This section describes an interpreter for the functional language. It employs an implementation of normal-order evaluation known as call by need evaluation. The interpreter evaluates an expression (program) represented by a parse tree and produces and prints a value. Expressions and values are quite separate kinds of things. There are integer, boolean and other simple values. Evaluating a function abstraction produces a function value. A function value contains some code (an expression) and an environment to execute the code in. An environment is a list of bindings of names to values. When a name is used its value is found in the environment. Being a lazy interpreter, there is a deferred value for expressions that have been put-off until later. A deferred value has not yet been evaluated. It consists of an expression to be evaluated and an environment to evaluate it in if need be.
type Env = ^ Binding;

     Value = ^ValNode;
     Binding = record id :alfa; v:Value; next:Env end;

     ValueClass = (intval, boolval, charval, emptyval,
                   listval, nilval, funcval, deferval);
     ValNode = record case tag :ValueClass of
               intval: (n :integer );
               boolval:(b :boolean );
               charval:(ch:char );
               nilval, emptyval:();
               listval:(hd, tl :Value);
               funcval, deferval:( e:tree; r:Env )

{\fB Environment and Value Types. \fP}

Execution is driven by output. The interpreter turns the input expression into a deferred value and has it printed.

procedure execute(prog:tree);

#include "lazy.type.P"

   var evals, envcells, conscells :integer; { statistics }
       LastId :alfa;                 { debugging}
       Answer :Value;

   procedure error( m:alfa );
   begin writeln; writeln('Error: ', m, ' LastId=', LastId);
         goto 99  {error abort}

#include "lazy.mkval.P"   { Make various Values }

function eval( x:tree; rho:Env ):Value; forward;
procedure force( v:Value ); forward;

#include "lazy.env.P"     { manipulate Environment }
#include "lazy.D.P"       { Execute Declarations }
#include "lazy.apply.P"   { Apply a Function }
#include "lazy.U.P"       { Execute Unary Operators }
#include "lazy.O.P"       { Execute Binary Operators }
#include "lazy.eval.P"    { eval and force an Expression }
#include "lazy.show.P"    { Output Values }

     evals := 0; envcells := 0; conscells := 0; {zero counters}
     LastId   := '-start-   ';
   Answer := defer(prog, {Env=}nil);
   ShowValue(Answer);  { Execution is print driven }
     writeln; write( evals, ' evals');
     write( envcells, ' env cells used, ');
     writeln( conscells, ' cells used')

{\fB Shell of Interpreter for Functional Language. \fP}

{Do not remove: Lazy.p, Strict.p, lazy.*.P, strict.*.P, lex.*.P, & syntax.*.P }
{ are released under Gnu `copyleft' General Public Licence (GPL)              }
{ - L. Allison, CSSE, Monash Uni., .au, 7/2003.                               }

The print routine prints the various kinds of value. Note that printing a list is recursive. A deferred value must be forced or turned into a non-deferred value before it can be printed.

procedure ShowValue( v:Value );
begin with v^ do 
      case tag of
      intval:  write( n:1 );
      boolval: write( b );
      charval: write( ch );
      emptyval:write( '()' );
      nilval:  write('nil');
      listval: begin write('('); ShowValue(hd); writeln('::'); {flush buffer}
                     ShowValue(tl); write(')')
      funcval: write('function');
      deferval:begin force(v); ShowValue(v) end { evaluation is o/p driven }
end {ShowValue};

{\fB Output Values. \fP}

Expressions are evaluated by force and by eval. Being part of a lazy interpreter, eval does as little work as possible. In particular, the components of a list, the head and the tail, are not evaluated but are deferred. The head and tail are only evaluated further if they are printed or if some strict operator, eg. +, is applied to them. When eval returns a structure, only the top most node is guaranteed not to be deferred; substructures may be deferred. This condition is known as weak head normal form. Note that force overwrites a deferred value with the evaluated value. This is efficient because values can be shared, particularly in recursive structures and when parameters are passed. Overwriting ensures that a value is only evaluated once. Functions O and U execute binary and unary operators respectively (see appendix).

function eval { (x:tree; rho:Env) :Value   forwarded };
{ eval :Exp -> Env -> Value  Note: evaluates an Expression and returns a Value}
{POST: result tag is not deferval, weak head normal form}
   var func, switch :Value;
begin case x^.tag of
         ident:     eval:=applyenv(rho, x^.id);
         intcon:    eval:=mkint(x^.n);
         boolcon:   eval:=mkbool(x^.b);
         charcon:   eval:=mkchar(x^.ch);
         nilcon:    eval:=mkvalue(nilval);
         emptycon:  eval:=mkvalue(emptyval);
         lambdaexp: eval:=mkfunc(x, rho);
            begin func := eval(x^.fun, rho);
                  if func^.tag=funcval then
                     eval:=apply(func, defer(x^.aparam, rho))
                  else error('apply ~fn ')
         unexp:   eval:=U(x^.unopr, eval(x^.unarg, rho));
         binexp:  if x^.binopr=conssy then { cons should not eval its params }
                       eval:=O(x^.binopr, defer(x^.left,rho),
                  else eval:=O(x^.binopr, eval(x^.left,rho),   {others strict}
            begin switch:=eval(x^.e1, rho);
                  if switch^.tag=boolval then
                     if switch^.b then eval:=eval(x^.e2, rho)
                                  else eval:=eval(x^.e3, rho)
                  else error('if ~bool  ')
         block:   eval:=eval( x^.exp, D(x^.decs, rho))
      end {case}
      ; evals := evals + 1 { statistics }
end {eval};

procedure force { ( v :Value )  forwarded } ;
   var fv :Value;
begin if v^.tag=deferval then
         begin fv := eval( v^.e, v^.r ); v^ := fv^ {overwrite} end

{\fB Evaluate an Expression. \fP}

{Do not remove: Lazy.p, Strict.p, lazy.*.P, strict.*.P, lex.*.P, & syntax.*.P }
{ are released under Gnu `copyleft' General Public Licence (GPL)              }
{ - L. Allison, CSSE, Monash Uni., .au, 7/2003.                               }

Bind adds a new binding to the environment. It is called during the processing of declarations and of function application. Applyenv returns a variable's value. It is only called by eval so it forces the variable's value.

function bind( x:alfa; val:Value; r:Env ):Env; { :Ide -> Value -> Env -> Env }
   var p:Env;
begin new(p); envcells:=envcells+1;
      with p^ do begin id:=x; v:=val; next:=r end;
end {bind};

function applyenv( r:Env; x:alfa ):Value;      { :Env -> Ide -> Value }
begin LastId := x; {debugging}
      if r=nil then error('undec id  ')
      else if r^.id=x then
      begin force( r^.v );   {only called from eval}
            applyenv := r^.v
      else applyenv := applyenv( r^.next, x )
end {applyenv};

{\fB Build and Search Environment. \fP}

A function is applied by binding the actual parameter value to the formal parameter name to form a new environment. The body of the function is evaluated in this new environment. Some type-checking is done to ensure that it really is a function that is being applied. If the formal parameter is empty `( )' a check is made that the actual parameter is also empty.

function apply( fn, ap :Value ):Value; { apply a function fn to param ap }
   { apply : (Value->Value) -> Value -> Value }
begin if fn^.e^.fparam^.tag = emptycon then { (L().e)ap }
      begin force(ap);
            if ap^.tag = emptyval then apply := eval(fn^.e^.body, fn^.r)
            else error('L().e exp ')
      else apply := eval(fn^.e^.body, bind(fn^.e^.fparam^.id, ap, fn^.r))
end {apply};

{\fB Apply a Function to a Parameter. \fP}

A declaration is processed much like a function application (recall that `let x=e in f' is equivalent to `(lambda x.f)e') and the declared name is bound to the defining value. Note that this value is deferred. If a group of declarations is recursive, the environment used contains them also, otherwise the enclosing environment is used.

function D( decs:tree; rho:Env ):Env;    { D :Decs -> Env -> Env }
   var localrho :Env;

   function D2( decs :tree; local, global :Env ):Env;
   begin if decs=nil then D2:=global
         else D2:=bind(decs^.hd^.name, defer(decs^.hd^.val,local),
                       D2(decs^.tl, local, global))

begin if decs=nil then D:=rho
      begin if decs^.recursive then
            begin localrho:=bind('-dummy----', nil, rho);
                  localrho^.next:=D2( decs, localrho, rho );
            else  D:=D2( decs, rho, rho )
end {D};

{\fB Execute Declarations. \fP}

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