace" +//1rt @Code "@FootSect" +} +// +@LittlePage { +|0.5rt - 2 - +//1.2vx @Code "@TextPlace" +//1rt @Code "@FootSect" +} +//0.2c +8p @Font @Code "@PageList 3" +} +Similarly, we may define @Code "@FootSect" like this: +@ID @OneRow @Code { +"def @FootSect" +"{" +" def @FootList" +" right @Num" +" {" +" @FootPlace" +" //1v" +" @FootList @Next @Num" +" }" +"" +" 1i @Wide @HLine" +" //1v" +" @FootList 1" +"}" +} +so that an invocation of @Code "@FootSect" produces +@ID @OneRow @Code { +1i @Wide @HLine +"@FootPlace" +"@FootPlace" +"@FootPlace" +"..." +} +The expansion process is very similar to a BNF derivation, and would be +attempted only on demand. +@PP +Clearly, deciding which expansions to take and replacing @Code "@TextPlace" +and {@Code "@FootPlace"} by the appropriate actual text will not be easy; +this is the subject of Section {@NumberOf galleys}. The important point +for now is that we have here a very simple and flexible method of specifying +the layout of pages, which requires no specialized language features. +@End @SubSection diff --git a/doc/design/s3_3 b/doc/design/s3_3 new file mode 100644 index 0000000..d04a8db --- /dev/null +++ b/doc/design/s3_3 @@ -0,0 +1,143 @@ +@SubSection + @Tag { modules } + @Title { Modules } +@Begin +@PP +It is well accepted that the visibility of symbols is not adequately +controlled by Algol block structure. The author is aware of several +major problems of this kind in document formatting. +@PP +One problem is that some symbols should be visible only within +restricted parts of a document. For example, we naturally expect +equation formatting to be accomplished like this: +@ID @OneRow @Code { +"surrounding text" +"@Eq { {x sup 2 + 1} over 4 }" +"surrounding text" +} +with the symbols {@Code "sup"}, {@Code "over"}, etc., visible only within +the equation, not in the surrounding text. +@PP +It seems natural to define these symbols within {@Code "@Eq"}, since +they are local to equations. It only remains then to decree that +symbols local to @Code "@Eq" are to be visible within its actual right +parameter, and this is done by replacing the right formal parameter with a +@I body parameter: +@ID @OneRow @Code { +"export sup over" +"def @Eq" +" body @Body" +"{" +" def sup ..." +" def over ..." +"" +" Slope @Font @Body" +"}" +} +The @Code export clause lists the identifiers which are permitted to be +visible outside their usual range, the body of {@Code "@Eq"}; and the +@Code body declaration imports them into (makes them visible within) +the actual right parameter of each invocation of {@Code "@Eq"}. This +arrangement has proven very convenient for defining a variety of +special-purpose packages. +@PP +Another problem arises when global symbols, such as the ones used for +headings and paragraph separators, call on values that the non-expert +user will need to modify, such as the initial font or paragraph +indent. These values are like parameters of the document as a whole, so +it is natural to try this: +@ID @OneRow @Code { +"export @Heading @PP ..." +"def @BookLayout" +" named @InitialFont { Times Base 12p }" +" named @InitialBreak { adjust 14p }" +" named @ColumnWidth { 6i }" +" ..." +"{" +" def @Heading ..." +" def @PP ..." +"}" +} +Now @Code "@Heading" and @Code "@PP" may invoke @Code "@InitialFont" +and the other parameters. To make @Code "@Heading" and @Code "@PP" +visible throughout the document, we need only add a body parameter to +@Code "@BookLayout" and present the entire document as +@ID @OneRow @Code { +"@BookLayout" +" @InitialFont { Helvetica Base 10p }" +" @InitialBreak { adjust 12p }" +"{" +" The document." +"}" +} +but for practical reasons given below we prefer not to enclose the +entire document in braces. Instead, we write +@ID @OneRow @Code { +"@Use { @BookLayout" +" @InitialFont { Helvetica Base 10p }" +" @InitialBreak { adjust 12p }" +"}" +"The document." +} +which has the same effect: @Code "@Use" makes the exported symbols of +@Code "@BookLayout" visible for the remainder of the document, and is +permitted only at the beginning. +@PP +The third feature that affects visibility, and which will prove useful +for cross referencing (Section {@NumberOf cross}), is the @Code "@Open" +symbol. It makes the exported symbols of its left parameter visible +within its right parameter, and is therefore similar to the Pascal @Code +with statement. +@PP +It could be argued that Lout is over-supplied with these visibility modifying +features: the body parameter, @Code "@Use" and @Code "@Open" do not seem +sufficiently different from each another. The @Code "@Open" symbol is +the most general, being capable of replacing the other two. For +example, +@ID @OneRow @Code { +"@Use { x }" +"@Use { y }" +"Body of document" +} +can be replaced by +@ID @OneRow @Code { +"x @Open {" +"y @Open {" +"Body of document" +"}}" +} +and, taking the @Code "@Eq" symbol above as example, we could eliminate +its body parameter, add +@ID @Code "def @Body right x { Slope @Font x }" +to the exported definitions of {@Code "@Eq"}, and replace +@ID @Code "@Eq { object }" +by +@ID @Code "@Eq @Open { @Body { object } }" +If @Code "@Eq" is a galley (Section {@NumberOf galleys}), @Code "@Body" +must take over that function. But one would not want to write these +clumsy expressions in practice, and the enclosure of large quantities +of input in extra braces could cause Basser Lout to run out of memory +(Section {@NumberOf lookahead}). +@PP +A quite separate kind of visibility problem arises when expert +users wish to define an object or operator for repeated use within, say, +equations: +@ID @Code "def isum { sum from i=1 to n }" +As it stands this can only be placed within the @Code "@Eq" package itself, +where @Code "sum" and the other symbols are visible, but it is not desirable +to modify the source code of a standard package. Lout provides an +@Code "import" clause to solve this problem: +@ID @OneRow @Code { +"import @Eq" +"def isum { sum from i=1 to n }" +} +may appear after @Code "@Eq" is defined, and it will make the exported symbols +of @Code "@Eq" visible within the body of {@Code "isum"}. This feature +complicates the treatment of environments (Section {@NumberOf defs.impl}), +and even introduces an insecurity, when @Code isum is invoked outside an +equation. A simpler approach would be to allow only one symbol in an +@Code import clause, and treat the following definition exactly like a +local definition of that symbol; but then it would not be possible +to define symbols using the resources of more than one of the standard +packages. +@End @SubSection diff --git a/doc/design/s3_4 b/doc/design/s3_4 new file mode 100644 index 0000000..7b0f5bc --- /dev/null +++ b/doc/design/s3_4 @@ -0,0 +1,51 @@ +@SubSection + @Tag { defs.impl } + @Title { Implementation of definitions } +@Begin +@PP +Input is processed by a hybrid parser which employs operator precedence +for objects and simple recursive descent for the headers of +definitions. A symbol table stores the body of each definition as a +parse tree, except for macros which are lists of tokens, and manages the +usual stack of static scopes, accepting @I PushScope and @I PopScope +operations as the parser enters and leaves scope regions, including +actual body parameters and the right parameter of the @Code "@Open" +operator. +@PP +As the parse proceeds, a complete call graph is constructed, recording, +for each symbol, which symbols are invoked within its body. Immediately +after the last definition is read, the transitive closure of the call +graph is computed, and used to determine whether each non-parameter +symbol is recursive or receptive (Section {@NumberOf galleys}), and +whether each parameter is invoked exactly once or not. +@PP +Purely functional systems may evaluate symbol invocations in applicative +order (where parameters are evaluated before substitution into bodies), +or in normal order (substitution before evaluation), and they may also +share the value of a parameter among all uses of it. But in Basser +Lout, the presence of context-sensitive style information (Section +{@NumberOf style}) forces normal order evaluation and prevents sharing +of parameter values. +@PP +To evaluate an unsized object (pure parse tree), its {@I environment}, +the equivalent of the stack frames in Algol-like languages, must be +available, containing the actual values of all formal parameters +that are visible within the unsized object. Environment handling is +a well-known implementation technique, so it will be discussed +only briefly here. +@PP +Environments are extra subtrees hung from the objects they refer +to. This organization makes excellent use of the ordered dag to +permit environments to be shared, and deleted when the last +reference to them is removed. Several optimizations have been +implemented. Actual parameters known to be invoked only once are moved +in from the environment, not copied; copying could lead to quadratic time +complexity. Actual parameters of the form @Code "@Next" @I object +receive an applicative pre-evaluation which prevents long chains of +@Code "@Next" symbols from forming during the generation of large page +numbers. Some environments which provably contribute nothing are +deleted, most notably when a symbol invocation has no symbols within its +actual parameters and no import list, so that only the environment of its +body need be kept; this saves a great deal of space when objects with +environments are written to auxiliary files (Section {@NumberOf cross}). +@End @SubSection diff --git a/doc/design/s3_9 b/doc/design/s3_9 new file mode 100644 index 0000000..648a1b6 --- /dev/null +++ b/doc/design/s3_9 @@ -0,0 +1,2 @@ +@EndSubSections +@End @Section diff --git a/doc/design/s4_0 b/doc/design/s4_0 new file mode 100644 index 0000000..5f89426 --- /dev/null +++ b/doc/design/s4_0 @@ -0,0 +1,88 @@ +@Section + @Tag { functional } + @Title { Implementation of the functional subset } +@Begin +@PP +The objects and definitions of Lout are very similar to those found in +other functional languages, and they form a natural subset of the +language. So we pause here and present an overview of the Basser Lout +object evaluation algorithm. +@PP +The problem is to take an unsized object (pure parse tree), its +environment (Section {@NumberOf defs.impl}), and its style +(Section {@NumberOf style}), and to produce a PostScript file for +rendering the object on an output device. This file is essentially a +sequence of instructions to print a given string of characters in a +given font at a given point. +@PP +Before the algorithm begins, the parse tree must be obtained, either by +parsing input or by copying from the symbol table. Afterwards the data +structure must be disposed. The algorithm proper consists of five +passes, each a recursive traversal of the structure from the root down +to the leaves and back. +@DP +@I {1. Evaluation of unsized objects.} On the way down, calculate +environments and replace non-recursive, non-receptive symbols by their +bodies (Section {@NumberOf defs.impl}); broadcast fonts to the leaves, +and paragraph breaking and spacing styles to the paragraph nodes. On the +way back up, delete @Eq { FONT }, @Eq { BREAK }, and @Eq { SPACE } nodes, +and insert @Eq { SPLIT }, @Eq { COL }, and @Eq { ROW } nodes +(Section {@NumberOf objects}). +@DP +@I {2. Width calculations and breaking.} Calculate the width of every +subobject from the bottom up. As described in Section {@NumberOf objects}, +@Eq { WIDE } nodes may trigger object breaking sub-traversals during this pass. +@DP +@I {3. Height calculations.} Calculate the height of every subobject, +from the bottom up. +@DP +@I {4. Horizontal coordinates.} Calculate the horizontal coordinate of +each subobject from the top down, and store each leaf's coordinate in +the leaf. +@DP +@I {5. Vertical coordinates and PostScript generation.} Calculate the +vertical coordinate of every subobject from the top down, and at each +leaf, retrieve the character string, font, and horizontal coordinate, +and print the PostScript instruction for rendering that leaf. +@DP +Figure {@NumberOf components} gives the amount of code required for each + +@Figure + @Tag { components } + @Caption { Major components of the Basser Lout interpreter, showing +the approximate number of lines of C code. } +@Begin +@Tab + vmargin { 0.5vx } + @Fmta { @Col @RR A ! @Col B ! @Col @RR C } + @Fmtb { @Col @RR A ! @Col B ! @Col C } +{ + @Rowa A { 1. } B { Initialization } C { 200 } + @Rowa A { 2. } B { Memory allocation, ordered dag operations } C { 400 } + @Rowa A { 3. } B { Lexical analysis, macros, file handling } C { 1,350 } + @Rowa A { 4. } B { Parsing of objects and definitions } C { 1,150 } + @Rowa A { 5. } B { Symbol table and call graph } C { 600 } + @Rowa A { 6. } B { Evaluation of pure parse trees } C { 1,650 } + @Rowa A { 7. } B { Reading, storing, and scaling of fonts } C { 600 } + @Rowa A { 8. } B { Cross references and databases } C { 1,000 } + @Rowa A { 9. } B { Width and height calculations, and breaking } C { 700 } + @Rowa A { 10. } B { @I Constrained and @I AdjustSize } C { 700 } + @Rowa A { 11. } B { Transfer of sized objects into galley tree } C { 450 } + @Rowa A { 12. } B { Galley flushing algorithm } C { 1,500 } + @Rowa A { 13. } B { Coordinate calculations and PostScript output } C { 700 } + @Rowa A { 14. } B { Debugging and error handling } C { 1,200 } + @Rowb vmargin { 0.1c } C { @Line } + @Rowa C { 12,200 } +} +@End @Figure + +pass. Symmetry between horizontal and vertical is exploited throughout +Basser Lout, and passes 2 and 3, as well as 4 and 5, are executed on +shared code. +@PP +The author can see no simple way to reduce the number of passes. The +introduction of horizontal galleys (Section {@NumberOf horizontal}) +would remove the need for the object breaking transformations within this +algorithm that are the principal obstacles in the way of the merging of +passes 2 and 3. +@End @Section diff --git a/doc/design/s5_0 b/doc/design/s5_0 new file mode 100644 index 0000000..d176f77 --- /dev/null +++ b/doc/design/s5_0 @@ -0,0 +1,11 @@ +@Section + @Title { Galleys } +@Begin +@PP +With objects and definitions under control, the author faced the problem +of getting body text, footnotes, floating figures and tables, +references, index entries, and entries in the table of contents into +their places. The resulting investigation occupied three months of +full-time design work, and proceeded approximately as described in +Section {@NumberOf galleys}; the implementation occupied the years 1987-89. +@BeginSubSections diff --git a/doc/design/s5_1 b/doc/design/s5_1 new file mode 100644 index 0000000..ab65bb9 --- /dev/null +++ b/doc/design/s5_1 @@ -0,0 +1,123 @@ +@SubSection + @Tag { galleys } + @Title { The galley abstraction } +@Begin +@PP +Let us take the footnote as a representative example. At some point in +the document, we wish to write +@ID @OneRow @Code { +"preceding text" +"@FootNote { footnote text }" +"following text" +} +and we expect the formatter to remove the footnote from this context and +place it at the bottom of the current page, possibly splitting some or +all of it onto a following page if space is insufficient. +@PP +An object appears in the final document at the point it is invoked, but +this basic property does not hold for footnotes: the point of +invocation and the point of appearance are different. In some way, the +footnote is attached to the document at both points, introducing a cross +linking (Section {@NumberOf genesis}) that cannot be described in purely +functional terms. +@PP +Since the interpretation of any object depends on an environment and +style inherited from the context, the first question must be whether +the footnote inherits them through the invocation point or through +the point(s) of appearance. +@PP +If symbols are to be interpreted statically as heretofore, then environments +must be inherited through the invocation point alone. Dynamic inheritance +through the point of appearance is enticing in some ways: it might +replace the body parameter, and it might help with automatic numbering, +since the number of a footnote is known only at the point of appearance; +but the implementation problems are severe, and static inheritance seems +much simpler and more comprehensible to the user. Style, at least its +available width and height part, must of necessity be inherited through +the point of appearance. For consistency, the entire style should be +inherited in this way. There is a suggestive analogy here with actual +parameters, which have a point of invocation from which they inherit an +environment, and a point of appearance within the body of the enclosing +definition, from which they inherit a style. It may be possible to treat +a footnote as the actual parameter of some symbol, therefore, although +the details seem very obscure. +@PP +But the most profound consequence of having two types of attachment +point is that it leads to two distinctive tree structures. Considering +invocation points only leads to static trees like this one: +@ID @I @Fig margin { 0.3c } { @Tree { +@Node @Ellipse { body text } +@LeftSub { @Node @Ellipse footnote } +@RightSub { + @Node @Ellipse figure + @FirstSub { @Node @Ellipse footnote } +} +}} +which shows that the body text contains a footnote and a figure, the +latter itself containing a footnote. Considering points of appearance +only gives a completely different, dynamic tree: +@ID @I @Fig margin { 0.3c } { @Tree { +@Node @Ellipse { sequence of pages } +@FirstSub { @Node @Ellipse { body text } } +@NextSub { @Node @Ellipse { footnote } } +@NextSub { @Node @Ellipse { figure } } +@NextSub { @Node @Ellipse { footnote } } +}} +The tree can be deeper, for example with sections appearing within +chapters which appear within the body text, which appears within the +final sequence of pages. Document formatting languages generally shirk +the issues raised by this dual tree structure, by making the dynamic +tree built-in, by limiting one or both trees to two levels, and so on, +providing a classic example of the impoverishing effect of failing to +permit language features to attain their natural level of generality. +@PP +We are thus led to propose a second abstraction for document formatting, +which we name the @I galley in recognition of its similarity to the +galleys used in manual typesetting. A galley consists of an object (such +as a footnote) together with a sequence of places where that object may +appear (such as the bottoms of the current and following pages). Splitting +occurs quite naturally when space at any place is insufficient to hold +the entire object. +@PP +In Lout, a footnote galley and its place of appearance are defined +as follows: +@ID @OneRow @Code { +"def @FootPlace { @Galley }" +"" +"def @FootNote into { @FootPlace&&following }" +" right x" +"{ x }" +} +The @Code "@FootPlace" symbol contains the special symbol {@Code "@Galley"}, +indicating that it is a point of appearance for a galley. By placing +invocations of @Code "@FootPlace" at the bottoms of pages, as in Section +{@NumberOf recursion}, we define the desired points of appearance for +footnotes. Symbols whose body contains @Code "@Galley" either directly +or indirectly are called receptive symbols, meaning receptive to +galleys, and they are expanded only on demand. The effect of the +@Code "into" clause is to make each invocation of @Code "@FootNote" a +galley whose object is the result of the invocation in the usual way, +and whose sequence of points of appearance is specified by the @Code "into" +clause; in this example, the sequence of all @Code "@FootPlace" symbols +following the invocation point. +@PP +Lout permits galleys to be invoked within other galleys to arbitrary +depth, so that one may have footnotes within figures within the body +text galley, for example, creating arbitrary static trees. Receptive +symbols like @Code "@FootPlace" may appear within any galley, creating +arbitrary dynamic trees as well. The root of the dynamic tree, which +would normally consist of the sequence of pages of the complete assembled +document, is considered to be a galley whose point of appearance is the +output file. Points of appearance may be @Code preceding or @Code following +the invocation point; entries in tables of contents are the main users +of {@Code preceding}. +@PP +The galley abstraction is adequate for all of the applications listed at +the beginning of this section, except that there is no provision for +sorting index entries and references. Sorting of galleys has been added +to Lout as a built-in feature, invoked by adding a special @Code "@Key" +parameter to the galleys, and using its value as the sort key. The author +was at a loss to find any other way, or any useful generalization of this +feature. Its implementation will be discussed in Section +{@NumberOf cross.impl}. +@End @SubSection diff --git a/doc/design/s5_2 b/doc/design/s5_2 new file mode 100644 index 0000000..a81630d --- /dev/null +++ b/doc/design/s5_2 @@ -0,0 +1,372 @@ +@SubSection + @Tag { flushing } + @Title { The galley flushing algorithm } +@Begin +@PP +Galley components are promoted one by one into the point of appearance in +the dynamic parent galley, then carried along with it, ultimately to the +root galley and the output file. This process is called @I galley +{@I flushing}: the galleys are rivers running together to the sea, and +each component is a drop of water. +@PP +Here is a snapshot of a small dynamic tree, based on the @Code "@PageList" +definitions of Section {@NumberOf recursion}: +@ID @Fig { + +@I 10p @Font { output file } A:: @Box linestyle { noline } margin { 0c } + +||2c + +{ +@I 10p @Font { root galley } +//0.2c +B:: @Box margin { 0c } linestyle { noline } +// +@LittlePage { +|0.5rt - 1 - +//1.2vx &2m A small +//1.2vx @Code "@Galley" * C:: @Box margin { 0.01c } linestyle { noline } +//1rt @Code "@FootSect" +} +// +@Box margin { 0.3c } 2.8c @Wide 8p @Font @Code "@PageList 2" +} + +||2c + +{ +//0.9c @I 10p @Font { body text } +//0.2c D:: @Box margin { 0.3c } 2.8c @Wide 8p @Font paragraph +// @Box margin { 0.3c } 2.8c @Wide 8p @Font { of text. } +// @Box margin { 0.3c } 2.8c @Wide @Code 8p @Font "@Input" +} + +// @Arrow from { B@W } to { A@E } +// @Arrow from { D@W } to { C@E } + +} +The components of the body text galley are lines, except for the special +receptive symbol @Code "@Input" which is a placeholder for as yet unread +input (Section {@NumberOf lookahead}). The components of the root galley are +pages, except for the concluding unexpanded invocation of {@Code "@PageList"}, +which is an inexhaustible source of more pages, expanded on demand. +@PP +The concrete data structure used by Basser Lout permits the galley +flushing algorithm to navigate the dynamic tree and find significant +features quickly: +@ID 10p @Font @Fig maxlabels { 100 } { + +A:: @Ellipse @I { HEAD } + +||1.5c + +@OneCol @OneRow { +B:: @Ellipse @I { RECEIVING * } +// @Arrow from { A@CTR ++ {A@CTR @Angle B@W A@CIRCUM} } to { B@W } +//0.6c +C:: @Ellipse @I { RECEPTIVE } +// @Arrow from { A@CTR ++ {A@CTR @Angle C@W A@CIRCUM} } to { C@W } +//0.6c +D:: @Box margin { 0c } linestyle { noline } +// @Arrow from { A@CTR ++ {A@CTR @Angle D@NW A@CIRCUM} } to { D@NW } +// +@LittlePage { +|0.5rt - 1 - +//1.2vx &2m A small +//1.2vx E:: @Box margin { 0c } linestyle { noline } @Code "@Galley " +//1rt F:: @Box margin { 0c } linestyle { noline } @Code "@FootSect " +} +// @FunnyArrow arrow { forward } from { B@E } to { E@E } +// @FunnyArrow arrow { forward } from { C@E } to { F@E } +//0.6c +C:: @Ellipse @I { GAP } +// @Arrow from { A@CTR ++ {A@CTR @Angle C@W A@CIRCUM} } to { C@W } +//0.6c +C:: @Ellipse @I { RECEPTIVE } +// @Arrow from { A@CTR ++ {A@CTR @Angle C@W A@CIRCUM} } to { C@W } +//0.6c +D:: @Box margin { 0.3c } 2.8c @Wide 8p @Font @Code "@PageList 2" +// @Arrow from { A@CTR ++ {A@CTR @Angle D@NW A@CIRCUM} } to { D@NW } +// @FunnyArrow from { C@E } to { D@W ++ { 1.8 cm 0 } } +} + +||1.0c + +A:: @Ellipse @I { HEAD } +& @Arrow from { B@E } to { A@W } + +||1.5c + +@OneCol @OneRow { +B:: @Box margin { 0.3c } 2.8c @Wide 8p @Font paragraph +// @Arrow from { A@CTR ++ {A@CTR @Angle B@W A@CIRCUM} } to { B@W } +//0.6c +B:: @Ellipse @I { GAP } +// @Arrow from { A@CTR ++ {A@CTR @Angle B@W A@CIRCUM} } to { B@W } +//0.6c +B:: @Box margin { 0.3c } 2.8c @Wide 8p @Font { of text. } +// @Arrow from { A@CTR ++ {A@CTR @Angle B@NW A@CIRCUM} } to { B@NW } +//0.6c +B:: @Ellipse @I { GAP } +// @Arrow from { A@CTR ++ {A@CTR @Angle B@W A@CIRCUM} } to { B@W } +//0.6c +B:: @Ellipse @I { RECEPTIVE } +// @Arrow from { A@CTR ++ {A@CTR @Angle B@W A@CIRCUM} } to { B@W } +//0.6c +C:: @Box margin { 0.3c } 2.8c @Wide 8p @Font @Code "@Input" +// @Arrow from { A@CTR ++ {A@CTR @Angle C@NW A@CIRCUM} } to { C@NW } +// @FunnyArrow from { B@E } to { C@W ++ { 1.2 cm 0 } } +} + +} +Each galley has a @Eq { HEAD } node whose children are its component +objects, separated by @Eq { GAP } nodes recording the inter-component +gaps. +@PP +Each component is preceded by zero or more @I {galley index nodes} of +various types. Every receptive symbol has a @Eq { RECEPTIVE } index pointing +to it, so that it can be found without searching through its +component. If the symbol is currently the target of a galley, it has a +@Eq { RECEIVING } index instead which is also linked to the incoming +galley. Galleys that are currently without a target are linked to the +dynamic tree by @Eq { UNATTACHED } galley indexes, either just after their +most recent target if there has been one, or else at their point of +invocation. +@PP +Each galley should be thought of as a concurrent process, although the +implementation in C uses coroutines implemented by procedures. A galley +may promote its first component only if it has a target, sufficient space +is available at the target to receive the component, and the component +contains no receptive symbols. This last condition seems to be the key +to galley synchronization: it forces a bottom-up promotion regime, +preventing pages from flushing to output before text flushes into them, +for example. +@PP +Each galley contains a number of binary semaphores, shown as asterisks +in our snapshots when set. At any given moment, a galley process is +either running or else is suspended on one of its own semaphores. The +@Eq { HEAD } node contains a semaphore which is set when the galley has tried +to find a target and failed. Each receptive symbol has a semaphore +which is set when that symbol is preventing the first component from +being promoted. +@PP +For example, in the snapshot at the beginning of this section, the root +galley is suspended on the @Code "@Galley" symbol, but the text galley +is running. It will suspend on the @Code "@Input" symbol after the +first two components are promoted. +@PP +Every galley {@I G}, be it a list of pages, body text, a footnote, or +whatever, executes the following algorithm in parallel with every other +galley: +@DP +1. Initially @I G is unattached. Search forwards or backwards from its +@Eq { UNATTACHED } index as required, to find a receptive symbol @I S which +can expand to reveal a target for {@I G}. +@DP +2. If no @I S can be found, suspend on the attachment semaphore. Resume +later from step 1. +@DP +3. Expand @I S to reveal the target of {@I G}. Preserve {@I S}'s +semaphore by moving it to the first receptive symbol within the +expansion of {@I S}. +@DP +4. Calculate the available width and height at the target, and if +@I G is still a pure parse tree, use the environment attached to @I G +and the style information from the target to evaluate @I G as in +Section {@NumberOf functional}. +@DP +5. Examine the components of @I G one by one. For each component there +are three possibilities: +@PP +@I ACCEPT. If the component fits into the available space, and has +no other problems, then promote it into the target. If this is the +first component promoted into this target, and @I G is a forcing +galley (Section {@NumberOf lookahead}), delete every receptive symbol +preceding the target in the parent galley. If @I G is the root galley, +render the component on the output file and dispose it; +@PP +@I REJECT. If the component is too large for the available space, or a +@Eq { FOLLOWS } index (described below) forbids its promotion into this +target, then detach @I G from the target. If this was the first component +at this target, @I S has been a complete failure, so undo step 3 (Basser +Lout is not able to undo step 4); otherwise delete the target. Return to +step 1 and continue immediately; +@PP +@I SUSPEND. If the component contains a receptive symbol, it cannot be +promoted yet. If this symbol is the target of a galley that was written +to an auxiliary file on a previous run, read in that galley and flush +it. Otherwise suspend on the receptive symbol's semaphore; resume later +from step 4. +@DP +6. Terminate when the galley is empty. +@DP +At various points in this algorithm, receptive symbols (and their +semaphores) are deleted in the dynamic parent galley, possibly +permitting it to resume flushing. When this happens, Basser Lout resumes +the parent immediately after @I G suspends or terminates. Also, +whenever a component is promoted, any child galleys connected to +it by @Eq { UNATTACHED } indexes must be resumed, since these +galleys may be able to find a target now. A good example of this +situation occurs when a line of body text with one or more footnotes +is promoted onto a page. Basser Lout gives priority to such children, +suspending @I G while each is given a chance to flush. +@PP +Basser Lout searches for the first target of @I G only in regions of the +dynamic tree that will clearly precede or follow {@I G}'s invocation +point in the final printed document, whichever is specified in the +@Code into clause; subsequent targets are sought later in the same +galley as the first. An exception to this rule, whose necessity will +be made clear later, is that a first @Code following target will be +sought within a dynamic sibling galley preceding {@I G}'s invocation +point: +@ID 10p @Font @Fig { + +{ +@I { dynamic parent } +//0.2c +@Box 2.8c @Wide 4.5c @High +{ + //0.5c A:: @Box margin { 0c } linestyle { noline } @Code "@XTarget" + //1.0c C:: @Box margin { 0c } linestyle { noline } @Eq { UNATTACHED } + //1.3c @Code "@XTarget" +} +} + +||1.5c + +{ +//0.6c +B:: @Box margin {0c} linestyle {noline} @Code "X into { @XTarget&&following }" +//0.2c +@Box 2.8c @Wide 1.5c @High { //0.8c @Code "@GTarget" } +//1.0c +D:: @Box margin {0c} linestyle {noline} @Code "G into { @GTarget&&following }" +//0.2c +@Box 2.8c @Wide 2.5c @High {} +} + +// @Arrow from { A@E ++ {0.2 cm 0} } to { B@W -- {0.2 cm 0} } +// @Arrow from { C@E ++ {0.2 cm 0} } to { D@W -- {0.2 cm 0} } + +} +Here @I G will find the @Code "@GTarget" target within {@I X}. This is +dangerous, since if the first component of @I G is then promoted via +@I X into the first {@Code "@XTarget"} rather than into the second, +{@I G}'s target will not appear later in the final printed document than +its invocation point, as required by the @Code into clause. +@PP +Accordingly, when such a target is chosen, two special galley indexes +are inserted and linked together: a @Eq { PRECEDES } index at {@I G}'s +invocation point, and a @Eq { FOLLOWS } index at the first component of +{@I G}. The algorithm checks before promoting any @Eq { FOLLOWS } index +that its promotion would not place it earlier than the corresponding +@Eq { PRECEDES } index in the same galley, and rejects the component if +it would. Since @Eq { PRECEDES } and @Eq { FOLLOWS } indexes are rarely used, +this check can be implemented by linear search. +@PP +When two components are separated by {@Code "/"}, as opposed to the more +usual {@Code "//"}, each influences the horizontal position of the +other. Because of this, the @I SUSPEND action is in fact taken if a +receptive symbol occurs in any component separated from the first by +{@Code "/"} operators only. Again, linear search forwards to the first +{@Code "//"} suffices for this check. +@PP +A good illustration of these unusual cases is afforded by the +@Code "@Align" symbols from the standard DocumentLayout package. These +are used to produce displayed equations, aligned on their equals signs +despite being separated by arbitrary body text. +@PP +The @Code "@Align" symbols are packaged neatly for the convenience of +the non-expert user, but we will show just the essence of the +implementation here. First, an @Code "@AlignList" galley is created +which contains an infinite supply of @Code "@AlignPlace" receptive +symbols separated by @Code "/" operators: +@ID @Fig { + +{ +@I { body text galley } +//0.2c +@Box 2.8c @Wide 4.0c @High +{ //1.5c + A:: @Box margin { 0c } linestyle { noline } @Code "@Galley" +} +} + +||1.5c + +{ +//2.4c +B:: @Box margin { 0c } linestyle { noline } @Code "@AlignList" +//0.2c +@Box { + @Code "@AlignPlace" +//1vx @Code "@AlignPlace" +//1vx @Code "..." +//1vx @Code "@EndAlignList" +} + +} + +// @Arrow from { A@E ++ {0.2 cm 0} } to { B@W -- {0.2 cm 0} } +} +Then equations like +@ID @ShowMarks @Eq { f(x) ^= g(x) + 2 } +are created and sent to @Code "@AlignPlace&&following" targets. They +collect in the @Code "@AlignList" galley and are aligned there: +@ID @Fig { + +{ +@I { body text galley } +//0.2c +@Box 2.8c @Wide 4.0c @High +{ //1.5c + A:: @Box margin { 0c } linestyle { noline } @Code "@Galley" +} +} + +||1.5c + +{ +//2.4c +B:: @Box margin { 0c } linestyle { noline } @Code "@AlignList" +//0.2c +@Box { + @Line linestyle { dashed } from { xmark ysize } to { xmark 0 } + { + @Eq { f(x) ^= g(x) + 2 } + /1vx @Eq { f(x) - g(x) ^= 2 } + /1vx @Code "..." + /1vx @Code "@EndAlignList" + } +} + +} + +// @Arrow from { A@E ++ {0.2 cm 0} } to { B@W -- {0.2 cm 0} } +} +The @Code "@AlignList" galley does not flush, because its first +component is connected to a receptive symbol by @Code "/" operators. +@PP +After the last equation, an empty forcing galley is sent to +{@Code "@EndAlignList"}, deleting the two remaining receptive symbols from +the @Code "@AlignList" galley and permitting it to flush. @Eq { FOLLOWS } +indexes ensure that each equation finds a target placed in the body text +just after its point of invocation, so the equations return, aligned, to +approximately the points where they were invoked. Notice that the flushing +of body text is suspended until the list of equations is completed, as it +must be, since the horizontal position of the first equation cannot +be known until the last equation is added to the list. +@PP +Layout quality can occasionally be improved by rejecting a component +that could be promoted -- for example, a component of body text that +carries a footnote too large to fit on the current page. Since Lout +does not specify how breaking decisions are made, beyond the basic +constraints imposed by available space and @Code into clauses, in +principle such high quality breaking could be added to the +implementation with no change to the language. However, the +generality of the galley flushing algorithm, and its already +considerable complexity, make this a daunting problem in practice, +although a fascinating one. @TeX [9], with its unnested +set of `floating insertions' clearly identifiable as each page is begun, +has the advantage in this respect. +@End @SubSection diff --git a/doc/design/s5_3 b/doc/design/s5_3 new file mode 100644 index 0000000..3ff9881 --- /dev/null +++ b/doc/design/s5_3 @@ -0,0 +1,125 @@ +@SubSection + @Tag { constraints } + @Title { Size constraints and size adjustments } +@Begin +@PP +The galley flushing algorithm needs to know the available width and +height at each receptive symbol. These symbols may lie within +arbitrarily complex objects, and they may compete with each other for +available space (as body text and footnote targets do), so this +information must be extracted from the tree structure when required. +@PP +For example, consider the object +@ID @Code "5i @Wide { a / b }" +and suppose that the width of @Code { a } is @Eq { 1i, 2i } (@Eq {1i} to +the left of the mark, @Eq { 2i } to the right). What then is the +available width at {@Code { b }}? If we let the width of @Code b be +@Eq {l,r}, we must have +@ID @Eq { (1i up l) + (2i up r) <= 5i } +with the @Eq {non up } (i.e. max) operations arising from mark +alignment. Eliminating them gives +@ID @OneRow @Eq { +matrix { + { 1i + 2i ^<= 5i } +mabove { l + 2i ^<= 5i } +mabove { 1i + r ^<= 5i } +mabove { l + r ^<= 5i } +} +} +and since we assume that @Code a fits into the available space, the +first inequality may be dropped, leaving +@ID @OneRow @Eq { +matrix { + { l ^<= 3i } +mabove { l + r ^<= 5i } +mabove { r ^<= 4i } +} +} +Object @Code b may have width @Eq {l, r} for any @Eq { l } and +@Eq { r } satisfying these inequalities, and no others. +@PP +Here is another example: +@ID @Code "5i @High { a /2ix b }" +Assuming that @Code a has height @Eq {1i,1i}, the height @Eq {l, r} of +@Code b must satisfy +@ID @Eq { 1i + ((1i + l) up 2i) + r <= 5i } +This time the @Eq { non up } operation arises from the mark-to-mark gap +mode, which will widen the @Eq { 2i } gap if necessary to prevent +@Code a and @Code b from overlapping. This inequality can be rewritten as +@ID @OneRow @Eq { +matrix { + { l ^<= infinity } +mabove { l + r ^<= 3i } +mabove { r ^<= 2i } +} +} +In general, Lout is designed so that the available width or height at +any point can be expressed by three inequalities of the form +@ID @OneRow @Eq { +matrix { + { l ^<= x } +mabove { l + r ^<= y } +mabove { r ^<= z } +} +} +where @Eq {x }, @Eq {y} and @Eq {z} may be @Eq { infinity }. We +abbreviate these three inequalities to @Eq { l, r <= x, y, z }, and we +call @Eq {x, y, z} a {@I{size constraint}}. +@PP +The two examples above showed how to propagate the size constraint +@Eq { infinity, 5i, infinity } for +@Code "a / b" down one level to the child {@Code b}. Basser Lout +contains a complete set of general rules for all node types, too +complicated to give here. Instead, we give just one example of how +these rules are derived, using the object +@ID @OneRow { +@Eq {x sub 1} @Code "/" @Eq {x sub 2} @Code "/" @Eq {ldots} @Code +"/" @Eq {x sub n} +} +where @Eq { x sub j } has width @Eq { l sub j , r sub j } for all @Eq {j}. +@PP +Suppose the whole object has width constraint @OneCol @Eq {X,Y,Z}, and we +require the width constraint of {@Eq { x sub i }}. Let +@Eq { L = max sub j ` l sub j } and @Eq { R = max sub j ` r sub j }, +so that @OneCol @Eq {L, R} is the width of the whole object. We assume +@Eq {L, R <= X,Y,Z}. Then @Eq { x sub i } can be enlarged to any size +@Eq { l sub i ` , r sub i } satisfying +@ID @Eq { ( l sub i up L), ( r sub i up R) <= X, Y, Z } +which expands to eight inequalities: +@ID @OneRow @Eq { +matrix { + { l sub i ^<= X } +mabove { L ^<= X } +mabove { l sub i + r sub i ^<= Y } +mabove { l sub i + R ^<= Y } +mabove { L + r sub i ^<= Y } +mabove { L + R ^<= Y } +mabove { r sub i ^<= Z } +mabove { R ^<= Z } +} +} +Three are already known, and slightly rearranging the others gives +@ID @OneRow @Eq { +matrix { + { l sub i ^<= X } +mabove { l sub i ^<= Y - R } +mabove { l sub i + r sub i ^<= Y } +mabove { r sub i ^<= Z } +mabove { r sub i ^<= Y - L } +} +} +Therefore the width constraint of @Eq { x sub i } is +@ID @Eq { min(X, Y-R), Y, min(Z, Y-L) } +The size constraint of any node can be found by climbing the tree to a +@I WIDE or @I HIGH node where the constraint is trivial, then propagating +it back down to the node, and this is the function of procedure +{@I Constrained} in Basser Lout. +@PP +After some components have been promoted into a target, the sizes stored +in its parent and higher ancestors must be adjusted to reflect the +increased size. This is done by yet another set of recursive rules, +upward-moving this time, which cease as soon as some ancestor's size +does not change. These rules are embodied in procedure @I AdjustSize +of Basser Lout. The adjustment must be done before relinquishing +control to any other galley, but not after every component. +@End @SubSection diff --git a/doc/design/s5_4 b/doc/design/s5_4 new file mode 100644 index 0000000..b91d7ce --- /dev/null +++ b/doc/design/s5_4 @@ -0,0 +1,97 @@ +@SubSection + @Tag { lookahead } + @Title { The limited lookahead problem } +@Begin +@PP +Basser Lout assumes that there will be enough internal memory to hold +the symbol table plus a few pages, but not an entire document. This +section describes the consequent problems and how they were solved. +Other interpreters, notably interactive editors running on virtual +memory systems, would not necessarily need this assumption. +@PP +Although Basser Lout can read and format any legal input, its memory +consumption will be optimized when the bulk of the document resides in +galleys whose targets can be identified at the moment they are +encountered. Let us take the typical example of a root galley which +is a list of pages, a @Code "@BodyText" galley targeted into the +pages, @Code "@Chapter" galleys targeted into {@Code "@BodyText"}, +and @Code "@Section" galleys targeted into the @Code "@Chapter" +galleys: +@ID @OneRow @Code { +"@PageList" +"//" +"@BodyText" +"//" +"@Chapter {" +" @Section { ... }" +" @Section { ... }" +" ..." +" @Section { ... }" +"}" +"@Chapter {" +" ..." +"}" +} +Basser Lout is able to read and process such galleys one paragraph at +a time (strictly, from one @Code "//" at the outer level of a galley +to the next), as we now describe. +@PP +When the parser encounters the beginning of a galley, like @Code "@Chapter" +or {@Code "@Section"}, it initiates a new galley process. The special +receptive symbol @Code "@Input" is substituted for the as yet +unread right parameter of the galley. As each paragraph of the right +parameter is read, it is deleted from the parse tree and injected into +the galley's {@Code "@Input"}. The galley is then resumed. The parser +thus acts as an extra +concurrent process; it has low priority, so that input is read only when +there is nothing else to do. Since galleys may be nested, a stack of +@Code "@Input" symbols is needed, each with its own environment and +style. If a galley is encountered for which a target is not immediately +identifiable (a footnote, for example), it is read in its entirety and +hung in pure parse tree form from an @I UNATTACHED index in the usual way, +with an environment but without a style. It will be flushed later +when its component is promoted. +@PP +In addition to producing a steady flow of components from input, we must +also ensure that receptive symbols do not unduly block their +promotion. The @Code "@FootSect" symbol at the foot of each page is a +typical example: until it is deleted the page cannot be printed. +@PP +Receptive symbols are expanded only on demand, so @Code "@FootSect" can +be deleted as soon as we can prove that it is not wanted. The symbol +table can tell us that only @Code "@FootNote" galleys (with +@Code "@FootPlace&&following" targets) want it, so it might be possible +to deduce that @Code "@FootSect" may be deleted as soon as body text +enters the following page. +@PP +The author was unable to make this work, so Basser Lout requires the +user to identify those galleys which will carry the bulk of the document +({@Code "@Chapter"}, {@Code "@Section"}, {@Code "@BodyText"}) as +{@I {forcing galleys}}, by writing @Code "force into" instead of +@Code "into" in their definitions. As described in the previous +section, when a forcing galley attaches to a target, all receptive +symbols preceding the target in its galley are deleted, removing all +impediments to flushing. For example, when a forcing body text galley +enters a new page, the @Code "@FootSect" symbol on the preceding page +will be deleted. It seems likely that a system which could afford to +wait until all input was read before deleting any receptive symbols +would not need forcing galleys. +@PP +Galleys whose targets are a long way from their invocation points can be +a problem. If the direction is {@Code "following"}, such galleys are +held in internal memory for a long time, unless they are to be +sorted. If the direction is +{@Code "preceding"}, then either the entire intervening document must be +held in memory (prevented by the target from flushing), or else some +forcing galley prematurely deletes the target, leaving the galley bereft. +@PP +The typical example of the latter case occurs when the galley is an +entry in the table of contents, launched backwards from the beginning of +a chapter or section. Its target in the table of contents will have +been deleted long before, to permit the rest of the document to print, +so the galley ultimately emerges as an unattached galley promoted out of +the root galley. All such galleys are written to an auxiliary file, +indexed by the missing target. On the next run, just before that target +is deleted, the auxiliary file is checked and any galleys for it are +read in and flushed. +@End @SubSection diff --git a/doc/design/s5_5 b/doc/design/s5_5 new file mode 100644 index 0000000..af4d88b --- /dev/null +++ b/doc/design/s5_5 @@ -0,0 +1,109 @@ +@SubSection + @Tag { horizontal } + @Title { Horizontal galleys } +@Begin +@PP +There is a strong analogy between breaking a column of text into +page-sized pieces, and breaking a paragraph into line-sized pieces. In +fact, the two differ only in direction: vertical for body text, +horizontal for paragraphs. In this section we define {@I{horizontal +galleys}}, and show how they provide an unlimited number of paragraph +breaking styles, as well as solve some other problems. Regrettably, +lack of time has prevented their incorporation into the Basser Lout +interpreter. +@PP +Imagine a galley whose components are separated by horizontal +concatenation operators instead of vertical ones, perhaps indicated by a +@Code { horizontally into } clause. Then all object breaking, including +paragraph breaking, could be replaced by galley component promotion like +this: +@ID @OneRow @Code { +"def @Paragraph right x" +"{" +" def @LinePlace { @Galley }" +"" +" def @LineList" +" {" +" @HExpand @LinePlace" +" //1vx @LineList" +" }" +"" +" def @Par horizontally into { @LinePlace&&preceding }" +" right x" +" { x }" +"" +" @LineList // @Par { 0.2i @Wide {} &0i x &1rt }" +"}" +} +The @Code "@HExpand" operator, which is a primitive of Basser Lout, +horizontally expands the gaps in its right parameter until the result +fills the available space, thus implementing line adjustment, except +when the parameter contains tabulation gaps like {@Code "&1rt"}, which +cause the parameter to be already expanded. The result of +@ID @Code "@Paragraph { A short paragraph of text. }" +would then be something like +@ID 1.5i @Wide { +0.2i @Wide {} & A short paragraph of text. +} +depending on the available horizontal space. An unlimited range of +paragraph breaking styles could be defined, including ragged right, ragged +left, break-and-center, and so on. +@PP +In Basser Lout, indented paragraphs are produced by preceding them with +a horizontal concatenation operator, for example {@Code "|0.5i"}. This +has the unfortunate effect of making an indented paragraph into a single +component of the enclosing galley, so that it will always be kept +together on one page. Horizontal galleys solve this problem with a +simple change to {@Code "@LineList"}: +@ID @OneRow @Code { +"def @LineList" +"{" +" |0.5i @HExpand @LinePlace" +" //1vx @LineList" +"}" +} +showing the flexibility that comes from bringing the full power of the +Lout language to bear on paragraph layout. It is easy to make provision +for a tag on the first line. +@PP +Although Basser Lout permits receptive symbols within paragraphs, they +are of little use, because their available width is calculated after +paragraph breaking, and the incoming galley cannot spread over more than +one line. With horizontal galleys, such symbols would have infinite +available width, and we could easily produce a filled paragraph of +footnotes like this: +@ID 3.5i @Wide { +@OneRow { -2p @Font 1 ^/0.3vo } & See Jones and Saunders (1982). &2m +@OneRow { -2p @Font 2 ^/0.3vo } & Or so Jacobsen (1973) asserts. &2m +@OneRow { -2p @Font 3 ^/0.3vo } & {@I ibid}, p. 327. +} +based on an infinite horizontal sequence of @Code "@FootPlace" symbols +inside a horizontal galley. +@PP +When body text is placed on pages, the length of each column varies +depending on the available vertical space. Horizontal galleys could +analogously produce lines of varying length, and so could fill +non-rectangular shapes. +@PP +An important theoretical benefit of horizontal galleys is that they +would permit horizontal and vertical to be treated in a perfectly +symmetrical way, whereas at present paragraph breaking is horizontal +only, and galley breaking is vertical only. This must simplify the +treatment of non-European languages which fill in unusual directions, +although it is not itself sufficient to implement them. +@PP +There are a few minor problems with horizontal galleys. First, the +syntactic overhead of enclosing each paragraph in @Code "@Paragraph { ... }" +or whatever is unacceptable. Permitting user-defined operators to have lower +precedence than the white space between two words might help here. Second, +the built-in paragraph breaker includes hyphenation, and it permits line +breaks in the input to determine line breaks in the output, if +desired. These features must somehow be preserved. Finally, we have +explained how the Basser Lout interpreter assigns equal width to the +wider columns of tables (Section {@NumberOf style}). The equivalent +situation in vertical galleys occurs when two receptive symbols compete +for vertical space (e.g. @Code "@TextPlace" and {@Code "@FootSect"}), +and there it is conventional to grant as much as required to the first +arrival. It is not clear to the author how these different approaches +can be reconciled. +@End @SubSection diff --git a/doc/design/s5_9 b/doc/design/s5_9 new file mode 100644 index 0000000..648a1b6 --- /dev/null +++ b/doc/design/s5_9 @@ -0,0 +1,2 @@ +@EndSubSections +@End @Section diff --git a/doc/design/s6_0 b/doc/design/s6_0 new file mode 100644 index 0000000..07fb62e --- /dev/null +++ b/doc/design/s6_0 @@ -0,0 +1,18 @@ +@Section + @Title { Cross references } +@Begin +@PP +Cross references, such as `see page 57' and `see Figure 5,' are a useful +but highly error-prone feature of documents. Scribe [7] +introduced a method of keeping them up to date automatically as the +document changes: the user gives each referenced entity a tag, and +operators are provided that return the page or sequence number of the +entity with a given tag. +@PP +A cross reference takes an object (such as a page number) from one point +in the document and copies it to another, and this generalization +suggests other applications. For example, a running header is copied +from the title of a nearby chapter, and a reference is copied from a +bibliographic database. Making the unity of these applications manifest +is an interesting language design problem. +@BeginSubSections diff --git a/doc/design/s6_1 b/doc/design/s6_1 new file mode 100644 index 0000000..0ffc70d --- /dev/null +++ b/doc/design/s6_1 @@ -0,0 +1,85 @@ +@SubSection + @Tag { cross } + @Title { The cross reference abstraction } +@Begin +@PP +In developing the cross reference abstraction, it seemed best to begin +with the database application, since it is the simplest. Database +relations are naturally mapped into Lout definitions: +@ID @OneRow @Code { +"def @Reference" +" named @Tag {}" +" named @Author {}" +" named @Title {}" +" named @Journal {}" +"{}" +} +The set of all invocations of @Code "@Reference" is a relation whose +attributes are the parameters, and whose tuples are the invocations. To +complete the correspondence, we need only declare that the @Code "@Tag" +parameter is special, serving as the key attribute. +@PP +Following the database model, we next need a notation for retrieving the +invocation with a given tag: +@ID @Code "@Reference&&kingston91" +This @I {cross reference} is like an arrow pointing to the invocation. To +access its attributes, we write +@ID @Code "@Reference&&kingston91 @Open { @Author, @Title }" +The @Code "@Open" operator evaluates its right parameter in an +environment which includes the exported parameters of its left. +@PP +An invocation is chosen to be a running header because of its proximity +to the place where it is used, rather than by its tag. Such proximity +is naturally expressed by two special tags, {@Code preceding} and +{@Code following}; for example, @Code "@Sym&&following" will point to +the closest following invocation of @Code "@Sym" in the final printed +document. This is much simpler conceptually than reference to the +internal state of the document formatter at a critical moment, the usual +approach to running headers. +@PP +It turns out that the above design solves all the cross referencing +problems encountered in practice except one, which may be typified by +the problem of finding the number of the page on which the chapter whose +tag is @Code "intro" begins. Two cross referencing steps are needed, +first to {@Code "@Chapter&&intro"}, then from there to +{@Code "@Page&&preceding"}, where the page number is known. +@PP +Given our success so far, this last problem proves to be +surprisingly difficult. We first try +@ID @OneRow @Code { +"@Chapter&&intro @Open {" +" @Page&&preceding @Open { @PageNum }" +"}" +} +but this fails because @Code "@Page&&preceding" is evaluated in the +present context, not in the context of @Code "@Chapter&&intro" as +required. So our next attempt is +@ID @OneRow @Code { +"def @Chapter" +" named @PageNum { @Page&&preceding @Open { @PageNum } }" +" ..." +} +with the @Code "@Page&&preceding" cross reference attached to the +chapter; we write +@ID @Code "@Chapter&&intro @Open { @PageNum }" +This also fails, because parameters are evaluated after substitution, so +once again @Code "@Page&&preceding" is evaluated in the wrong context. We +could of course define a new operator specifically for this case: +@ID @Code "@Page&&{ @Preceding @Chapter&&intro }" +or some such. This is free of the annoying context-sensitivity, but it +seems quite complex, and the expected cross reference @Code "@Page&&preceding" +does not appear. +@PP +The author was lost in these obscurities for some time, and ultimately +rescued himself by looking ahead to the implementation of the +@Code preceding and @Code following tags, to see if a simple extension +of it would solve the problem. This led to the @Code "@Tagged" operator: +@ID @Code "@Page&&preceding @Tagged intro" +placed at the beginning of the body of the chapter will attach @Code intro +as an extra tag to the closest preceding invocation of {@Code "@Page"}, +so that +@ID @Code "@Page&&intro @Open { @PageNum }" +yields the desired page number. There is something low-level and ad hoc +about the @Code "@Tagged" operator, but the two cross references do +appear naturally, and it works. +@End @SubSection diff --git a/doc/design/s6_2 b/doc/design/s6_2 new file mode 100644 index 0000000..2df5478 --- /dev/null +++ b/doc/design/s6_2 @@ -0,0 +1,79 @@ +@SubSection + @Tag { cross.impl } + @Title { Implementation of cross references } +@Begin +@PP +Before an object can be sized and printed, the values of any cross +references within it must be known. If they refer to invocations that +have not yet been read, there is a problem. Scribe [7] +solves it by capitalizing on the fact that documents are formatted +repeatedly during the drafting process. All tagged invocations are +copied to an auxiliary file during the first run, and indexed for quick +retrieval on the second. A new auxiliary file is written during the second +run, for retrieval on the third, and so on. Cross references always lag +one run behind the rest of the document; a perfect copy may be produced +by formatting the same version twice, except in a few pathological cases +that fail to converge. +@PP +Cross referencing in Lout is implemented on top of a simple database +system. Each database is either writable or readable but not both at +once, and holds a set of key-value entries: the keys are @S ASCII +strings, and the values are Lout objects, possibly with environments, +written in Lout source. Operations are provided for writing an entry, +converting from writable to readable, retrieval by key, and sequential +retrieval in key order. +@PP +The implementation, which is quite unsophisticated, employs one or more +@S ASCII {@I{ database files}}, containing the values, and one @S ASCII +{@I{ index file}} per database, containing the keys. To write an entry, +the value is first appended to a database file, then a line like +@ID @Code "@Chapter&&intro ch1.ld 57" +is appended to the index file, giving the file and offset where the value +is stored. To convert from writable to readable, the index file is +sorted. Then retrieval by key requires a binary search of the index +file and one seek into a database file, and sequential retrieval by key +is trivial. +@PP +This database system is used in several ways. For an external database, +say of bibliographic references, the user creates the database file of +values (without environments), Lout creates the index file whenever it +cannot find one, and retrievals by key proceed as usual. Cross +references with tags other than @Code preceding and @Code following are +treated as described above, by writing all tagged invocations (with +environments) to a single database, which is converted to readable at +the end of the run for retrievals on the next run. Sorted galleys, such +as index entries, are written out indexed by target and key and retrieved +sequentially on the next run. Unsorted galleys with preceding targets +which pop off the top of the root galley without finding a target, such +as entries in tables of contents, are treated similarly, except that they +are indexed by target and a sequence number that preserves their relative +order during the sort. +@PP +When Lout processes a multi-file document, one cross reference database +file is written for each input file, but they share a common index +file. At end of run, the new index file is sorted and merged with the +old one in such a way as to preserve entries relating to files not read +on the current run. This provides some support for piecemeal +formatting, but eventually the files must all be formatted together. +@PP +When a @Code preceding or @Code following cross reference is found, +it is attached to a galley index of type @Eq { CROSS_PREC } or +{@Eq { CROSS_FOLL }}, together with an automatically generated tag composed +of the current file name and a sequence number. When a tagged +invocation is found, it is attached to a @Eq { CROSS_TARG } index. These +galley indexes are carried along through the dynamic tree, and +eventually pop off the top of the root galley, at which point it is easy +to determine which cross references refer to which invocations, since +the indexes are now in final printed document order. Each referenced +invocation is then written to the cross reference database, multiply indexed +by the generated tags of the associated cross references. On the next +run, when the same @Code preceding and @Code following cross references +are found, chances are good that the same tags will be generated, and +the appropriate values can be retrieved from the database immediately. +@PP +This approach was the genesis of the @Code "@Tagged" operator, whose +implementation is now immediate: for each @Code "@Tagged" operator we +produce one @Eq { CROSS_PREC } or @Eq { CROSS_FOLL } galley index, +replacing the generated tag with the right parameter of the @Code "@Tagged" +operator. Nothing more is required. +@End @SubSection diff --git a/doc/design/s6_9 b/doc/design/s6_9 new file mode 100644 index 0000000..648a1b6 --- /dev/null +++ b/doc/design/s6_9 @@ -0,0 +1,2 @@ +@EndSubSections +@End @Section diff --git a/doc/design/s7_0 b/doc/design/s7_0 new file mode 100644 index 0000000..2cb4245 --- /dev/null +++ b/doc/design/s7_0 @@ -0,0 +1,84 @@ +@Section + @Title { Conclusion } +@Begin +@PP +Since its public release in October 1991, the Basser Lout interpreter +has been ported without incident to a wide variety of Unix systems and +hardware. It was tested extensively before release on its own +documentation, and the few minor bugs which have emerged since then have +all been fixed in the second release, scheduled to appear in mid-1992. +@PP +Seven substantial packages of definitions are distributed with Basser +Lout. The DocumentLayout package, and its variants ReportLayout and +BookLayout, provide the standard features that all documents +require: pages, columns, paragraphs, headings, footnotes, floating +figures and tables, chapters and sections, displays and lists, access +to bibliographic databases, cross references, and so on +[11]. The BookLayout package has extra features +needed by books, including an automatically generated table of contents, +Roman page numbers for the prefatory material, running page headers, +odd and even page layouts, and a sorted index. The Eq package formats +equations, and Pas formats Pascal programs [10]; Tab +formats tables [12]; and Fig draws figures +[6]. +@PP +The non-expert user who uses these packages perceives a system of a +standard quite similar to other fully developed batch formatters, +although the interface is considerably more coherent than, say, the troff +family's [8]. The expert user perceives a system which +is radically different from previous ones, in which a great deal can be +achieved very quickly. To take an extreme example, Pas was designed, +implemented, tested, and documented in one afternoon. Eq took about +a week, but most of that time was spent in marshalling the vast +repertoire of mathematical symbols, and fine-tuning the spacing. Most +of the effort seems to go into designing a good interface; most symbols +are implemented in just one or a few lines of Lout. +@PP +A group of about 20 satisfied non-expert users has grown up within +the author's department, mainly Honours students with no investment +in older systems to hold them back. Basser Lout has been advertised +on the Internet news as available via anonymous {@I ftp}, so the +extent of its outside user community is hard to gauge. About 50 +people have mailed comments or questions to the author; many +of these people have ported the program, written small definitions, +and modified the standard packages. +@PP +Future work could usefully begin with the improvements suggested in this +paper: overlapping spanning columns, better semantics for available +space, and especially horizontal galleys. Support for non-European +languages is also needed. However, the main task is the development of +an interactive document editor based on Lout. A structure editor similar +to Lilac [13], which already has objects and user-defined +symbols, is envisaged; since cross references are easy when the whole +document is available, the only major new problem is the treatment of +galleys, including the expansion and retraction of receptive symbols. +@LP +@LP +@B { Note. } Since the above was written the author has completed a +revised version of Basser Lout, in which the problem concerning +available space mentioned in Section {@NumberOf style} has been resolved. +@LP +@LP +@B { Acknowledgment. } The author gratefully acknowledges many +valuable discussions with Douglas W. Jones, especially during the +development of the galley abstraction; and also many helpful comments on +presentation by the anonymous referee. +@DP +@DP +@Heading { References } +@NumberedList +@LI @RefPrint kingston91 +@LI @RefPrint kingston91over +@LI @RefPrint kingston91basser +@LI @RefPrint furuta82 +@LI @RefPrint kernighan75 +@LI @RefPrint kingston91fig +@LI @RefPrint reid80 +@LI @RefPrint ossanna76 +@LI @RefPrint knuth84 +@LI @RefPrint kingston91eq +@LI @RefPrint kingston91begin +@LI @RefPrint kingston91tab +@LI @RefPrint brooks91 +@EndList +@End @Section |