@Section
   @Title { Concatenation symbols and paragraphs }
   @Tag { concatenation }
@Begin
@PP
There are ten concatenation symbols, in three families:
concatenation. @Index { Concatenation symbols }
@ID @Tab
   vmargin { 0.5vx }
   @Fmta { @Col @Code A ! @Col @Code B ! @Col @Code C ! @Col @Code D ! @Col E }
{
@Rowa A { "/" } B { "^/" } C { "//" } D { "^//" } E { Vertical concatenation }
@Rowa A { "|" } B { "^|" } C { "||" } D { "^||" } E { Horizontal concatenation }
@Rowa A { "&" } B { "^&" } C {      } D {       } E {In-paragraph concatenation}
}
Each symbol produces an object which combines together the two
parameters.  The right parameter must be separated from the symbol by at
least one white space character.
@PP
The vertical concatenation symbol @Code "/" places its left parameter
vertical.concatenation @Index { Vertical concatenation }
above its right parameter with their column marks aligned.  If one
parameter has more column marks than the other, empty columns are
inserted at the right to equalize the numbers.  The variant @Code "//"
ignores column marks and left-justifies the objects.
@PP
The horizontal concatenation symbols @Code "|" and @Code "||" are horizontal
horizontal.concatenation @Index { Horizontal concatenation }
analogues of @Code "/" and {@Code "//"}:  they place their two parameters side
by side, with row mark alignment or top-justification respectively.  The
in.paragraph.concatenation @Index { In-paragraph concatenation }
in-paragraph concatenation symbol @Code "&" produces horizontal concatenation
within a paragraph; its special properties are treated in detail at the
end of this section.
@PP
The concatenation symbols in any one family are @I { mutually associative },
which means that
@ID {
@Code "{"  @I x  {@Code "|"}{@I p}  @I y  @Code "}"  {@Code "|"}{@I q}  @I z
}
is always the same as
@ID {
@I x  {@Code "|"}{@I p}  @Code "{"  @I y  {@Code "|"}{@I q}  @I z  @Code "}"
}
for any objects {@I x}, {@I y}, and {@I z}, any gaps @I p and @I q (defined
below), and any choice of {@Code "|"}, {@Code "^|"}, {@Code "||"}, and
{@Code "^||"}.  In practice we always omit such braces, since they are
redundant and can be misleading.  The result of the complete sequence of
concatenations will be called the {@I{whole concatenation object}}, and
the objects which make it up will be called the {@I components}.
@PP
One mark is designated as the @I { principal mark }, usually the mark of
principal.mark @Index { Principal mark }
the first component.  A later mark can be chosen for this honour by
attaching {@Code "^"} to the preceding concatenation symbol.  See Section
{@NumberOf onerow} for examples.
@PP
A {@I gap},
gap @Index Gap
specifying the distance between the two
parameters, may follow any concatenation symbol.  There may be no spaces
between a concatenation symbol and its gap.  A missing gap is taken
to be {@Code 0ie}.  The gap is effectively a third parameter of the
concatenation symbol, and it may be an arbitrary object provided that it
evaluates to a juxtaposition of simple words.  In general, the gap must
be enclosed in braces, like this:
@ID @Code {
"//{  @Style&&mystyle @Open { @TopMargin }  }"
}
but the braces may be omitted when the object is a juxtaposition of
simple words or an invocation of a symbol without parameters, as in
@Code "//0.3vx" and {@Code "||@Indent"}.
@PP
A gap consists of a length plus a gap mode plus an optional indication
of unbreakability.  A @I length
length @Index { Length }
is represented by an decimal number (which may not be negative) followed
by a unit of measurement.  For example, @Code "2.5c" represents the
length 2.5 centimetres.  Figure {@NumberOf units} gives the full selection
of units of measurement.
c.unit @Index { @Code c unit }
p.unit @Index { @Code p unit }
m.unit @Index { @Code m unit }
f.unit @Index { @Code f unit }
s.unit @Index { @Code s unit }
v.unit @Index { @Code v unit }
w.unit @Index { @Code w unit }
b.unit @Index { @Code b unit }
r.unit @Index { @Code r unit }
d.unit @Index { @Code d unit }

@Figure
   @Caption { The thirteen units of measurement provided by Lout. }
   @Tag { units }
@Begin
   @Tab
      vmargin { 0.3v }
      side { yes }
      @Fmta { @Col @Code A ! @Col B }
   {
      @Rowa above { yes } A { c } B { Centimetres. }
      @Rowa A { i } B { Inches.
}
      @Rowa A { p } B { Points ({@Code 72p} = {@Code 1i}).
}
      @Rowa A { m } B { Ems ({@Code 12m} = {@Code 1i}).
}
      @Rowa A { f } B {
One @Code f equals the size of the current font, as specified by
the @@Font symbol (Section {@NumberOf font}).  This unit is
appropriate for lengths that should change with the font size.
}
      @Rowa A { s } B {
One @Code s equals the preferred gap between two words in the
current font, as specified in the definition of the font, or by the
@@Space symbol (Section {@NumberOf break}).
}
      @Rowa A { v } B {
One @Code v equals the current gap between lines introduced during
paragraph breaking, as specified by the @@Break symbol (Section
{@NumberOf break}).  This unit is appropriate for lengths, such as the
spaces between paragraphs, which should change with the inter-line gap.
}
      @Rowa A { w } B {
One @Code w equals the width of the following component, or its height if the
symbol is vertical concatenation.
}
      @Rowa A { b } B {
One @Code b equals the width of the whole concatenation object,
or its height if the symbol is vertical concatenation.
}
      @Rowa A { r } B {
One @Code r equals one @Code b minus one {@Code w}.  This unit is used
for centring, and for left and right justification.
}
      @Rowa A { d } B {
Degrees.  This unit may only be used with the @Code "@Rotate" symbol.
}
      @Rowa A { y } B {
One @Code y equals the current value set by the @Code "@YUnit"
symbol (Section {@NumberOf yunit}).  This unit is not used internally
by Lout; it is included for the convenience of application packages.
}
      @Rowa below { yes } A { z } B {
One @Code z equals the current value set by the @Code "@ZUnit"
symbol (Section {@NumberOf yunit}).  This unit is not used internally
by Lout; it is included for the convenience of application packages.
}
   }
@End @Figure

@PP
After the length comes an optional @I {gap mode},
gap.mode @Index { Gap mode }
which is a single letter following the length, indicating how the length
is to be measured.  As shown in Figure {@NumberOf gapmodes},

@Figure
   @Tag { gapmodes }
   @Caption { The six gap modes provided by Lout. }
@Begin
@Fig {
{ /2.5vx Edge-to-edge |0.3i   {@Code "|"} &1p {@I l} &1p {@Code e}
  /4vx Hyphenation    |0.3i   {@Code "|"} &1p {@I l} &1p {@Code h}
  /4vx Overstrike     |0.3i   {@Code "|"} &1p {@I l} &1p {@Code o}
  /4vx Mark-to-mark   |0.3i   {@Code "|"} &1p {@I l} &1p {@Code x}
  /4vx Kerning        |0.3i   {@Code "|"} &1p {@I l} &1p {@Code k}
  /4vx Tabulation     |0.3i   {@Code "|"} &1p {@I l} &1p {@Code t}
}
||0.5i
@Box margin { 0c } 6c @Wide 13.2c @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 l } }
  }
  //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 l } }
  }
  //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 l } }
  }
  //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 { max( {@I {l, a+b+l"/10"}}) } }
     @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 { 1.2c @Wide 1.5c @High } @Put { @DoubleArrow 3.3c }
     @At { 1.2c @Wide 1.7c @High }
	@Put { 3.3c @Wide { |0.5rt max( {@I {l, 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 l }
  }
  //5vx
  @DoubleArrow 6c
  //0.1c |0.5rt @I { current bound }
}

}
@End @Figure
with edge-to-edge gap mode
edge.to.edge @Index { Edge-to-edge gap mode }
e.gap.mode @Index { @Code e gap mode }
the length @I l is measured from the trailing edge
of the first object to the leading edge of the second.  Edge-to-edge is the
default mode:  the @Code e may be omitted.  Hyphenation gap mode is
hyphenation.gap @Index { Hyphenation gap mode }
h.gap.mode @Index { @Code h gap mode }
similar, except as explained at the end of this section.
@PP
Mark-to-mark,
mark.to.mark @Index { Mark-to-mark gap mode }
x.gap.mode @Index { @Code x gap mode }
overstrike,
overstrike @Index { Overstrike gap mode }
o.gap.mode @Index { @Code o gap mode }
and kerning
kerning.mode @Index { Kerning gap mode }
k.gap.mode @Index { @Code k gap mode }
measure the length from the last mark
of the first object to the first mark of the second.  In the case of
mark-to-mark, if the length is too small to prevent the objects
almost overlapping, it is widened until they no longer do.  (The extra
@I { "l/10" } is not applied when plain text output is in effect.)  Kerning
also widens, with the aim of preventing the mark of either object from
overlapping the other object; this mode is used for subscripts and
superscripts.
@PP
tabulation @Index { Tabulation gap mode }
t.gap.mode @Index { @Code t gap mode }
centring @Index { Centring }
right.justif @Index { Right justification }
Tabulation ignores the first object and places the leading edge of the
second object at a distance @I l from the left edge of the whole
concatenation object.  It is the main user of the @Code b and @Code r
units of measurement; for example, @Code "|1rt" will right-justify the
following component, and @Code "|0.5rt" will centre it.
@PP
The value @Code "|0rt" separating the first and second items in a
sequence of horizontally concatenated objects is somewhat special in
that it denotes left justification of the object to its left in the
available space.  This is identical with @Code "|0ie" when the object to
the left also has the principal mark; but when it does not, @Code "|0rt"
will cause the object to the left to appear further to the left than it
would otherwise have done, if space to do so is available.
@PP
A gap is optionally concluded with an indication of unbreakability,
which is a letter @Code "u" appended to the gap.  A paragraph will
never be broken at an unbreakable gap, nor will a galley be broken
across two targets at such a gap.  Basser Lout's implementation is
slightly defective in that it ignores any unbreakable indication
in the gap separating the first component promoted into any target
from the second.
@PP
When two objects are separated only by zero or more white space
white.space.when @SubIndex { when significant }
space.f.when @SubIndex { when significant }
characters (spaces, tabs, newlines, and formfeeds), Lout inserts
{@Code "&"}{@I k}{@Code "s"} between the two objects, where @I k is the
number of spaces.  Precisely, @I k is determined by discarding all space
characters and tabs that precede newlines (these are invisible so are
better ignored), then counting 1 for each newline, formfeed or space,
and 8 for each tab character.  The gap will be unbreakable if @I k
is zero.
@PP
A sequence of two or more objects separated by @Code "&" symbols is a
paragraph.breaking.in.detail @SubIndex { in detail }
{@I paragraph}.  Lout breaks paragraphs into lines automatically as
required, by converting some of the @Code "&" symbols into
{@Code "//1vx"}.  Unbreakable gaps are not eligible for this
conversion.  `Optimal' line breaks are chosen, using a
method adapted from @TeX @Cite { $knuth1984tex }.
tex @RawIndex { @TeX }
tex.optimal @SubIndex { optimal paragraph breaking }
@PP
If an @Code "&" symbol whose gap has hyphenation mode
hyphenation @Index { Hyphenation gap mode }
tex.hyphenation @SubIndex { hyphenation }
is chosen for replacement by {@Code "//1vx"}, a hyphen will be appended to
the preceding object, unless that object is a word which already ends with
a hyphen.  For example,
@ID @Code {
Long words may be "hyph &0ih enat &0ih ed."
}
could have the following result, depending where the line breaks fall:
@ID 2i @Wide {
Long words may be hyph &0ih enat &0ih ed.
}
Basser Lout inserts hyphenation gaps automatically as required, again
following the method of @TeX, which approximates the hyphenations in
Webster's dictionary.  However it does not insert hyphenation gaps
in words on either side of a concatenation symbol which already has
hyphenation mode.  To prevent the hyphenation of a single word,
enclose it in quotes.  Further control over paragraph breaking and
hyphenation is provided by the @@Break and @@Space symbols (Sections
{@NumberOf break} and {@NumberOf space}).
@End @Section