path: root/new/trans.c

/* MIRANDA TRANS */
/* performs translation to combinatory logic */

/**************************************************************************
 * Copyright (C) Research Software Limited 1985-90.  All rights reserved. *
 * The Miranda system is distributed as free software under the terms in  *
 * the file "COPYING" which is included in the distribution.              *
 *------------------------------------------------------------------------*/

#include "data.h"

 /* miscellaneous declarations  */
extern word nill,Void;
extern word listdiff_fn,count_fn,from_fn;
extern word diagonalise,concat;
extern word lastname,initialising;
extern word current_id,echoing;
extern word errs;
word newtyps=NIL;  /* list of typenames declared in current script */
word SGC=NIL; /* list of user defined sui-generis constructors */
#define sui_generis(k) (/* k==Void|| */ member(SGC,k))
                       /* 3/10/88 decision to treat `()' as lifted */

abstract(x,e) /* abstraction of template x from compiled expression e */
word x,e;
{ switch(tag[x])
  { case ID:
    	if(isconstructor(x))
      	return(sui_generis(x)?ap(K,e):
	       	ap2(Ug,primconstr(x),e));
    	else return(abstr(x,e));
    case CONS:
    	if(hd[x]==CONST)
	  if(tag[tl[x]]==INT)return(ap2(MATCHINT,tl[x],e));
	  else return(ap2(MATCH,tl[x]==NILS?NIL:tl[x],e));
    	else return(ap(U_,abstract(hd[x],abstract(tl[x],e))));
    case TCONS:
    case PAIR: /* tuples */
    	return(ap(U,abstract(hd[x],abstract(tl[x],e))));
    case AP:
  	if(sui_generis(head(x)))
    	return(ap(Uf,abstract(hd[x],abstract(tl[x],e))));
  	if(tag[hd[x]]==AP&&hd[hd[x]]==PLUS) /* n+k pattern */
    	return(ap2(ATLEAST,tl[hd[x]],abstract(tl[x],e)));
  	while(tag[x]==AP)
    	     { e= abstract(tl[x],e);
       	       x= hd[x]; }
           /* now x must be a constructor */
    default: ; }
  if(isconstructor(x))
    return(ap2(Ug,primconstr(x),e));
  printf("error in declaration of \"%s\", undeclared constructor in pattern: ",
	 get_id(current_id));  /* something funny here - fix later */
  out(stdout,x);
  printf("\n");
  return(NIL);
}

primconstr(x)
word x;
{ x=id_val(x);
  while(tag[x]!=CONSTRUCTOR)x=tl[x];
  return(x);
  /* => constructor values are of the form TRY f k where k is the
     original constructor value, and ! constructors are of the form
     MKSTRICT i k */
}

memb(l,x)  /* tests if x is a member of list "l" - used in testing for 
              repeated names - see rule for "v2" in MIRANDA RULES */
word l,x;
{ if(tag[x]==TVAR)  /* type variable! */
    while(l!=NIL&&!eqtvar(hd[l],x))l= tl[l];
  else while(l!=NIL&&hd[l]!=x)l= tl[l];
  return(l!=NIL); }

abstr(x,e)   /*  "bracket abstraction" of variable x from code e */
word x,e;
{ switch(tag[e])
  { case TCONS:
    case PAIR:
    case CONS: return(liscomb(abstr(x,hd[e]),abstr(x,tl[e])));
    case AP: if(hd[e]==BADCASE||hd[e]==CONFERROR)
               return(ap(K,e)); /* don't go inside error info */
             return(combine(abstr(x,hd[e]),abstr(x,tl[e])));
    case LAMBDA:
    case LET:
    case LETREC:
    case TRIES:
    case LABEL:
    case SHOW:
    case LEXER:
    case SHARE: fprintf(stderr,"impossible event in abstr (tag=%d)\n",tag[e]),
		exit(1);
    default: if(x==e||isvar_t(x)&&isvar_t(e)&&eqtvar(x,e))
               return(I); /* see note */
             return(ap(K,e));
}} /* note - we allow abstraction wrt tvars - see genshfns() */

#define mkindex(i)  ((i)<256?(i):make(INT,i,0))
   /* will fall over if i >= IBASE */

abstrlist(x,e)  /* abstraction of list of variables x from code e */
word x,e;
{ switch(tag[e])
  { case TCONS:
    case PAIR:
    case CONS: return(liscomb(abstrlist(x,hd[e]),abstrlist(x,tl[e])));
    case AP: if(hd[e]==BADCASE||hd[e]==CONFERROR)
               return(ap(K,e)); /* don't go inside error info */
             else return(combine(abstrlist(x,hd[e]),abstrlist(x,tl[e])));
    case LAMBDA: case LET: case LETREC: case TRIES: case LABEL: case SHOW:
    case LEXER:
    case SHARE: fprintf(stderr,
			"impossible event in abstrlist (tag=%d)\n",tag[e]),
		exit(1);
    default: { word i=0;
	       while(x!=NIL&&hd[x]!=e)i++,x=tl[x];
	       if(x==NIL)return(ap(K,e));
	       return(ap(SUBSCRIPT,mkindex(i))); }
}}

word rv_script=0; /* flags readvals in use (for garbage collector) */

codegen(x) /* returns expression x with abstractions performed */
word x;
{ extern word debug,commandmode,cook_stdin,common_stdin,common_stdinb,rv_expr;
  switch(tag[x])
  { case AP: if(commandmode /* beware of corrupting lastexp */
		&&x!=cook_stdin&&x!=common_stdin&&x!=common_stdinb) /* but share $+ $- */
	       return(make(AP,codegen(hd[x]),codegen(tl[x])));
             if(tag[hd[x]]==AP&&hd[hd[x]]==APPEND&&tl[hd[x]]==NIL)
               return(codegen(tl[x])); /* post typecheck reversal of HR bug fix */
              hd[x]=codegen(hd[x]); tl[x]=codegen(tl[x]);
	       /* otherwise do in situ */
	      return(tag[hd[x]]==AP&&hd[hd[x]]==G_ALT?leftfactor(x):x);
    case TCONS:
    case PAIR: return(make(CONS,codegen(hd[x]),codegen(tl[x])));
    case CONS: if(commandmode)
		 return(make(CONS,codegen(hd[x]),codegen(tl[x])));
	       /* otherwise do in situ (see declare) */
               hd[x]=codegen(hd[x]); tl[x]=codegen(tl[x]);
	       return(x);
    case LAMBDA: return(abstract(hd[x],codegen(tl[x])));
    case LET: return(translet(hd[x],tl[x]));
    case LETREC: return(transletrec(hd[x],tl[x]));
    case TRIES: return(transtries(hd[x],tl[x]));
    case LABEL: return(codegen(tl[x]));
    case SHOW: return(makeshow(hd[x],tl[x]));
    case LEXER:
         { word r=NIL,uses_state=0;;
           while(x!=NIL)
              { word rule=abstr(mklexvar(0),codegen(tl[tl[hd[x]]]));
                rule=abstr(mklexvar(1),rule);
                if(!(tag[rule]==AP&&hd[rule]==K))uses_state=1;
                r=cons(cons(hd[hd[x]], /* start condition stuff */
                            cons(ap(hd[tl[hd[x]]],NIL),   /* matcher [] */
                                 rule)),
                       r);
                x=tl[x]; }
           if(!uses_state)  /* strip off (K -) from each rule */
             { for(x=r;x!=NIL;x=tl[x])tl[tl[hd[x]]]=tl[tl[tl[hd[x]]]];
               r = ap(LEX_RPT,ap(LEX_TRY,r)); }
           else r = ap(LEX_RPT1,ap(LEX_TRY1,r));
           return(ap(r,0)); } /* 0 startcond */
    case STARTREADVALS:
	 if(ispoly(tl[x]))
	   { extern word cook_stdin,polyshowerror,ND;
	     printf("type error - %s used at polymorphic type :: [",
	             cook_stdin&&x==hd[cook_stdin]?"$+":"readvals or $+");
	     out_type(redtvars(tl[x])),printf("]\n");
             polyshowerror=1;
             if(current_id)
	       ND=add1(current_id,ND),
               id_type(current_id)=wrong_t,
               id_val(current_id)=UNDEF;
	     if(hd[x])sayhere(hd[x],1); }
	 if(commandmode)rv_expr=1; else rv_script=1;
	 return(x);
    case SHARE: if(tl[x]!= -1) /* arbitrary flag for already visited */
		  hd[x]=codegen(hd[x]),tl[x]= -1;
		return(hd[x]);
    default: if(x==NILS)return(NIL);
             return(x); /* identifier, private name, or constant */
}}

word lfrule=0;

leftfactor(x)

/* grammar optimisations - x is of the form ap2(G_ALT,...)
   G_ALT(G_SEQ a b) a  => G_SEQ a (G_ALT b G_UNIT)
   G_ALT(G_SEQ a b)(G_SEQ a c) => G_SEQ a (G_ALT b c)
   G_ALT(G_SEQ a b)(G_ALT a d) => G_ALT(G_SEQ a (G_ALT b G_UNIT)) d
   G_ALT(G_SEQ a b)(G_ALT(G_SEQ a c) d) => G_ALT(G_SEQ a (G_ALT b c)) d
*/
word x;
{ word a,b,c,d;
  if(tag[c=tl[hd[x]]]==AP&&tag[hd[c]]==AP&&hd[hd[c]]==G_SEQ)
    a=tl[hd[c]],b=tl[c];  else return(x);
  if(same(a,d=tl[x])) 
    { hd[x]=ap(G_SEQ,a), tl[x]=ap2(G_ALT,b,G_UNIT); lfrule++;
      /* printob("rule1: ",x); */
      return(x); }
  if(tag[d]==AP&&tag[hd[d]]==AP)
    c=hd[hd[d]]; else return(x);
  if(c==G_SEQ&&same(a,tl[hd[d]])) 
    { c=tl[d], 
      hd[x]=ap(G_SEQ,a), tl[x]=leftfactor(ap2(G_ALT,b,c)); lfrule++;
      /* printob("rule2: ",x); */
      return(x); }
  if(c!=G_ALT)return(x);
  if(same(a,c=tl[hd[d]]))
    { d=tl[d];
      hd[x]=ap(G_ALT,ap2(G_SEQ,a,ap2(G_ALT,b,G_UNIT)));
      tl[x]=d; lfrule++;
      /* printob("rule3: ",x); */
      return(leftfactor(x)); }
  if(tag[c]==AP&&tag[hd[c]]==AP&&hd[hd[c]]==G_SEQ
     &&same(a,tl[hd[c]]))
    { c=tl[c],d=tl[d], 
      hd[x]=ap(G_ALT,ap2(G_SEQ,a,leftfactor(ap2(G_ALT,b,c))));
      tl[x]=d; lfrule++;
      /* printob("rule4: ",x); */
      return(leftfactor(x)); }
  return(x);
}

same(x,y) /* structural equality */
word x,y;
{ if(x==y)return(1);
  if(tag[x]==ATOM||tag[y]==ATOM||tag[x]!=tag[y])return(0);
  if(tag[x]<INT)return(hd[x]==hd[y]&&tl[x]==tl[y]);
  if(tag[x]>STRCONS)return(same(hd[x],hd[y])&&same(tl[x],tl[y]));
  return(hd[x]==hd[y]&&same(tl[x],tl[y])); /* INT..STRCONS */
}

static word was_poly;
word polyshowerror;

makeshow(here,type)
word here,type;
{ word f;
  extern word ND;
  was_poly=0; f=mkshow(0,0,type);
  /* printob("showfn=",f); /* DEBUG */
  if(here&&was_poly)
    { extern char *current_script;
      printf("type error in definition of %s\n",get_id(current_id));
      sayhere(here,0);
      printf(" use of \"show\" at polymorphic type ");
      out_type(redtvars(type));
      putchar('\n');
      id_type(current_id)=wrong_t;
      id_val(current_id)=UNDEF;
      polyshowerror=1;
      ND=add1(current_id,ND);
      was_poly=0; }
  return(f);
}

mkshow(s,p,t) /* build a show function appropriate to type t */
word s,p,t; /* p is precedence - 0 for top level, 1 for internal */
           /* s flags special case invoked from genshfns */
{ extern word shownum1,showbool,showchar,showlist,showstring,showparen,
             showvoid,showpair,showfunction,showabstract,showwhat;
  word a=NIL;
  while(tag[t]==AP)a=cons(tl[t],a),t=hd[t];
  switch(t)
  { case num_t: return(p?shownum1:SHOWNUM);
    case bool_t: return(showbool);
    case char_t: return(showchar);
    case list_t: if(hd[a]==char_t)return(showstring);
		 return(ap(showlist,mkshow(s,0,hd[a])));
    case comma_t: return(ap(showparen,ap2(showpair,mkshow(s,0,hd[a]),
					   mkshowt(s,hd[tl[a]]))));
    case void_t: return(showvoid);
    case arrow_t:return(showfunction);
    default: if(tag[t]==ID)
	       { word r=t_showfn(t);
		 if(r==0) /* abstype without show function */
		   return(showabstract);
		 if(r==showwhat) /* dont apply to parameter showfns */
		   return(r);
	         while(a!=NIL)r=ap(r,mkshow(s,1,hd[a])),a=tl[a];
		 if(t_class(t)==algebraic_t)r=ap(r,p);
		 return(r);
		   /* note that abstype-showfns have only one precedence
		      and show their components (if any) at precedence 1
		      - if the latter is a problem could do parenthesis
		      stripping */
	       }
	     if(isvar_t(t)){ if(s)return(t); /* see genshfns */
			     was_poly=1; 
			     return(showwhat); }
			/* arbitrary - could be any strict function */
	     if(tag[t]==STRCONS) /* pname */ /* DEBUG */
	       { printf("warning - mkshow applied to suppressed type\n");
		 return(showwhat); }
	     else { printf("impossible event in mkshow ("),
	            out_type(t), printf(")\n");
	            return(showwhat); }
  }
}

mkshowt(s,t) /* t is a (possibly singleton) tuple type */
word s,t; /* flags special call from genshfns */
{ extern word showpair;
  if(tl[t]==void_t)return(mkshow(s,0,tl[hd[t]]));
  return(ap2(showpair,mkshow(s,0,tl[hd[t]]),mkshowt(s,tl[t])));
}

word algshfns=NIL; /* list of showfunctions for all algebraic  types in scope
		     (list of pnames) - needed to make dumps */

genshfns() /* called after meta type check - create show functions for
	      algebraic types */
{ word s;
  for(s=newtyps;s!=NIL;s=tl[s])
  if(t_class(hd[s])==algebraic_t)
     { word f=0,r=t_info(hd[s]); /* r is list of constructors */
       word ush= tl[r]==NIL&&member(SGC,hd[r])?Ush1:Ush;
       for(;r!=NIL;r=tl[r])
	  { word t=id_type(hd[r]),k=id_val(hd[r]);
	    while(tag[k]!=CONSTRUCTOR)k=tl[k];/* lawful and !'d constructors*/
	    /* k now holds constructor(i,hd[r]) */
	    /* k=constructor(hd[k],datapair(get_id(tl[k]),0));
	      /* this `freezes' the name of the constructor */
	      /* incorrect, makes showfns immune to aliasing, should be
		 done at mkshow time, not genshfn time - FIX LATER */
            while(isarrow_t(t))
		 k=ap(k,mkshow(1,1,tl[hd[t]])),t=tl[t]; /* NB 2nd arg */
	    k=ap(ush,k);
	    while(iscompound_t(t))k=abstr(tl[t],k),t=hd[t];
				/* see kahrs.bug.m (this is the fix) */
	    if(f)f=ap2(TRY,k,f);
	    else f=k;
	  }
       /* f~=0, placeholder types dealt with in specify() */
       pn_val(t_showfn(hd[s]))=f;
       algshfns=cons(t_showfn(hd[s]),algshfns);
     }
  else 
  if(t_class(hd[s])==abstract_t) /* if showfn present check type is ok */
     if(t_showfn(hd[s]))
     if(!abshfnck(hd[s],id_type(t_showfn(hd[s]))))
       printf("warning - \"%s\" has type inappropriate for a show-function\n",
	      get_id(t_showfn(hd[s]))),t_showfn(hd[s])=0;
}

abshfnck(t,f) /* t is an abstype, is f right type for its showfn? */
word t,f;
{ word n=t_arity(t),i=1;
  while(i<=n)
       if(isarrow_t(f))
       { word h=tl[hd[f]];
	 if(!(isarrow_t(h)&&isvar_t(tl[hd[h]])&&gettvar(tl[hd[h]])==i
	      &&islist_t(tl[h])&&tl[tl[h]]==char_t))return(0);
         i++,f=tl[f]; 
       } else return(0);
  if(!(isarrow_t(f)&&islist_t(tl[f])&&tl[tl[f]]==char_t))return(0);
  f=tl[hd[f]];
  while(iscompound_t(f)&&isvar_t(tl[f])&&gettvar(tl[f])==n--)f=hd[f];
  return(f==t);
}

transtries(id,x)
word id,x; /* x is a list of alternative values, in reverse order */
{ word  r,h=0,earliest;
  if(fallible(hd[x])) /* add default last case */
    { word oldn=tag[id]==ID?datapair(get_id(id),0):0;
      r=ap(BADCASE,h=cons(oldn,0));
	 /* 0 is placeholder for here-info */
         /* oldn omitted if id is pattern - FIX LATER */ }
  else r=codegen(earliest=hd[x]), x = tl[x];
  while(x!=NIL)r=ap2(TRY,codegen(earliest=hd[x]),r), x=tl[x];
  if(h)tl[h]=hd[earliest]; /* first line-no is the best marker */
  return(r);
}

translet(d,e) /* compile block with body e and def d */
word d,e;
{ word x=mklazy(d);
  return(ap(abstract(dlhs(x),codegen(e)),codegen(dval(x))));
}
/* nasty bug, codegen(dval(x)) was interfering with abstract(dlhs(x)...
   to fix made codegen on tuples be NOT in situ 20/11/88  */

transletrec(dd,e) /* better method,  using list indexing - Jan 88 */
word e,dd;
{ word lhs=NIL,rhs=NIL,pn=1;
  /* list of defs (x=e) is combined to listwise def `xs=es' */
  for(;dd!=NIL;dd=tl[dd])
     { word x=hd[dd];
       if(tag[dlhs(x)]==ID)  /* couldn't be constructor, by grammar */
         lhs=cons(dlhs(x),lhs),
         rhs=cons(codegen(dval(x)),rhs);
       else { word i=0,ids,p=mkgvar(pn++); /* see note 1 */
	      x=new_mklazy(x); ids=dlhs(x);
	      lhs=cons(p,lhs),rhs=cons(codegen(dval(x)),rhs);
              for(;ids!=NIL;ids=tl[ids],i++)
		 lhs=cons(hd[ids],lhs),
		 rhs=cons(ap2(SUBSCRIPT,mkindex(i),p),rhs);
	    }
     }
  if(tl[lhs]==NIL) /* singleton */
    return(ap(abstr(hd[lhs],codegen(e)),ap(Y,abstr(hd[lhs],hd[rhs]))));
  return(ap(abstrlist(lhs,codegen(e)),ap(Y,abstrlist(lhs,rhs))));
}
/* note 1: we here use the alternative `mklazy' transformation
   pat = e =>  x1=p!0;...;xn=p!(n-1);p=(lambda(pat)[xs])e|conferror;
   where p is a private name (need be unique only within a given letrec)
*/

mklazy(d) /* transforms local p=e to ids=($p.ids)e|conferror */
word d;
{ if(irrefutable(dlhs(d)))return(d);
{ word ids=mktuple(dlhs(d));
  if(ids==NIL){ printf("impossible event in mklazy\n"); return(d); }
  dval(d)=ap2(TRY,ap(lambda(dlhs(d),ids),dval(d)),
			  ap(CONFERROR,cons(dlhs(d),here_inf(dval(d)))));
  dlhs(d)=ids;
  return(d);
}}

new_mklazy(d) /* transforms local p=e to ids=($p.ids)e|conferror
                 with ids a LIST (not tuple as formerly) */
word d;
{ word ids=get_ids(dlhs(d));
  if(ids==NIL){ printf("impossible event in new_mklazy\n"); return(d); }
  dval(d)=ap2(TRY,ap(lambda(dlhs(d),ids),dval(d)),
			  ap(CONFERROR,cons(dlhs(d),here_inf(dval(d)))));
  dlhs(d)=ids;
  return(d);
}

here_inf(rhs) /* rhs is of form tries(id,val_list) */
word rhs;
{ word x=tl[rhs];
  while(tl[x]!=NIL)x=tl[x]; /* find earliest alternative */
  return(hd[hd[x]]); /* hd[x] is of form label(here_info,value) */
}

irrefutable(x) /* x built from suigeneris constr's and (unrepeated) names */
word x;
{ if(tag[x]==CONS)return(0); /* includes constants */
  if(isconstructor(x))return(sui_generis(x));
  if(tag[x]==ID)return(1);
  if(tag[x]==AP&&tag[hd[x]]==AP&&hd[hd[x]]==PLUS) /* n+k pattern */
    return(0);
  return(irrefutable(hd[x])&&irrefutable(tl[x]));
}

combine(x,y)
word x,y;
{ word a,b,a1,b1;
  a= tag[x]==AP&&hd[x]==K;
  b= tag[y]==AP&&hd[y]==K;
  if(a&&b)return(ap(K,ap(tl[x],tl[y])));
            /* rule of K propagation */
  if(a&&y==I)return(tl[x]);
               /* rule 'eta */
  b1= tag[y]==AP&&tag[hd[y]]==AP&&hd[hd[y]]==B;
  if(a)if(b1)return(ap3(B1,tl[x],tl[hd[y]],tl[y])); else
       /* Mark Scheevel's new B1 introduction rule -- adopted Aug 83 */
       if(tag[tl[x]]==AP&&tag[hd[tl[x]]]==AP&&hd[hd[tl[x]]]==COND)
	 return(ap3(COND,tl[hd[tl[x]]],ap(K,tl[tl[x]]),y));
       else return(ap2(B,tl[x],y));
  a1= tag[x]==AP&&tag[hd[x]]==AP&&hd[hd[x]]==B;
  if(b)if(a1)if(tag[tl[hd[x]]]==AP&&hd[tl[hd[x]]]==COND)
	       return(ap3(COND,tl[tl[hd[x]]],tl[x],y));
	     else return(ap3(C1,tl[hd[x]],tl[x],tl[y]));
       else return(ap2(C,x,tl[y]));
  if(a1)if(tag[tl[hd[x]]]==AP&&hd[tl[hd[x]]]==COND)
	  return(ap3(COND,tl[tl[hd[x]]],tl[x],y));
	else return(ap3(S1,tl[hd[x]],tl[x],y));
  else return(ap2(S,x,y)); }

liscomb(x,y)  /* the CONSy analogue of "combine" */
word x,y;
{ word a,b;
  a= tag[x]==AP&&hd[x]==K;
  b=  tag[y]==AP&&hd[y]==K;
  if(a&&b)return(ap(K,cons(tl[x],tl[y])));
                       /* K propagation again */
  if(a)if(y==I)return(ap(P,tl[x])); /* eta P - new rule added 20/11/88 */
       else return(ap2(B_p,tl[x],y));
  if(b)return(ap2(C_p,x,tl[y]));
  return(ap2(S_p,x,y)); }
/* B_p,C_p,S_p are the CONSy analogues of B,C,S
   see MIRANDA REDUCE for their definitions */

compzf(e,qq,diag) /* compile a zf expression with body e and qualifiers qq
		     (listed in reverse order); diag is 0 for sequential
		     and 1 for diagonalising zf expressions */
word e,qq,diag;
{ word hold=NIL,r=0,g1= -1; /* r is number of generators */
  while(qq!=NIL) /* unreverse qualifier list */
       { if(hd[hd[qq]]==REPEAT)qq=fixrepeats(qq);
         hold=cons(hd[qq],hold);
	 if(hd[hd[qq]]==GUARD)r++; /* count filters */
	 qq = tl[qq]; }
  for(qq=hold;qq!=NIL&&hd[hd[qq]]==GUARD;qq=tl[qq])r--; /* less leading filters */
  if(hd[hd[hold]]==GENERATOR)g1=tl[tl[hd[hold]]]; /* rhs of 1st generator */
  e=transzf(e,hold,diag?diagonalise:concat);
  /* diagonalise [ // ] comprehensions, but not [ | ] ones */
  if(diag)
    while(r--)e=ap(concat,e); /* see funny version of rule 3 below */
  return(e==g1?ap2(APPEND,NIL,e):e); /* test in g1 is to fix HR bug */
}
/* HR bug - if Rule 1 applied at outermost level, type info is lost
   eg [p|p<-3] ==> 3  (reported by Ham Richards, Nov 89)
*/

transzf(e,qq,conc)  /* Bird and Wadler page 63 */
word e,qq,conc;
{ word q,q2;
  if(qq==NIL)return(cons(e,NIL));
  q=hd[qq];
  if(hd[q]==GUARD)
    return(ap3(COND,tl[q],transzf(e,tl[qq],conc),NIL));
  if(tl[qq]==NIL)
    if(hd[tl[q]]==e&&isvariable(e))return(tl[tl[q]]); /* Rule 1 */
    else if(irrefutable(hd[tl[q]]))
	 return(ap2(MAP,lambda(hd[tl[q]],e),tl[tl[q]])); /* Rule 2 */
	 else /* Rule 2 warped for refutable patterns */
	 return(ap2(FLATMAP,lambda(hd[tl[q]],cons(e,NIL)),tl[tl[q]]));
  q2=hd[tl[qq]];
  if(hd[q2]==GUARD)
    if(conc==concat) /* Rule 3 */
    { tl[tl[q]]=ap2(FILTER,lambda(hd[tl[q]],tl[q2]),tl[tl[q]]);
      tl[qq]=tl[tl[qq]];
      return(transzf(e,qq,conc)); }
    else  /* funny [//] version of Rule 3 to avoid creating weak lists */
    { e=ap3(COND,tl[q2],cons(e,NIL),NIL);
      tl[qq]=tl[tl[qq]];
      return(transzf(e,qq,conc)); } /* plus wrap result with concat */
  return(ap(conc,transzf(transzf(e,tl[qq],conc),cons(q,NIL),conc)));
  /* Rule 4 */
}

fixrepeats(qq)  /* expands multi-lhs generators in zf expressions */
word qq;
{ word q = hd[qq];
  word rhs = q;
  qq = tl[qq];
  while(hd[rhs]==REPEAT)rhs = tl[tl[rhs]];
  rhs = tl[tl[rhs]];  /* rhs now contains the common right hand side */
  while(hd[q]==REPEAT)
    { qq = cons(cons(GENERATOR,cons(hd[tl[q]],rhs)),qq);
      q = tl[tl[q]];
    }
  return(cons(q,qq));
} /* EFFICIENCY PROBLEM - rhs gets re-evaluated for each lhs, fix later */
  /* likewise re-typechecked, although this probably doesn't matter */

lastlink(x) /* finds last link of a list -- needed with zf body elision */
word x;
{ while(tl[x]!=NIL)x=tl[x];
  return(x);
}

#define ischar(x) ((x)>=0&&(x)<=255)

genlhs(x) /* x is an expression found on the lhs of <- and genlhs returns
             the corresponding pattern */
word x;
{ word hold;
  switch(tag[x])
  { case AP:
  	if(tag[hd[x]]==AP&&hd[hd[x]]==PLUS&&isnat(tl[x]))
          return(ap2(PLUS,tl[x],genlhs(tl[hd[x]])));  /* n+k pattern */
    case CONS:
    case TCONS:
    case PAIR:
  	hold=genlhs(hd[x]); return(make(tag[x],hold,genlhs(tl[x])));
    case ID:
    	if(member(idsused,x))return(cons(CONST,x));
    	if(!isconstructor(x))idsused=cons(x,idsused); return(x);
    case INT: return(cons(CONST,x));
    case DOUBLE: syntax("floating point literal in pattern\n");
		 return(nill);
    case ATOM: if(x==True||x==False||x==NILS||x==NIL||ischar(x))
		 return(cons(CONST,x));
    default: syntax("illegal form on left of <-\n");
	     return(nill);
}}

#ifdef OBSOLETE
genexp(x) /* undoes effect of genlhs - sorry about that! (see qualifiers1)*/
word x;
{ switch(tag[x])
  { case AP: return(ap(genexp(hd[x]),genexp(tl[x])));
    case TCONS: return(tcons(genexp(hd[x]),genexp(tl[x])));
    case PAIR: return(pair(genexp(hd[x]),genexp(tl[x])));
    case CONS: return(hd[x]==CONST?tl[x]
		      :cons(genexp(hd[x]),genexp(tl[x])));
    default: return(x);  /* must be ID or constant */
}}
#endif

word speclocs=NIL; /* list of cons(id,hereinfo) giving location of spec for
		     ids both defined and specified - needed to locate errs
		     in meta_tcheck, abstr_mcheck */
getspecloc(x)
word x;
{ word s=speclocs;
  while(s!=NIL&&hd[hd[s]]!=x)s=tl[s];
  return(s==NIL?id_who(x):tl[hd[s]]); }

declare(x,e)    /* translates  <pattern> = <exp>  at top level  */
word x,e;
{ if(tag[x]==ID&&!isconstructor(x))decl1(x,e);else
  { word bindings=scanpattern(x,x,share(tries(x,cons(e,NIL)),undef_t),
			     ap(CONFERROR,cons(x,hd[e])));
			     /* hd[e] is here-info */
  /* note creation of share node to force sharing on code generation
     and typechecking */
    if(bindings==NIL){ errs=hd[e];
		       syntax("illegal lhs for definition\n");
		       return; }
    lastname=0;
    while(bindings!=NIL)
	 { word h;
	   if(id_val(h=hd[hd[bindings]])!=UNDEF)
	     { errs=hd[e]; nameclash(h); return; }
	   id_val(h)=tl[hd[bindings]];
	   if(id_who(h)!=NIL)speclocs=cons(cons(h,id_who(h)),speclocs);
	   id_who(h)=hd[e]; /* here-info */
           if(id_type(h)==undef_t)addtoenv(h);
	   bindings = tl[bindings];
         }
}}

scanpattern(p,x,e,fail) /* declare ids in x as components of `p=e', each as
		           n = ($p.n)e,  result is list of bindings */
word p,x,e,fail;
{ if(hd[x]==CONST||isconstructor(x))return(NIL);
  if(tag[x]==ID){ word binding=
		  cons(x,ap2(TRY,ap(lambda(p,x),e),fail));
		  return(cons(binding,NIL)); }
  if(tag[x]==AP&&tag[hd[x]]==AP&&hd[hd[x]]==PLUS) /* n+k pattern */
    return(scanpattern(p,tl[x],e,fail));
  return(shunt(scanpattern(p,hd[x],e,fail),scanpattern(p,tl[x],e,fail)));
}

get_ids(x) /* return list of names in pattern x (without repetitions) */
word x;
{ if(hd[x]==CONST||isconstructor(x))return(NIL);
  if(tag[x]==ID)return(cons(x,NIL));
  if(tag[x]==AP&&tag[hd[x]]==AP&&hd[hd[x]]==PLUS) /* n+k pattern */
    return(get_ids(tl[x]));
  return(UNION(get_ids(hd[x]),get_ids(tl[x])));
}

mktuple(x) /* extract tuple-structure of names from pattern x */
word x;
{ if(hd[x]==CONST||isconstructor(x))return(NIL);
  if(tag[x]==ID)return(x);
  if(tag[x]==AP&&tag[hd[x]]==AP&&hd[hd[x]]==PLUS) /* n+k pattern */
    return(mktuple(tl[x]));
{ word y=mktuple(tl[x]); x=mktuple(hd[x]);
  return(x==NIL?y:y==NIL?x:pair(x,y));
}}

decl1(x,e)  /* declare name x to have the value denoted by e */
word x,e;
{ if(id_val(x)!=UNDEF&&lastname!=x)
    { errs=hd[e]; nameclash(x); return; }
  if(id_val(x)==UNDEF)
    { id_val(x)= tries(x,cons(e,NIL));
      if(id_who(x)!=NIL)speclocs=cons(cons(x,id_who(x)),speclocs);
      id_who(x)= hd[e]; /* here-info */
      if(id_type(x)==undef_t)addtoenv(x);
    } else
  if(!fallible(hd[tl[id_val(x)]]))
    errs=hd[e],
    printf("%ssyntax error: unreachable case in defn of \"%s\"\n",
	    echoing?"\n":"",get_id(x)),
                acterror();
  else tl[id_val(x)]= cons(e,tl[id_val(x)]);
/* multi-clause definitions are composed as tries(id,rhs_list)
   where id is included purely for diagnostic purposes
   note that rhs_list is reversed - put right by code generation */
}

fallible(e) /* e is "fallible" rhs - if not sure, says yes */
word e;
{ for(;;)
  { if(tag[e]==LABEL)e=tl[e];
    if(tag[e]==LETREC||tag[e]==LET)e=tl[e]; else
    if(tag[e]==LAMBDA)
      if(irrefutable(hd[e]))e=tl[e];
      else return(1); else
    if(tag[e]==AP&&tag[hd[e]]==AP&&tag[hd[hd[e]]]==AP&&hd[hd[hd[e]]]==COND)
	 e=tl[e]; else
    return(e==FAIL);   /* test for nested (COND a b FAIL) */
  }
} /* NOTE
     When an rhs contains FAIL as a result of compiling an elseless guard set
     it is of the form
	XX ::= ap3(COND,a,b,FAIL) | let[rec](def[s],XX) | lambda(pat,XX)
     an rhs is fallible if
	1) it is an XX, as above, or
	2) it is of the form lambda(pat1,...,lambda(patn,e)...)
	   where at least one of the patterns pati is refutable.
  */

/* combinator to select i'th out of n args *//*
k(i,n)
int i,n;
{ if(i==1)return(n==1?I:n==2?K:ap2(B,K,k(1,n-1)));
  if(i==2&&n==2)return(KI); /* redundant but saves space *//*
  return(ap(K,k(i-1,n-1)));
} */

#define arity_check if(t_arity(tf)!=arity)\
  printf("%ssyntax error: \
wrong number of parameters for typename \"%s\" (%d expected)\n",\
          echoing?"\n":"",get_id(tf),t_arity(tf)),errs=here,acterror()

decltype(tf,class,info,here)  /* declare a user defined type */
word tf,class,info,here;
{ word arity=0;
  extern word errs;
  while(tag[tf]==AP)arity++,tf=hd[tf];
  if(class==synonym_t&&id_type(tf)==type_t&&t_class(tf)==abstract_t
     &&t_info(tf)==undef_t)
    { /* this is binding for declared but not yet bound abstract typename */
      arity_check;
      id_who(tf)=here;
      t_info(tf)=info;
      return; }
  if(class==abstract_t&&id_type(tf)==type_t&&t_class(tf)==synonym_t)
    { /* this is abstype declaration of already bound typename */
      arity_check;
      t_class(tf)=abstract_t;
      return; }
  if(id_val(tf)!=UNDEF)
    { errs=here; nameclash(tf); return; }
  if(class!=synonym_t)newtyps=add1(tf,newtyps);
  id_val(tf)=make_typ(arity,class==algebraic_t?make_pn(UNDEF):0,class,info);
  if(id_type(tf)!=undef_t){ errs=here; respec_error(tf); return; }
  else addtoenv(tf);
  id_who(tf)=here;
  id_type(tf)=type_t;
}

declconstr(x,n,t)  /* declare x to be constructor number n of type t */
word x,n,t;   /* x must be an identifier */
{ id_val(x)=constructor(n,x);
  if(n>>16)
    { syntax("algebraic type has too many constructors\n"); return; }
  if(id_type(x)!=undef_t){ errs=id_who(x); respec_error(x); return; }
  else addtoenv(x);
  id_type(x) = t;
} /* the value of a constructor x is constructor(constr_tag,x)
     where constr_tag is a small natural number */

/* #define DEPSDEBUG .
    /* switches on debugging printouts for dependency analysis in block() */
#ifdef DEPSDEBUG
pd(def)
word def;
{ out1(stdout,dlhs(def)); }

pdlist(defs)
word defs;
{ putchar('(');
  for(;defs!=NIL;defs=tl[defs])
     pd(hd[defs]),printf(tl[defs]==NIL?"":",");
  putchar(')');
}
#endif

block(defs,e,keep) /* semantics of "where" - performs dependency analysis */
/* defs has form list(defn(pat,typ,val)), e is body of block */
/* if `keep' hold together as single letrec */
word defs,e,keep;
{ word ids=NIL,deftoids=NIL,g=NIL,d;
  extern word SYNERR,detrop;
  /* return(letrec(defs,e)); /* release one semantics was just this */
  if(SYNERR)return(NIL);  /* analysis falls over on empty patterns */
  for(d=defs;d!=NIL;d=tl[d])  /* first collect all ids defined in block */
     { word x = get_ids(dlhs(hd[d]));
       ids=UNION(ids,x);
       deftoids=cons(cons(hd[d],x),deftoids);
     }
  defs=sort(defs);
  for(d=defs;d!=NIL;d=tl[d]) /* now build dependency relation g */
     { word x=intersection(deps(dval(hd[d])),ids),y=NIL;
       for(;x!=NIL;x=tl[x])  /* replace each id by corresponding def */
	  y=add1(invgetrel(deftoids,hd[x]),y);
       g=cons(cons(hd[d],add1(hd[d],y)),g);
       /* treat all defs as recursive for now */
     }
  g=reverse(g); /* keep in address order of first components */
#ifdef DEPSDEBUG
  { word g1=g;
    printf("g=");
    for(;g1!=NIL;g1=tl[g1])
       pd(hd[hd[g1]]),putchar(':'),pdlist(tl[hd[g1]]),putchar(';');
    printf("\n"); }
#endif
/* g is list(cons(def,defs)) 
   where defs are all on which def immediately depends, plus self */
  g = tclos(g);  /* now g is list(cons(def,ultdefs)) */
#ifdef DEPSDEBUG
  { word g1=g;
    printf("tclos(g)=");
    for(;g1!=NIL;g1=tl[g1])
       pd(hd[hd[g1]]),putchar(':'),pdlist(tl[hd[g1]]),putchar(';');
    printf("\n"); }
#endif
  { /* check for unused definitions */
    word x=intersection(deps(e),ids),y=NIL,*g1= &g;
    for(;x!=NIL;x=tl[x])
       { word d=invgetrel(deftoids,hd[x]);
         if(!member(y,d))y=UNION(y,getrel(g,d)); }
    defs=setdiff(defs,y);  /* these are de trop */
    if(defs!=NIL)detrop=append1(detrop,defs);
    if(keep)             /* if local polymorphism not required */
    return(letrec(y,e)); /* analysis was solely to find unwanted defs */
    /* remove redundant entries from g */
    /* no, leave in for typecheck - could remove afterwards
    while(*g1!=NIL&&defs!=NIL)
         if(hd[hd[*g1]]==hd[defs])*g1=tl[*g1]; else
         if(hd[hd[*g1]]<hd[defs])g1= &tl[*g1];
         else defs=tl[defs]; */
  }
  g = msc(g);    /* g is list(defgroup,ultdefs) */
#ifdef DEPSDEBUG
  { word g1=g;
    printf("msc(g)=");
    for(;g1!=NIL;g1=tl[g1])
       pdlist(hd[hd[g1]]),putchar(':'),pdlist(tl[hd[g1]]),putchar(';');
    printf("\n"); }
#endif
  g = tsort(g);  /* g is list(defgroup) in dependency order */
#ifdef DEPSDEBUG
  { word g1=g;
    printf("tsort(g)=");
    for(;g1!=NIL;g1=tl[g1])
       pdlist(hd[g1]),putchar(';');
    printf("\n"); }
#endif
  g = reverse(g); /* reconstruct block inside-first */
  while(g!=NIL)
       { if(tl[hd[g]]==NIL &&
	    intersection(get_ids(dlhs(hd[hd[g]])),deps(dval(hd[hd[g]])))==NIL
	   )e=let(hd[hd[g]],e);  /* single non-recursive def */
         else e=letrec(hd[g],e);
	 g=tl[g]; }
  return(e);
}
/* Implementation note:
   tsort will fall over if there is a non-list strong component because it
   was originally written on assumption that relation is over identifiers.
   Whence need to pretend all defs recursive until after tsort.
   Could do better - some defs may be subsidiary to others */

tclos(r) /* fast transitive closure - destructive in r */
word r;   /* r is of form list(cons(x,xs)) */
{ word r1;
  for(r1=r;r1!=NIL;r1=tl[r1])
     { word x= less1(tl[hd[r1]],hd[hd[r1]]);
	     /* invariant x intersect tl[hd[r1]] = NIL */
       while(x!=NIL)
	    { x=imageless(r,x,tl[hd[r1]]);
	      tl[hd[r1]]=UNION(tl[hd[r1]],x); }
     }
  return(r);
}

getrel(r,x) /* r is list(cons(x,xs)) - return appropriate xs, else NIL */
word r,x;
{ while(r!=NIL&&hd[hd[r]]!=x)r=tl[r];
  return(r==NIL?NIL:tl[hd[r]]);
}

invgetrel(r,x) /* return first x1 such that `x1 r x' error if none found */
word r,x;
{ while(r!=NIL&&!member(tl[hd[r]],x))r=tl[r];
  if(r==NIL)fprintf(stderr,"impossible event in invgetrel\n"),exit(1);
  return(hd[hd[r]]);
}


imageless(r,y,z) /* image of set y in reln r, less set z */
word r,y,z;
{ word i=NIL;
  while(r!=NIL&&y!=NIL)
       if(hd[hd[r]]==hd[y])
         i=UNION(i,less(tl[hd[r]],z)),r=tl[r],y=tl[y]; else
       if(hd[hd[r]]<hd[y])r=tl[r];
       else y=tl[y];
  return(i);
}

less(x,y)  /* non-destructive set difference x-y */
word x,y;
{ word r=NIL;
  while(x!=NIL&&y!=NIL)
       if(hd[x]==hd[y])x=tl[x],y=tl[y]; else
       if(hd[x]<hd[y])r=cons(hd[x],r),x=tl[x];
       else y=tl[y];
  return(shunt(r,x));
}

less1(x,a)  /* non-destructive set difference x- {a} */
word x,a;
{ word r=NIL;
  while(x!=NIL&&hd[x]!=a)r=cons(hd[x],r),x=tl[x];
  return(shunt(r,x==NIL?NIL:tl[x]));
}

sort(x) /* into address order */
word x;
{ word a=NIL,b=NIL,hold=NIL;
  if(x==NIL||tl[x]==NIL)return(x);
  while(x!=NIL) /* split x */
       { hold=a,a=cons(hd[x],b),b=hold;
	 x=tl[x]; }
  a=sort(a),b=sort(b);
  /* now merge two halves back together */
  while(a!=NIL&&b!=NIL)
  if(hd[a]<hd[b])x=cons(hd[a],x),a=tl[a];
  else x=cons(hd[b],x),b=tl[b];
  if(a==NIL)a=b;
  while(a!=NIL)x=cons(hd[a],x),a=tl[a];
  return(reverse(x));
}

sortrel(x) /* sort relation into address order of first components */
word x;  /* x is a list of cons(y,ys) */
{ word a=NIL,b=NIL,hold=NIL;
  if(x==NIL||tl[x]==NIL)return(x);
  while(x!=NIL) /* split x */
       { hold=a,a=cons(hd[x],b),b=hold;
	 x=tl[x]; }
  a=sortrel(a),b=sortrel(b);
  /* now merge two halves back together */
  while(a!=NIL&&b!=NIL)
  if(hd[hd[a]]<hd[hd[b]])x=cons(hd[a],x),a=tl[a];
  else x=cons(hd[b],x),b=tl[b];
  if(a==NIL)a=b;
  while(a!=NIL)x=cons(hd[a],x),a=tl[a];
  return(reverse(x));
}

specify(x,t,h) /* semantics of a "::" statement */
word x,t,h;  /* N.B. t not yet in reduced form */
{ extern word showwhat;
  if(tag[x]!=ID&&t!=type_t){ errs=h;
			     syntax("incorrect use of ::\n");
                             return; }
  if(t==type_t)
    { word a=0;
      while(tag[x]==AP)a++,x=hd[x];
      if(!(id_val(x)==UNDEF&&id_type(x)==undef_t))
	{ errs=h; nameclash(x); return; }
      id_type(x)=type_t; 
      if(id_who(x)==NIL)id_who(x)=h; /* premise always true, see above */
        /* if specified and defined, locate by definition */
      id_val(x)=make_typ(a,showwhat,placeholder_t,NIL);/* placeholder type */
      addtoenv(x);
      newtyps=add1(x,newtyps);
      return; }
  if(id_type(x)!=undef_t){ errs=h; respec_error(x); return; }
  id_type(x)=t;
  if(id_who(x)==NIL)id_who(x)=h; /* as above */
  else speclocs=cons(cons(x,h),speclocs);
  if(id_val(x)==UNDEF)addtoenv(x);
}

respec_error(x) /* only one type spec per name allowed - IS THIS RIGHT? */
word x;
{ extern word primenv;
  if(echoing)putchar('\n');
  printf("syntax error: type of \"%s\" already declared%s\n",get_id(x),
	 member(primenv,x)?" (in standard environment)":"");
  acterror();
}

nameclash(x) /* only one top level binding per name allowed */
word x;
{ extern word primenv;
  if(echoing)putchar('\n');
  printf("syntax error: nameclash, \"%s\" already defined%s\n",get_id(x),
	 member(primenv,x)?" (in standard environment)":"");
  acterror();
}

nclashcheck(n,dd,hr) /* is n already bound in list of definitions dd */
word n,dd,hr;
{ while(dd!=NIL&&!nclchk(n,dlhs(hd[dd]),hr))dd=tl[dd];
}

nclchk(n,p,hr)  /* is n already bound in pattern p */
word n,p,hr;
{ if(hd[p]==CONST)return(0);
  if(tag[p]==ID)
    { if(n!=p)return(0);
      if(echoing)putchar('\n');
      errs=hr,
      printf(
"syntax error: conflicting definitions of \"%s\" in where clause\n",
      get_id(n)),
      acterror();
      return(1); }
  if(tag[p]==AP&&hd[p]==PLUS) /* hd of n+k pattern */
    return(0);
  return(nclchk(n,hd[p],hr)||nclchk(n,tl[p],hr));
}

transtypeid(x)  /* recognises literal type constants - see RULES */
word x;
{ char *n=get_id(x);
  return(strcmp(n,"bool")==0?bool_t:
         strcmp(n,"num")==0?num_t:
         strcmp(n,"char")==0?char_t:
         x);
}

/* end of MIRANDA TRANS */