\documentclass{article}
\usepackage{noweb,multicol,tabularx}
\title{CS655: Stage 1 Garbage-Collecting LISP Interpreter}
\author{Norman Ramsey}
\begin{document}
@
\tableofcontents

\section{Introduction}
This is the LISP interpreter of chapter 2 with an arena-based
allocator.
Sections of code that are different from chapter 2 are in <i>italics</i>.

\section{Declarations}
<<*>>=
program lisp (input, output);

label 99;

const
   NAMELENG = 20;      (* Maximum length of a name *)
   MAXNAMES = 300;     (* Maximum number of different names *)
   MAXINPUT = 4000;    (* Maximum length of an input *)
   PROMPT = '-> ';
   PROMPT2 = '> ';
   COMMENTCHAR = ';';
   TABCODE = 9;        (* in ASCII *)
   ARENASIZE = 48;     (* number of S-expressions allocated at one time *)   (*nr1*)
<<*>>=
type
   NAMESIZE = 0..NAMELENG;
   NAMESTRING = packed array [1..NAMELENG] of char;

   NAME = 1 .. MAXNAMES; (* a NAME is an index in printNames *)

   BUILTINOP = (IFOP,WHILEOP,SETOP,BEGINOP,PLUSOP,MINUSOP, 
                TIMESOP,DIVOP,EQOP,LTOP,GTOP,CONSOP,
                CAROP,CDROP,NUMBERPOP,SYMBOLPOP,
                LISTPOP,NULLPOP,PRINTOP);
   VALUEOP = PLUSOP .. PRINTOP;
   CONTROLOP = IFOP .. BEGINOP;
<<*>>=
   SEXP = ^SEXPREC;
   EXP = ^EXPREC;
   EXPLIST = ^EXPLISTREC;
   ENV = ^ENVREC;
   VALUELIST = ^VALUELISTREC;
   NAMELIST = ^NAMELISTREC;
   FUNDEF = ^FUNDEFREC;

   SEXPTYPE = (NILSXP,NUMSXP,SYMSXP,LISTSXP);
   SEXPREC = record
               case sxptype: SEXPTYPE of
                  NILSXP: ();
                  NUMSXP: (intval: integer);
                  SYMSXP: (symval: NAME);
                  LISTSXP: (carval, cdrval: SEXP)
            end;
<<*>>=
   EXPTYPE = (VALEXP,VAREXP,APEXP);
   EXPREC = record
               case etype: EXPTYPE of
                  VALEXP: (sxp: SEXP);
                  VAREXP: (varble: NAME);
                  APEXP: (optr: NAME; args: EXPLIST)
            end;

   EXPLISTREC = record
               head: EXP;
               tail: EXPLIST
            end;
<<*>>=
   VALUELISTREC = record
               head: SEXP;
               tail: VALUELIST
            end;

   NAMELISTREC = record
               head: NAME;
               tail: NAMELIST
            end;

   ENVREC = record
               vars: NAMELIST;
               values: VALUELIST
            end;
   FUNDEFREC = record
               funname: NAME;
               formals: NAMELIST;
               body: EXP;
               nextfundef: FUNDEF
            end;
@ 
An arena is a pool of S-expressions.
Your job is to make them re-usable.
<<*>>=
   ARENA = ^ARENAREC;                                   (*nr1*)		 
   ARENAREC = record					(*nr1*)		 
                  pool: ARRAY [1..ARENASIZE] of SEXP;  	(*nr1*)		 
                  tail: ARENA				(*nr1*)		 
              end;                                      (*nr1*)		 
<<*>>=
var
   fundefs: FUNDEF;
   
   globalEnv: ENV;
   
   currentExp: EXP;
   
   userinput: array [1..MAXINPUT] of char;
   inputleng, pos: 0..MAXINPUT;
   
   printNames: array [NAME] of NAMESTRING;
   numNames, numBuiltins: NAME;

   nilValue, trueValue: SEXP;

   quittingtime: Boolean;
@ %def fundefs currentExp
@ 
These global variables keep track of the arenas.
<<*>>=
   heap, freeArena: ARENA;		       (*nr1*)	  
   freeCount : 0..ARENASIZE;                   (*nr1*)	  
@ %def allArena, freeArena, freeCount
\section{Allocator}
To create a fresh arena, allocate it and each of its S-expressions.
<<*>>=
function freshArena : ARENA;                                   (*nr1*)		 
var a: ARENA; i : 1..ARENASIZE; 			       (*nr1*)		 
begin							       (*nr1*)		 
  new(a);						       (*nr1*)		 
  for i := 1 to ARENASIZE do new(a^.pool[i]);		       (*nr1*)		 
  a^.tail := nil;					       (*nr1*)		 
  freshArena := a					       (*nr1*)		 
end;							       (*nr1*)		 
@ Enlarge the heap by adding an arena to the end of the list.
<<*>>=
procedure enlargeHeap;					       (*nr1*)		 
begin              					       (*nr1*)
  if freeArena = nil then begin				       (*nr1*)		 
    heap := freshArena;				       		(*nr1*)          
    freeArena := heap;                                 		(*nr1*)		 
    freeCount := ARENASIZE				       (*nr1*)		 
    end    						       (*nr1*)		 
  else begin						       (*nr1*)		 
    freeArena^.tail := freshArena;			       (*nr1*)		 
    freeArena := freeArena^.tail;			       (*nr1*)		 
    freeCount := ARENASIZE				       (*nr1*)		 
    end							       (*nr1*)		 
end;                                                           (*nr1*)
@ 
Allocate an S-expression from the current arena.
Because we don't have a collector yet, the current arena is always the
last arena, and when it's exhausted we simply enlarge the heap.
<<*>>=
procedure allocSexp(VAR s: SEXP);			       (*nr1*)	     
begin							       (*nr1*)	     
  if freeCount = 0 then enlargeHeap; 			       (*nr1*)	     
  s := freeArena^.pool[freeCount];       		       (*nr1*)	     
  dec(freeCount);					       (*nr1*)	     
end;                                                           (*nr1*)	     
@ 
\section{Data Structure Op'S}
<<*>>=
(* mkVALEXP - return an EXP of type VALEXP with sxp s            *)
function mkVALEXP (s: SEXP): EXP;
var e: EXP;
begin
   new(e);
   e^.etype := VALEXP;
   e^.sxp := s;
   mkVALEXP := e
end; (* mkVALEXP *)
<<*>>=
(* mkVAREXP - return an EXP of type VAREXP with varble nm        *)
function mkVAREXP (nm: NAME): EXP;
var e: EXP;
begin
   new(e);
   e^.etype := VAREXP;
   e^.varble := nm;
   mkVAREXP := e
end; (* mkVAREXP *)
<<*>>=
(* mkAPEXP - return EXP of type APEXP w/ optr op and args el     *)
function mkAPEXP (op: NAME; el: EXPLIST): EXP;
var e: EXP;
begin
   new(e);
   e^.etype := APEXP;
   e^.optr := op;
   e^.args := el;
   mkAPEXP := e
end; (* mkAPEXP *)
<<*>>=
(* mkSExp - return SEXP of type t (but no value)                 *)
function mkSExp (t: SEXPTYPE): SEXP;
var s: SEXP;
begin
   allocSexp(s);                     (*nr1*)
   s^.sxptype := t;
   mkSExp := s
end; (* mkSExp *)
<<*>>=
(* mkExplist - return an EXPLIST with head e and tail el         *)
function mkExplist (e: EXP; el: EXPLIST): EXPLIST;
var newel: EXPLIST;
begin
   new(newel);
   newel^.head := e;
   newel^.tail := el;
   mkExplist := newel
end; (* mkExplist *)
<<*>>=
(* mkNamelist - return a NAMELIST with head n and tail nl        *)
function mkNamelist (nm: NAME; nl: NAMELIST): NAMELIST;
var newnl: NAMELIST;
begin
   new(newnl);
   newnl^.head := nm;
   newnl^.tail := nl;
   mkNamelist := newnl
end; (* mkNamelist *)
<<*>>=
(* mkValuelist - return an VALUELIST with head s and tail vl     *)
function mkValuelist (s: SEXP; vl: VALUELIST): VALUELIST;
var newvl: VALUELIST;
begin
   new(newvl);
   newvl^.head := s;
   newvl^.tail := vl;
   mkValuelist := newvl
end; (* mkValuelist *)
<<*>>=
(* mkEnv - return an ENV with vars nl and values vl              *)
function mkEnv (nl: NAMELIST; vl: VALUELIST): ENV;
var rho: ENV;
begin
   new(rho);
   rho^.vars := nl;
   rho^.values := vl;
   mkEnv := rho
end; (* mkEnv *)
<<*>>=
(* lengthVL - return length of VALUELIST vl                      *)
function lengthVL (vl: VALUELIST): integer;
var i: integer;
begin
   i := 0;
   while vl <> nil do begin
      i := i+1;
      vl := vl^.tail
      end;
   lengthVL := i
end; (* lengthVL *)
<<*>>=
(* lengthNL - return length of NAMELIST nl                       *)
function lengthNL (nl: NAMELIST): integer;
var i: integer;
begin
   i := 0;
   while nl <> nil do begin
      i := i+1;
      nl := nl^.tail
      end;
   lengthNL := i
end; (* lengthNL *)

@ 
\section{Name Management}
<<*>>=
(* fetchFun - get function definition of fname from fundefs      *)
function fetchFun (fname: NAME): FUNDEF;
var
   f: FUNDEF;
   found: Boolean;
begin
   found := false;
   f := fundefs;
   while (f <> nil) and not found do
      if f^.funname = fname
      then found := true
      else f := f^.nextfundef;
   fetchFun := f
end; (* fetchFun *)
<<*>>=
(* newFunDef - add new function fname w/ parameters nl, body e   *)
procedure newFunDef (fname: NAME; nl: NAMELIST; e: EXP);
var f: FUNDEF;
begin
   f := fetchFun(fname);
   if f = nil (* fname not yet defined as a function *)
   then begin
           new(f);
           f^.nextfundef := fundefs; (* place new FUNDEFREC *)
           fundefs := f              (* on fundefs list *)
        end;
   f^.funname := fname;
   f^.formals := nl;
   f^.body := e
end; (* newFunDef *)
<<*>>=
(* initNames - place all pre-defined names into printNames       *)
procedure initNames;
var i: integer;
begin
   fundefs := nil;
   i := 1;
   printNames[i] := 'if                  '; i := i+1;
   printNames[i] := 'while               '; i := i+1;
   printNames[i] := 'set                 '; i := i+1;
   printNames[i] := 'begin               '; i := i+1;
   printNames[i] := '+                   '; i := i+1;
   printNames[i] := '-                   '; i := i+1;
   printNames[i] := '*                   '; i := i+1;
   printNames[i] := '/                   '; i := i+1;
   printNames[i] := '=                   '; i := i+1;
   printNames[i] := '<                   '; i := i+1;
   printNames[i] := '>                   '; i := i+1;
   printNames[i] := 'cons                '; i := i+1;
   printNames[i] := 'car                 '; i := i+1;
   printNames[i] := 'cdr                 '; i := i+1;
   printNames[i] := 'number?             '; i := i+1;
   printNames[i] := 'symbol?             '; i := i+1;
   printNames[i] := 'list?               '; i := i+1;
   printNames[i] := 'null?               '; i := i+1;
   printNames[i] := 'print               '; i := i+1;
   printNames[i] := 'T                   ';
   numNames := i;
   numBuiltins := i
end; (* initNames *)
<<*>>=
(* install - insert new name into printNames                     *)
function install (nm: NAMESTRING): NAME;
var
   i: integer;
   found: Boolean;
begin
   i := 1; found := false;
   while (i <= numNames) and not found
   do if nm = printNames[i]
      then found := true
      else i := i+1;
   if not found
   then begin
           if i > MAXNAMES
           then begin
                   writeln('No more room for names');
                   goto 99
                end;
           numNames := i;
           printNames[i] := nm
        end;
   install := i
end; (* install *)
<<*>>=
(* prName - print name nm                                        *)
procedure prName (nm: NAME);
var i: integer;
begin
   i := 1;
   while i <= NAMELENG
   do if printNames[nm][i] <> ' '
      then begin
              write(printNames[nm][i]);
              i := i+1
           end
      else i := NAMELENG+1
end; (* prName *)
<<*>>=
(* primOp - translate NAME optr to corresponding BUILTINOP       *)
function primOp (optr: NAME): BUILTINOP;
var
   op: BUILTINOP;
   i: integer;
begin
   op := IFOP; (* N.B. IFOP is first value in BUILTINOPS *)
   for i := 1 to optr-1 do op := succ(op);
   primOp := op
end; (* primOp *)
@ 
\section{Input}
<<*>>=
(* isDelim - check if c is a delimiter                           *)
function isDelim (c: char): Boolean;
begin
   isDelim := c in ['(', ')', ' ', COMMENTCHAR]
end; (* isDelim *)
<<*>>=
(* skipblanks - return next non-blank position in userinput      *)
function skipblanks (p: integer): integer;
begin
   while userinput[p] = ' ' do p := p+1;
   skipblanks := p
end; (* skipblanks *)
<<*>>=
(* matches - check if string nm matches userinput[s .. s+leng]   *)
function matches (s: integer; leng: NAMESIZE;
                   nm: NAMESTRING): Boolean;
var
   match: Boolean;
   i: integer;
begin
   match := true; i := 1;
   while match and (i <= leng) do begin
      if userinput[s] <> nm[i] then match := false;
      i := i+1;
      s := s+1
      end;
   if not isDelim(userinput[s]) then match := false;
   matches := match
end; (* matches *)
<<*>>=
(* reader - read char's into userinput; be sure input not blank  *)
procedure reader;
   
   (* readInput - read char's into userinput                        *)
   procedure readInput;

   var c: char;
     <<local procedures of [[readInput]]>>
   begin (* readInput *)
      write(PROMPT);
      pos := 0;
      repeat
         pos := pos+1;
         if pos = MAXINPUT
         then begin
                 writeln('User input too long');
                 goto 99
              end;
         nextchar(c);
         userinput[pos] := c;
         if userinput[pos] = '(' then readParens
      until eoln;
      inputleng := pos;
      userinput[pos+1] := COMMENTCHAR (* sentinel *)
   end; (* readInput *)

begin (* reader *)
    repeat
       readInput;
       pos := skipblanks(1);
    until pos <= inputleng (* ignore blank lines *)
end; (* reader *)

<<local procedures of [[readInput]]>>=
(* nextchar - read next char - filter tabs and comments          *)
procedure nextchar (var c: char);
begin
   read(c);
   if c = chr(TABCODE)
   then c := ' '
   else if c = COMMENTCHAR
        then begin while not eoln do read(c); c := ' ' end
end; (* nextchar *)
<<local procedures of [[readInput]]>>=
(* readParens - read char's, ignoring newlines, to matching ')'  *)
procedure readParens;
var
   parencnt: integer; (* current depth of parentheses *)
   c: char;
begin
   parencnt := 1; (* '(' just read *)
   repeat
      if eoln then write(PROMPT2);
      nextchar(c);
      pos := pos+1;
      if pos = MAXINPUT
      then begin
              writeln('User input too long');
              goto 99
           end;
      userinput[pos] := c;
      if c = '(' then parencnt := parencnt+1;
      if c = ')' then parencnt := parencnt-1
   until parencnt = 0
end; (* readParens *)
<<*>>=
(* parseName - return (installed) NAME starting at userinput[pos]*)
function parseName: NAME;
var
   nm: NAMESTRING; (* array to accumulate characters *)
   leng: NAMESIZE; (* length of name *)
begin
   leng := 0;
   while (pos <= inputleng) and not isDelim(userinput[pos])
   do begin
         if leng = NAMELENG
         then begin
                 writeln('Name too long, begins: ', nm);
                 goto 99
              end;
         leng := leng+1;
         nm[leng] := userinput[pos];
         pos := pos+1
      end;
   if leng = 0
   then begin
           writeln('Error: expected name, instead read: ',
                   userinput[pos]);
           goto 99
        end;
   for leng := leng+1 to NAMELENG do nm[leng] := ' ';
   pos := skipblanks(pos); (* skip blanks after name *)
   parseName := install(nm)
end; (* parseName *)
<<*>>=
(* isNumber - check if a number begins at pos                    *)
function isNumber (pos: integer): Boolean;

(* isDigits - check if sequence of digits begins at pos          *)
   function isDigits (pos: integer): Boolean;
   begin
      if not (userinput[pos] in ['0'..'9'])
      then isDigits := false
      else begin
              isDigits := true;
              while userinput[pos] in ['0'..'9'] do pos := pos+1;
              if not isDelim(userinput[pos])
              then isDigits := false
           end
   end; (* isDigits *)

begin (* isNumber *)
   isNumber := isDigits(pos) or
              ((userinput[pos] = '-') and isDigits(pos+1))
end; (* isNumber *)
<<*>>=
(* isValue - check if a number or quoted const begins at pos     *)
function isValue (pos: integer): Boolean;
begin
   isValue:= (userinput[pos] = '''') or isNumber(pos)
end; (* isValue *)
<<*>>=
(* parseVal - return S-expression starting at userinput[pos]     *)
function parseVal: SEXP;

(* parseSExp - return quoted S-expr starting at userinput[pos]   *)
   function parseSExp: SEXP;

   var s: SEXP;

      <<local functions of [[parseSexp]], to parse integers, symbols, and lists>>

   begin (* parseSExp *)
      if isNumber(pos)
      then parseSExp := parseInt
      else if userinput[pos] = '('
           then begin
                   pos := skipblanks(pos+1);
                   parseSExp := parseList
                end
           else parseSExp := parseSym
   end; (* parseSExp *)

begin (* parseVal *)
   if userinput[pos] = '''' then pos := pos+1;
   parseVal := parseSExp
end; (* parseVal *)
<<local functions of [[parseSexp]], to parse integers, symbols, and lists>>=
(* parseInt - return number starting at userinput[pos]           *)
function parseInt: SEXP;
var sum, sign: integer;
begin
   s := mkSExp(NUMSXP);
   sum := 0; sign := 1;
   if userinput[pos] = '-'
   then begin
           sign := -1;
           pos := pos+1
        end;
   while userinput[pos] in ['0'..'9'] do begin
      sum := 10*sum + (ord(userinput[pos]) - ord('0'));
      pos := pos+1
      end;
   s^.intval := sum * sign;
   pos := skipblanks(pos); (* skip blanks after number *)
   parseInt := s
end; (* parseInt *)
<<local functions of [[parseSexp]], to parse integers, symbols, and lists>>=
(* parseSym - return symbol starting at userinput[pos]           *)
function parseSym: SEXP;
begin
   s := mkSExp(SYMSXP);
   s^.symval := parseName;
   parseSym := s
end; (* parseSym *)
<<local functions of [[parseSexp]], to parse integers, symbols, and lists>>=
(* parseList - return list starting at userinput[pos]            *)
function parseList: SEXP;
var car, cdr: SEXP;
begin
   if userinput[pos] = ')'
   then begin
           parseList := mkSExp(NILSXP);
           pos := skipblanks(pos+1)
        end
   else begin
           car := parseSExp;
           cdr := parseList;
           s := mkSExp(LISTSXP);
           s^.carval := car;
           s^.cdrval := cdr;
           parseList := s
        end
end; (* parseList *)
<<*>>=
function parseEL: EXPLIST; forward;
<<*>>=
(* parseExp - return EXP starting at userinput[pos]              *)
function parseExp: EXP;
var
   nm: NAME;
   el: EXPLIST;
begin
   if userinput[pos] = '('
   then begin   (* APEXP *)
           pos := skipblanks(pos+1); (* skip '( ..' *)
           nm := parseName;
           el := parseEL;
           parseExp := mkAPEXP(nm, el)
        end
   else if isValue(pos)
        then parseExp := mkVALEXP(parseVal)   (* VALEXP *)
        else parseExp := mkVAREXP(parseName)  (* VAREXP *)
end; (* parseExp *)
<<*>>=
(* parseEL - return EXPLIST starting at userinput[pos]           *)
function parseEL;
var
   e: EXP;
   el: EXPLIST;
begin
   if userinput[pos] = ')'
   then begin
           pos := skipblanks(pos+1); (* skip ') ..' *)
           parseEL := nil
        end
   else begin
           e := parseExp;
           el := parseEL;
           parseEL := mkExplist(e, el)
        end
end; (* parseEL *)
<<*>>=
(* parseNL - return NAMELIST starting at userinput[pos]          *)
function parseNL: NAMELIST;
var
   nm: NAME;
   nl: NAMELIST;
begin
   if userinput[pos] = ')'
   then begin
           pos := skipblanks(pos+1); (* skip ') ..' *)
           parseNL := nil
        end
   else begin
           nm := parseName;
           nl := parseNL;
           parseNL := mkNamelist(nm, nl)
        end
end; (* parseNL *)
<<*>>=
(* parseDef - parse function definition at userinput[pos]        *)
function parseDef: NAME;
var
   fname: NAME;        (* function name *)
   nl: NAMELIST;       (* formal parameters *)
   e: EXP;             (* body *)
begin
   pos := skipblanks(pos+1); (* skip '( ..' *)
   pos := skipblanks(pos+6); (* skip 'define ..' *)
   fname := parseName;
   pos := skipblanks(pos+1); (* skip '( ..' *)
   nl := parseNL;
   e := parseExp;
   pos := skipblanks(pos+1); (* skip ') ..' *)
   newFunDef(fname, nl, e);
   parseDef := fname
end; (* parseDef *)
@ 
\section{Environments}
<<*>>=
(* emptyEnv - return an environment with no bindings             *)
function emptyEnv: ENV;
begin
   emptyEnv := mkEnv(nil, nil)
end; (* emptyEnv *)
<<*>>=
(* bindVar - bind variable nm to value s in environment rho      *)
procedure bindVar (nm: NAME; s: SEXP; rho: ENV);
begin
   rho^.vars := mkNamelist(nm, rho^.vars);
   rho^.values := mkValuelist(s, rho^.values)
end; (* bindVar *)
<<*>>=
(* findVar - look up nm in rho                                   *)
function findVar (nm: NAME; rho: ENV): VALUELIST;
var
   nl: NAMELIST;
   vl: VALUELIST;
   found: Boolean;
begin
   found := false;
   nl := rho^.vars;
   vl := rho^.values;
   while (nl <> nil) and not found do
      if nl^.head = nm
      then found := true
      else begin
              nl := nl^.tail;
              vl := vl^.tail
           end;
   findVar := vl
end; (* findVar *)
<<*>>=
(* assign - assign value s to variable nm in rho                 *)
procedure assign (nm: NAME; s: SEXP; rho: ENV);
var varloc: VALUELIST;
begin
   varloc := findVar(nm, rho);
   varloc^.head := s
end; (* assign *)
<<*>>=
(* fetch - return SEXP bound to nm in rho                        *)
function fetch (nm: NAME; rho: ENV): SEXP;
var vl: VALUELIST;
begin
   vl := findVar(nm, rho);
   fetch := vl^.head
end; (* fetch *)
<<*>>=
(* isBound - check if nm is bound in rho                         *)
function isBound (nm: NAME; rho: ENV): Boolean;
begin
   isBound := findVar(nm, rho) <> nil
end; (* isBound *)
@ 
\section{S-Expressions}
<<*>>=
(* prValue - print S-expression s                                *)
procedure prValue (s: SEXP);
var s1: SEXP;
begin
   with s^ do
      case sxptype of
         NILSXP: write('()');
         NUMSXP: write(intval:1);
         SYMSXP: prName(symval);
         LISTSXP:
            begin
               write('(');
               prValue(carval);
               s1 := cdrval;
               while s1^.sxptype = LISTSXP do begin
                  write(' ');
                  prValue(s1^.carval);
                  s1 := s1^.cdrval
                  end;
               write(')')
            end
      end (* case and with *)
end; (* prValue *)
<<*>>=
(* isTrueVal - return true if s is true (non-NIL) value          *)
function isTrueVal (s: SEXP): Boolean;
begin
   isTrueVal := s^.sxptype <> NILSXP
end; (* isTrueVal *)
<<*>>=
(* applyValueOp - apply VALUEOP op to arguments in VALUELIST vl  *)
function applyValueOp (op: VALUEOP; vl: VALUELIST): SEXP;

var
   result: SEXP;
   s1, s2: SEXP;

(* applyArithOp - apply binary, arithmetic VALUEOP to arguments  *)
   procedure applyArithOp (n1, n2: integer);
   begin
      result := mkSExp(NUMSXP);
      with result^ do
         case op of
            PLUSOP: intval := n1+n2;
            MINUSOP: intval := n1-n2;
            TIMESOP: intval := n1*n2;
            DIVOP: intval := n1 div n2
         end
   end; (* applyArithOp *)

(* applyRelOp - apply binary, relational VALUEOP to arguments    *)
   procedure applyRelOp (n1, n2: integer) ;
   begin
      case op of
         LTOP: if n1 < n2 then result := trueValue;
         GTOP: if n1 > n2 then result := trueValue
      end
   end; (* applyRelOp *)

(* arity - return number of arguments expected by op             *)
   function arity (op: VALUEOP): integer;
   begin
      if op in [PLUSOP .. CONSOP] then arity := 2 else arity := 1
   end; (* arity *)

begin (* applyValueOp *)
   if arity(op) <> lengthVL(vl)
   then begin
           write('Wrong number of arguments to ');
           prName(ord(op)+1);
           writeln;
           goto 99
        end;
   result := nilValue;
   s1 := vl^.head; (* 1st actual *)
   if arity(op) = 2 then s2 := vl^.tail^.head; (* 2nd actual *)
   if op in [PLUSOP .. DIVOP, LTOP .. GTOP]
   then if (s1^.sxptype = NUMSXP)
           and (s2^.sxptype = NUMSXP)
        then if op in [PLUSOP .. DIVOP]
             then applyArithOp(s1^.intval, s2^.intval)
             else applyRelOp(s1^.intval, s2^.intval)
        else begin
                write('Non-arithmetic arguments to ');
                prName(ord(op)+1);
                writeln;
                goto 99
             end
   else with s1^ do
           case op of
              EQOP:
                 if (sxptype = NILSXP)
                    and (s2^.sxptype = NILSXP)
                 then result := trueValue
                 else if (sxptype = NUMSXP)
                         and (s2^.sxptype = NUMSXP)
                         and (intval = s2^.intval)
                      then result := trueValue
                      else if (sxptype = SYMSXP)
                              and (s2^.sxptype = SYMSXP)
                              and (symval = s2^.symval)
                           then result := trueValue;
              CONSOP:
                 begin
                    result := mkSExp(LISTSXP);
                    with result^ do begin
                       carval := s1;
                       cdrval := s2
                       end
                 end;
              CAROP:
                 if sxptype <> LISTSXP
                 then begin
                         write('Error: car applied to non-list: ');
                         prValue(s1);
                         writeln
                      end
                 else result := carval;
              CDROP:
                 if sxptype <> LISTSXP
                 then begin
                         write('Error: cdr applied to non-list: ');
                         prValue(s1);
                         writeln
                      end
                 else result := cdrval;
              NUMBERPOP:
                 if sxptype = NUMSXP then result := trueValue;
              SYMBOLPOP:
                 if sxptype = SYMSXP then result := trueValue;
              LISTPOP:
                 if sxptype = LISTSXP then result := trueValue;
              NULLPOP:
                 if sxptype = NILSXP then result := trueValue;
              PRINTOP:
                 begin prValue(s1); writeln; result := s1 end
           end; (* case and with *)
   applyValueOp := result
end; (* applyValueOp *)
@ 
\section{Evaluation}
<<*>>=
(* eval - return value of expression e in local environment rho  *)
function eval (e: EXP; rho: ENV): SEXP;

var op: BUILTINOP;
   <<local functions of [[eval]] (which use [[rho]])>>

begin (* eval *)
   with e^ do
      case etype of
         VALEXP:
            eval := sxp;
         VAREXP:
            if isBound(varble, rho)
            then eval := fetch(varble, rho)
            else if isBound(varble, globalEnv)
                 then eval := fetch(varble, globalEnv)
                 else begin
                         write('Undefined variable: ');
                         prName(varble);
                         writeln;
                         goto 99
                      end;
         APEXP: 
            if optr > numBuiltins
            then eval := applyUserFun(optr, evalList(args))
            else begin
                    op := primOp(optr);
                    if op in [IFOP .. BEGINOP]
                    then eval := applyCtrlOp(op, args)
                    else eval := applyValueOp(op,
                                     evalList(args))
                 end
      end (* case and with *)
end; (* eval *)
<<local functions of [[eval]] (which use [[rho]])>>=
(* evalList - evaluate each expression in el                     *)
function evalList (el: EXPLIST): VALUELIST;
var
   h: SEXP;
   t: VALUELIST;
begin
   if el = nil then evalList := nil
   else begin
           h := eval(el^.head, rho);
           t := evalList(el^.tail);
           evalList := mkValuelist(h, t)
        end
end; (* evalList *)
<<local functions of [[eval]] (which use [[rho]])>>=
(* applyUserFun - look up definition of nm and apply to actuals  *)
function applyUserFun (nm: NAME; actuals: VALUELIST): SEXP;
var
   f: FUNDEF;
   rho: ENV;
begin
   f := fetchFun(nm);
   if f = nil
   then begin
           write('Undefined function: ');
           prName(nm);
           writeln;
           goto 99
        end;
   with f^ do begin
      if lengthNL(formals) <> lengthVL(actuals)
      then begin
              write('Wrong number of arguments to: ');
              prName(nm);
              writeln;
              goto 99
           end;
      rho := mkEnv(formals, actuals);
      applyUserFun := eval(body, rho)
      end
end; (* applyUserFun *)
<<local functions of [[eval]] (which use [[rho]])>>=
(* applyCtrlOp - apply CONTROLOP op to args in rho               *)
function applyCtrlOp (op: CONTROLOP;
                    args: EXPLIST): SEXP;
var s: SEXP;
begin
   with args^ do
      case op of
        IFOP:
           if isTrueVal(eval(head, rho))
           then applyCtrlOp := eval(tail^.head, rho)
           else applyCtrlOp := eval(tail^.tail^.head, rho);
        WHILEOP:
           begin
              s := eval(head, rho);
              while isTrueVal(s)
              do begin
                    s := eval(tail^.head, rho);
                    s := eval(head, rho)
                 end;
              applyCtrlOp := s
           end;
        SETOP:
           begin
              s := eval(tail^.head, rho);
              if isBound(head^.varble, rho)
              then assign(head^.varble, s, rho)
              else if isBound(head^.varble, globalEnv)
                   then assign(head^.varble, s, globalEnv)
                   else bindVar(head^.varble, s, globalEnv);
              applyCtrlOp := s
           end;
        BEGINOP: 
           begin
              while args^.tail <> nil do
                 begin
                    s := eval(args^.head, rho);
                    args := args^.tail
                 end;
              applyCtrlOp := eval(args^.head, rho)
           end
      end (* case and with *)
end; (* applyCtrlOp *)
@ 
\section{Read-Eval-Print Loop}
<<*>>=
begin (* lisp main *)
   initNames;

   nilValue := mkSExp(NILSXP);
   trueValue := mkSExp(SYMSXP); trueValue^.symval := numNames;

   globalEnv := emptyEnv;

   quittingtime := false;
99:
   while not quittingtime do begin
      reader;
      if matches(pos, 4, 'quit                ')
      then quittingtime := true
      else if (userinput[pos] = '(') and
              matches(skipblanks(pos+1), 6, 'define              ')
           then begin
                   prName(parseDef);
                   writeln
                end
           else begin
                   currentExp := parseExp;
                   prValue(eval(currentExp, emptyEnv));
                   writeln;
                   writeln
                end
      end (* while *)
end. (* lisp *)
@ 
\section{List of chunks}
\nowebchunks

\begin{multicols}{2}[\section{Index of identifiers}]
\nowebindex
\end{multicols}
@
\end{document}