diff -r 000000000000 -r a5a9c433f639 src/Pure/pattern.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/pattern.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,341 @@
+(*  Title: 	pattern
+    ID:         $Id$
+    Author: 	Tobias Nipkow and Christine Heinzelmann, TU Muenchen
+    Copyright   1993  TU Muenchen
+
+Unification of Higher-Order Patterns.
+
+See also:
+Tobias Nipkow. Functional Unification of Higher-Order Patterns.
+In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993.
+*)
+
+signature PATTERN =
+sig
+  type type_sig
+  type sg
+  type env
+  val eta_contract: term -> term
+  val match: type_sig -> term * term
+        -> (indexname*typ)list * (indexname*term)list
+  val eta_matches: type_sig -> term * term -> bool
+  val unify: sg * env * (term * term)list -> env
+  exception Unif
+  exception MATCH
+  exception Pattern
+end;
+
+functor PatternFun(structure Sign:SIGN and Envir:ENVIR): PATTERN =
+struct
+
+structure Type = Sign.Type;
+
+type type_sig = Type.type_sig
+type sg = Sign.sg
+type env = Envir.env
+
+exception Unif;
+exception Pattern;
+
+fun occurs(F,t,env) = 
+    let fun occ(Var(G,_))   = (case Envir.lookup(env,G) of
+                                 Some(t) => occ t
+                               | None    => F=G)
+          | occ(t1$t2)      = occ t1 orelse occ t2
+          | occ(Abs(_,_,t)) = occ t
+          | occ _           = false
+    in occ t end;
+
+(* Something's wrong *)
+fun ill_formed s = error ("Ill-formed argument in "^s);
+
+
+fun mapbnd f =
+    let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
+          | mpb d (Free(c,T))    = Free(c,T)
+          | mpb d (Const(c,T))   = Const(c,T)
+          | mpb d (Var(iname,T)) = Var(iname,T)
+          | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
+          | mpb d ((u1 $ u2))    = mpb d (u1)$ mpb d (u2)
+    in mpb 0 end;
+
+fun idx [] j     = ~10000
+  | idx(i::is) j = if i=j then length is else idx is j;
+
+val nth_type = snd o nth_elem;
+
+fun at xs i = nth_elem (i,xs);
+
+fun mkabs (binders,is,t)  =
+    let fun mk(i::is) = let val (x,T) = nth_elem(i,binders)
+                        in Abs(x,T,mk is) end 
+          | mk []     = t
+    in mk is end;
+
+val incr = mapbnd (fn i => i+1);
+
+(* termlist --> intlist *)
+fun ints_of []             = []
+  | ints_of (Bound i ::bs) = 
+      let val is = ints_of bs
+      in if i mem is then raise Pattern else i::is end
+  | ints_of _              = raise Pattern;
+
+
+fun app (s,(i::is)) = app (s$Bound(i),is)
+  | app (s,[])      = s;
+
+fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
+  | red s            is      jn = app (mapbnd (at jn) s,is);
+
+(* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
+fun split_type (T,0,Ts)                    = (Ts,T)
+  | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
+  | split_type _                           = ill_formed("split_type");
+
+fun type_of_G (T,n,is) =
+  let val (Ts,U) = split_type(T,n,[]) in map(at Ts)is ---> U end;
+
+fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));
+
+fun mknewhnf(env,binders,is,F as (a,_),T,js) =
+  let val (env',G) = Envir.genvar a (env,type_of_G(T,length is,js))
+  in Envir.update((F,mkhnf(binders,is,G,js)),env') end;
+
+
+fun devar env t = case strip_comb t of
+        (Var(F,_),ys) =>
+            (case Envir.lookup(env,F) of
+               Some(t) => devar env (red t (ints_of  ys) []) 
+             | None    => t)
+      |  _            => t;
+
+
+(* mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ] *)
+fun mk_proj_list is =
+    let fun mk(i::is,j) = if i >= 0 then j :: mk(is,j-1) else mk(is,j-1)
+          | mk([],_)    = []
+    in mk(is,length is - 1) end;
+
+fun proj(s,env,binders,is) =
+    let fun trans d i = if i<d then i else (idx is (i-d))+d;
+        fun pr(s,env,d,binders) = (case devar env s of
+              Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
+                            in (Abs(a,T,t'),env') end
+            | t => (case strip_comb t of
+                (c as Const _,ts) =>
+                         let val (ts',env') = prs(ts,env,d,binders)
+                         in (list_comb(c,ts'),env') end
+                 | (f as Free _,ts) =>
+                         let val (ts',env') = prs(ts,env,d,binders)
+                         in (list_comb(f,ts'),env') end
+                 | (Bound(i),ts) =>
+                         let val j = trans d i
+                         in if j < 0 then raise Unif
+                            else let val (ts',env') = prs(ts,env,d,binders)
+                                 in (list_comb(Bound j,ts'),env') end
+                         end
+                 | (Var(F as (a,_),Fty),ts) =>
+                      let val js = ints_of ts;
+                          val js' = map (trans d) js;
+                          val ks = mk_proj_list js';
+                          val ls = filter (fn i => i >= 0) js'
+                          val Hty = type_of_G(Fty,length js,ks)
+                          val (env',H) = Envir.genvar a (env,Hty)
+                          val env'' =
+                                Envir.update((F,mkhnf(binders,js,H,ks)),env')
+                      in (app(H,ls),env'') end
+                 | _  => raise Pattern))
+        and prs(s::ss,env,d,binders) =
+              let val (s',env1) = pr(s,env,d,binders)
+                  val (ss',env2) = prs(ss,env1,d,binders)
+              in (s'::ss',env2) end
+          | prs([],env,_,_) = ([],env)
+   in if downto0(is,length binders - 1) then (s,env)
+      else pr(s,env,0,binders)
+   end;
+
+
+(* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
+fun mk_ff_list(is,js) = 
+    let fun mk([],[],_)        = [] 
+          | mk(i::is,j::js, k) = if i=j then k :: mk(is,js,k-1)
+                                        else mk(is,js,k-1)
+          | mk _               = ill_formed"mk_ff_list"
+    in mk(is,js,length is-1) end;
+
+fun flexflex1(env,binders,F,Fty,is,js) =
+  if is=js then env
+  else let val ks = mk_ff_list(is,js)
+       in mknewhnf(env,binders,is,F,Fty,ks) end;
+
+fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
+  let fun ff(F,Fty,is,G as (a,_),Gty,js) =
+            if js subset is
+            then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
+                 in Envir.update((F,t),env) end
+            else let val ks = is inter js
+                     val Hty = type_of_G(Fty,length is,map (idx is) ks)
+                     val (env',H) = Envir.genvar a (env,Hty)
+                     fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
+                 in Envir.update((G,lam js), Envir.update((F,lam is),env'))
+                 end;
+  in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end
+
+val tsgr = ref(Type.tsig0);
+
+fun unify_types(T,U, env as Envir.Envir{asol,iTs,maxidx}) =
+  if T=U then env
+  else let val iTs' = Type.unify (!tsgr) ((U,T),iTs)
+       in Envir.Envir{asol=asol,maxidx=maxidx,iTs=iTs'} end
+       handle Type.TUNIFY => raise Unif;
+
+fun unif binders (env,(s,t)) = case (devar env s,devar env t) of
+      (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
+         let val name = if ns = "" then nt else ns
+         in unif ((name,Ts)::binders) (env,(ts,tt)) end
+    | (Abs(ns,Ts,ts),t) => unif ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
+    | (t,Abs(nt,Tt,tt)) => unif ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
+    | p => cases(binders,env,p)
+
+and cases(binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
+       ((Var(F,Fty),ss),(Var(G,Gty),ts)) => 
+         if F = G then flexflex1(env,binders,F,Fty,ints_of ss,ints_of ts)
+                  else flexflex2(env,binders,F,Fty,ints_of ss,G,Gty,ints_of ts)
+      | ((Var(F,_),ss),_)             => flexrigid(env,binders,F,ints_of ss,t)
+      | (_,(Var(F,_),ts))             => flexrigid(env,binders,F,ints_of ts,s)
+      | ((Const c,ss),(Const d,ts))   => rigidrigid(env,binders,c,d,ss,ts)
+      | ((Free(f),ss),(Free(g),ts))   => rigidrigid(env,binders,f,g,ss,ts)
+      | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB (env,binders,i,j,ss,ts) 
+      | ((Abs(_),_),_)                => raise Pattern
+      | (_,(Abs(_),_))                => raise Pattern
+      | _                             => raise Unif
+
+and rigidrigid (env,binders,(a,Ta),(b,Tb),ss,ts) =
+      if a<>b then raise Unif
+      else foldl (unif binders) (unify_types(Ta,Tb,env), ss~~ts)
+
+and rigidrigidB (env,binders,i,j,ss,ts) =
+     if i <> j then raise Unif else foldl (unif binders) (env ,ss~~ts)
+
+and flexrigid (env,binders,F,is,t) =
+      if occurs(F,t,env) then raise Unif
+      else let val (u,env') = proj(t,env,binders,is)
+           in Envir.update((F,mkabs(binders,is,u)),env') end;
+
+fun unify(sg,env,tus) = (tsgr := #tsig(Sign.rep_sg sg);
+                         foldl (unif []) (env,tus));
+
+
+(*Perform eta-contractions upon a term*)
+fun eta_contract (Abs(a,T,body)) = 
+      (case eta_contract body  of
+        body' as (f $ Bound i) => 
+	  if i=0 andalso not (0 mem loose_bnos f) then incr_boundvars ~1 f 
+	  else Abs(a,T,body')
+      | body' => Abs(a,T,body'))
+  | eta_contract(f$t) = eta_contract f $ eta_contract t
+  | eta_contract t = t;
+
+
+(* Pattern matching. Raises MATCH if non-pattern *)
+exception MATCH;
+(* something wron with types, esp in abstractions
+fun typ_match args = Type.typ_match (!tsgr) args
+                     handle Type.TYPE_MATCH => raise MATCH;
+
+fun match_bind(itms,binders,ixn,is,t) =
+  let val js = loose_bnos t
+  in if null is
+     then if null js then (ixn,t)::itms else raise MATCH
+     else if js subset is
+          then let val t' = if downto0(is,length binders - 1) then t
+                            else mapbnd (idx is) t
+               in (ixn, eta_contract(mkabs(binders,is,t'))) :: itms end
+          else raise MATCH
+  end;
+
+fun match_rr (iTs,(a,Ta),(b,Tb)) =
+      if a<>b then raise MATCH else typ_match (iTs,(Ta,Tb))
+
+(* Pre: pat and obj have same type *)
+fun mtch(binders,env as (iTs,itms),pat,obj) = case pat of
+      Var(ixn,_) => (case assoc(itms,ixn) of
+                       None => (iTs,match_bind(itms,binders,ixn,[],obj))
+                     | Some u => if obj aconv u then env else raise MATCH)
+    | Abs(ns,Ts,ts) =>
+        (case obj of
+           Abs(nt,Tt,tt) => mtch((nt,Tt)::binders,env,ts,tt)
+         | _ => let val Tt = typ_subst_TVars iTs Ts
+                in  mtch((ns,Tt)::binders,env,ts,(incr obj)$Bound(0)) end)
+    | _ => (case obj of
+              Abs(nt,Tt,tt) =>
+                mtch((nt,Tt)::binders,env,(incr pat)$Bound(0),tt)
+            | _ => cases(binders,env,pat,obj))
+
+and cases(binders,env as (iTs,itms),pat,obj) =
+  let fun structural() = case (pat,obj) of
+            (Const c,Const d) => (match_rr(iTs,c,d),itms)
+          | (Free f,Free g)   => (match_rr(iTs,f,g),itms)
+          | (Bound i,Bound j) => if i=j then env else raise MATCH
+          | (f$t,g$u)         => mtch(binders,mtch(binders,env,t,u),f,g)
+          | _                 => raise MATCH
+  in case strip_comb pat of
+       (Var(ixn,_),bs) =>
+         (let val is = ints_of bs
+          in case assoc(itms,ixn) of
+               None => (iTs,match_bind(itms,binders,ixn,is,obj))
+             | Some u => if obj aconv (red u is []) then env else raise MATCH
+          end (* if ints_of fails: *) handle Pattern => structural())
+     | _ => structural()
+  end;
+
+fun match tsg = (tsgr := tsg;
+                 fn (pat,obj) => 
+                   let val pT = fastype_of([],pat)
+                       and oT = fastype_of([],obj)
+                       val iTs = typ_match([],(pT,oT))
+                   in mtch([], (iTs,[]), pat, eta_contract obj)
+                      handle Pattern => raise MATCH
+                   end)
+
+(*Predicate: does the pattern match the object?*)
+fun matches tsig args = (match tsig args; true)
+                        handle MATCH => false;
+*)
+
+(*First-order matching;  term_match tsig (pattern, object)
+    returns a (tyvar,typ)list and (var,term)list.
+  The pattern and object may have variables in common.
+  Instantiation does not affect the object, so matching ?a with ?a+1 works.
+  A Const does not match a Free of the same name! 
+  Does not notice eta-equality, thus f does not match %(x)f(x)  *)
+fun match tsig (pat,obj) =
+  let fun typ_match args = (Type.typ_match tsig args)
+			   handle Type.TYPE_MATCH => raise MATCH;
+      fun mtch (tyinsts,insts) = fn
+	(Var(ixn,T), t)  =>
+	  if null (loose_bnos t)
+	  then case assoc(insts,ixn) of
+		  None => (typ_match (tyinsts, (T,fastype_of([],t))), 
+			   (ixn,t)::insts)
+		| Some u => if t aconv u then (tyinsts,insts) else raise MATCH
+	  else raise MATCH
+      | (Free (a,T), Free (b,U)) =>
+	  if  a=b  then (typ_match (tyinsts,(T,U)), insts)  else raise MATCH
+      | (Const (a,T), Const (b,U))  =>
+	  if  a=b  then (typ_match (tyinsts,(T,U)), insts)  else raise MATCH
+      | (Bound i, Bound j)  =>
+          if  i=j  then  (tyinsts,insts)  else raise MATCH
+      | (Abs(_,T,t), Abs(_,U,u))  =>
+	  mtch (typ_match (tyinsts,(T,U)),insts) (t,u)
+      | (f$t, g$u) => mtch (mtch (tyinsts,insts) (f,g)) (t, u)
+      | _ => raise MATCH
+  in mtch([],[]) (pat,obj) end;
+
+(*Predicate: does the pattern match the object?*)
+fun eta_matches tsig (pat,obj) =
+      (match tsig (eta_contract pat,eta_contract obj); true)
+      handle MATCH => false;
+
+end;