@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