@Section
    @Tag { dia_synt }
    @Title { Syntax diagrams }
@Begin
@PP
A variant of the @@Diag symbol, called {@Code "@SyntaxDiag"},
diagrams. @RawIndex { diagrams }
diagrams.syntax @SubIndex { syntax diagrams }
syntax.diagrams @Index { syntax diagrams }
railroad.diagrams @Index { railroad diagrams }
produces syntax diagrams (sometimes called railroad diagrams):
@CD @SyntaxDiag
    title { call-chain }
{
    @StartRight @Sequence
        A { @Optional @Sequence
                A { @BCell "super" }
                B { @CCell "!" }
          }
        B { @Loop
                A { @Sequence
                        A { @ACell identifier }
                        B { @Optional @Sequence
                                A { @CCell "(" }
                                B { @Loop
                                        A { @ACell expression }
                                        B { @CCell "," }
                                  }
                                C { @CCell ")" }
                          }
                  }
                B { @CCell "." }
          }
}
These are used to define the syntax of computer programming languages,
although they could be put to other uses.  We'll explain how to get
syntax diagrams first.  At the end of this section is an explanation of
how to change the formats of things, which people who use these diagrams
for other purposes will probably need to do.
@PP
A syntax diagram can be @I { right-moving }, which means it starts
at the left and heads right (like the example above), or it can be
@I { down-moving }, starting at the top and heading downwards.  The
@Code "@StartRight" and @Code "@StartDown" symbols are used at the start
of the diagram to say which of these directions is wanted:
@ID @OneRow @Code @Verbatim {
@SyntaxDiag
    title { call-chain }
{
    @StartRight ...
}
}
where @Code { ... } stands for the rest of the diagram, as we are about
to describe.  For completeness there are also @Code "@StartLeft" and
@Code "@StartUp" symbols, but diagrams never start off in these directions.
@PP
The @Code title option is optional; if given, the effect is as shown
(this option is also available with {@Code "@Diag"}).  Subsequent
examples will omit the enclosing {@Code "@SyntaxDiag { ... }"}.
@PP
The basic components of syntax diagrams are @I { category cells },
shown as boxes in the example above and obtained with the
@Code "@ACell" symbol; @I { keyword cells }, shown as curved boxes
and obtained with {@Code "@BCell"}; and @I { punctuation cells },
containing punctuation symbols small enough to be enclosed in circles,
and obtained with {@Code "@CCell"}.  After each symbol, place whatever
has to go inside the cell:
@ID @OneRow {
@Code @Verbatim { @StartRight @BCell loop }
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@SyntaxDiag {
@StartRight @BCell loop
}
}
Lout will insert the appropriate arrows, taking account of which
direction (right, up, left, or down) the diagram is currently
moving.  This is true for all the syntax diagram symbols; we
won't mention it again.
@FootNote {
This wonderfully useful effect is achieved by a dirty trick, one
of whose consequences is that if you see an error message
similar to `@Code { replacing unknown "@Case" option 0p by 1p }'
it means you've forgotten the initial @Code "@StartRight" or
whatever.
}
@PP
Occasionally, instead of a cell one wants the horizontal or
vertical line to continue uninterrupted.  For this there is
the @Code "@Skip" symbol:
@ID @OneRow {
@Code @Verbatim { @StartDown @Skip }
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@SyntaxDiag {
@StartDown @Skip
}
}
Some examples of its use in practice appear below.
@PP
There are three main ways to build up larger syntax diagrams out
of smaller ones:  @I { sequencing }, @I { selection }, and
@I { looping }.  For sequencing there is the @Code "@Sequence" symbol:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Sequence
    A { @BCell loop }
    B { @ACell statements }
    C { @BCell end }
}
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@SyntaxDiag {
@StartRight @Sequence
    A { @BCell loop }
    B { @ACell statements }
    C { @BCell end }
}
}
This is what the sequence looks like in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@Sequence
    A { @BCell loop }
    B { @ACell statements }
    C { @BCell end }
}
} }
Whatever the direction, the arrows go from option @Code A to option @Code B
to option @Code C and so on.  You can have up to twelve items in the
sequence, in options @Code A to {@Code L}; if more than twelve are needed,
just place another sequence inside any one of these options:  where one
syntax diagram is allowed, any syntax diagram is allowed, provided there
is enough space on the page (Lout makes a total mess of any diagram that
is too wide to fit on the page).
@PP
After sequencing comes selection, which is obtained with the
@Code "@Select" symbol:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Select
    A { @ACell asst }
    B { @ACell call-chain }
    C { @Sequence
           A { @BCell assert }
           B { @ACell condition }
      }
}
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@SyntaxDiag {
@StartRight @Select
    A { @ACell asst }
    B { @ACell call-chain }
    C { @Sequence
           A { @BCell assert }
           B { @ACell condition }
      }
}
}
This example shows right-moving selection of three alternatives,
the third being a sequence of things.  Here is the same example
in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@Select
    A { @ACell asst }
    B { @ACell call-chain }
    C { @Sequence
           A { @BCell assert }
           B { @ACell condition }
      }
} } }
When building up complex diagrams like this, it pays to keep the indenting
perfect in the source document.  As with sequences, there can be
up to twelve alternatives, in options from @Code A to {@Code L}.
@PP
To say that something is @I optional is to select either that thing or
nothing:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Select
    A { @Skip }
    B { @ACell parameters }
}
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@SyntaxDiag {
@StartRight @Select
    A { @Skip }
    B { @ACell parameters }
}
}
Since this case is so common, there is an @Code "@Optional" symbol for it:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Optional
@ACell parameters
}
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@SyntaxDiag {
@StartRight @Optional
@ACell parameters
}
}
@Code "@Optional" is exactly like @Code "@Select" with option @Code A
set to @Code "@Skip" and option @Code B set to the syntax diagram
following the @Code "@Optional" symbol.  Here is the same example in
the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@Optional @ACell parameters
} } }
There is another kind of `optional' layout, {@Code "@OptionalDiverted"}:
@ID @OneRow {
@Code @Verbatim {
@StartDown @OptionalDiverted
@Sequence
    A { @BCell creation }
    B { @ACell parameters }
}
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@SyntaxDiag {
@StartDown @OptionalDiverted @Sequence
    A { @BCell creation }
    B { @ACell parameters }
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartRight A | @Cell @StartUp A |
	      @Cell mr { 0i } @StartLeft A }
{
@Rowa A {
@OptionalDiverted @Sequence
    A { @BCell creation }
    B { @ACell parameters }
} } }
The optional material goes in a direction perpendicular to what
it would have otherwise:  right-moving if previously up or down, and
down-moving if previously left or right.
@PP
Another, related symbol is {@Code "@Diverted"}; it is similar to
@Code "@OptionalDiverted" but without the path which produces nothing:
@ID @OneRow {
@Code @Verbatim {
@StartDown @Diverted @Sequence
    A { @BCell creation }
    B { @ACell parameters }
}
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@SyntaxDiag {
@StartDown @Diverted @Sequence
    A { @BCell creation }
    B { @ACell parameters }
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartRight A | @Cell @StartUp A |
	      @Cell mr { 0i } @StartLeft A }
{
@Rowa A {
@Diverted @Sequence
    A { @BCell creation }
    B { @ACell parameters }
} } }
This symbol is a great aid to packing a big syntax diagram into a
compact shape.
@PP
A variant of the basic selection idea is when you want one thing
or another, or alternatively both in a particular order.  You can get
this with the @Code "@OneOrBoth" symbol, which takes exactly two
options, @Code "A" and {@Code "B"}:
@ID @OneRow {
@Code @Verbatim {
@StartRight @OneOrBoth
    A { @ACell type }
    B { @ACell body }
}
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@SyntaxDiag {
@StartRight @OneOrBoth
    A { @ACell type }
    B { @ACell body }
}
}
Although the concept extends to more than two options, the symnbol
doesn't.  The summary at the end of this chapter shows the other
three directions.
@PP
That covers sequencing and selection; now for looping.  The @Code "@Loop"
symbol produces a loop, with option @Code A going forwards and option
@Code B centred and going backwards:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Loop
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
}
||7ct
@SyntaxDiag {
@StartRight @Loop
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@Loop
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
} } }
One common case of looping is to have nothing on the way back.  We could
get this by placing @Code "@Skip" in option {@Code B} of {@Code "@Loop"},
but there is an even easier way, the {@Code "@Repeat"} symbol:
@ID @OneRow {
@Code @Verbatim {
@StartRight @Repeat
@ACell statement
}
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@SyntaxDiag {
@StartRight @Repeat
@ACell statement
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@Repeat
@ACell statement
} } }
Occasionally it looks better to have the empty returning arrow go on
the opposite side of the forward part; for that, there are
@Code "@LoopOpposite" and @Code "@RepeatOpposite" symbols:
@ID @OneRow {
@Code @Verbatim {
@StartRight @LoopOpposite
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
}
||7ct
@SyntaxDiag {
@StartRight @LoopOpposite
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartUp A | @Cell @StartLeft A |
	      @Cell mr { 0i } @StartDown A }
{
@Rowa A {
@LoopOpposite
    A { @Sequence
           A { @ACell identifier }
           B { @CCell : }
           C { @ACell type }
      }
    B { @CCell , }
} } }
@Code "@RepeatOpposite" is particularly useful around a large
{@Code "@Select"}:
@ID @OneRow {
@Code @Verbatim {
@StartRight @RepeatOpposite
@Select
    A { @ACell asst }
    B { @ACell call-chain }
    C { @BCell return }
    D { @Sequence
           A { @BCell assert }
           B { @ACell condition }
      }
    E { @ACell conditional }
    F { @ACell selection }
    G { @ACell loop }
}
||7ct
@SyntaxDiag {
@StartRight @RepeatOpposite
@Select
    A { @ACell asst }
    B { @ACell call-chain }
    C { @BCell return }
    D { @Sequence
           A { @BCell assert }
           B { @ACell condition }
      }
    E { @ACell conditional }
    F { @ACell selection }
    G { @ACell loop }
}
}
since it clearly distinguishes the loop from the selection.
@PP
Finally, the @Code "@RepeatDiverted" symbol combines the two ideas
of repetition and diversion:
@ID @OneRow {
@Code @Verbatim {
@StartDown @RepeatDiverted
@ACell statement
}
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@SyntaxDiag {
@StartDown @RepeatDiverted
@ACell statement
}
}
Here is the same example in the other three directions:
@CD @OneRow @SyntaxDiag {
@Tbl
    mh { 1f }
    mv { 0i }
    iv { top }
    aformat { @Cell ml { 0i } @StartRight A | @Cell @StartUp A |
	      @Cell mr { 0i } @StartLeft A }
{
@Rowa A {
@RepeatDiverted
@ACell statement
} } }
There is no {@Code "@LoopDiverted"} symbol, for good reason.
@PP
Every syntax diagram, from the simplest to the most complex, has
one arrow going into it, and one coming out.  There are no exceptions
to this rule.  In most syntax diagrams, these two arrows lie on the
same (invisible) line and point in the same direction, and this is
the direction that we say the diagram is moving.  There are two symbols
that produce syntax diagrams that lack this second property.  Because
of this lack, these symbols cannot be used at arbitrary places in a
complex diagram; they can only be used instead of the @Code "@StartRight"
or @Code "@StartDown" symbols at the beginning of a diagram.  The first
symbol, {@Code "@StartRightDown"}, prints its option @Code A right-moving
and its option @Code B down-moving like this:
@ID @OneRow {
@Code @Verbatim {
@StartRightDown
    A { @ACell A }
    B { @ACell B }
}
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@SyntaxDiag {
@StartRightDown
    A { @ACell A }
    B { @ACell B }
}
}
The second symbol, {@Code "@StartRightRight"}, prints both options
right-moving like this:
@ID @OneRow {
@Code @Verbatim {
@StartRightRight
    A { @ACell A }
    B { @ACell B }
}
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@SyntaxDiag {
@StartRightRight
    A { @ACell A }
    B { @ACell B }
}
}
As usual, the options to these symbols may contain arbitrarily complex
syntax diagrams.
@PP
Finally, a few words about changing things.  The @Code "@SyntaxDiag"
symbol used the {@Code "@ANode"}, {@Code "@BNode"}, and {@Code "@CNode"}
symbols of @@Diag to construct its three types of cells.  In fact, the
@Code "@SyntaxDiag" symbol is nothing more than this:
@ID @OneRow @Code @Verbatim {
@Diag
    avalign { mark }
    avstrut { yes }
    amargin { 0.2f }
    aoutline { box }
    afont { Italic }
    bvalign { mark }
    bvstrut { yes }
    bmargin { 0.2f }
    boutline { curvebox }
    bfont { Bold }
    cvalign { mark }
    cvstrut { yes }
    cmargin { 0.2f }
    coutline { circle }
    chsize { 1f }
    arrowlength { 0.4f }
}
So any of the other @Code "@Diag" options can be used freely with
{@Code "@SyntaxDiag"}; and the format of the three cell types can be
changed by using @Code "@Diag" instead of {@Code "@SyntaxDiag"}, and
choosing new values for these (and other) options.
@PP
If there are more than three cell types, it is necessary to fall back
on the {@Code "@XCell"} symbol, which produces a cell without nominating
any particular cell type.  After @Code "@XCell" there must be a regular
@Code "@Diag" node, like this:
@ID @OneRow {
@Code @Verbatim {
@StartRight @XCell @Ellipse INIT
}
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@SyntaxDiag {
@StartRight @XCell @Ellipse INIT
}
}
This way there is no limit to the number of different kinds of cells.  Also,
since (for example) @Code "@ACell" is merely an abbreviation for
@ID @OneRow @Code @Verbatim { @XCell @ANode }
any node options may follow {@Code "@ACell"}, {@Code "@BCell"}, and
{@Code "@CCell"}.  The appearance of the arrows can be changed in the usual
way, by setting options as has been done above for {@Code "arrowlength"}.
@PP
There are three options specifically related to syntax diagrams:
@ID @OneRow @Code @Verbatim {
@SyntaxDiag
    syntaxgap { 0.35f }
    syntaxbias { 1.0f }
    syntaxradius { 0.3f }
}
The @Code syntaxgap option determines the spacing between the various
elements; changing it causes the syntax diagrams to be set tighter or
looser in a consistent way.  The default value shown is 0.35 times the
current font size.  The @Code syntaxbias and @Code syntaxradius
options affect the appearance of curved lines, as in @Code "@RVLCurve"
and its relatives.  These options are also available with {@Code "@Diag"},
and in the setup file.  Note however that these options cannot be given to
individual elements in a syntax diagram, only to the diagram as a whole.
@End @Section