src/Pure/pattern.ML
author haftmann
Tue Sep 06 08:30:43 2005 +0200 (2005-09-06)
changeset 17271 2756a73f63a5
parent 17221 6cd180204582
child 17412 e26cb20ef0cc
permissions -rw-r--r--
introduced some new-style AList operations
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(*  Title:      Pure/pattern.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer
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Unification of Higher-Order Patterns.
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See also:
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Tobias Nipkow. Functional Unification of Higher-Order Patterns.
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In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993.
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TODO: optimize red by special-casing it
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*)
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infix aeconv;
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signature PATTERN =
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sig
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  val trace_unify_fail: bool ref
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  val aeconv: term * term -> bool
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  val eta_contract: term -> term
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  val eta_long: typ list -> term -> term
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  val beta_eta_contract: term -> term
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  val eta_contract_atom: term -> term
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  val match: theory -> term * term -> Type.tyenv * Envir.tenv
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  val first_order_match: theory -> term * term -> Type.tyenv * Envir.tenv
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  val matches: theory -> term * term -> bool
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  val matches_subterm: theory -> term * term -> bool
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  val unify: theory * Envir.env * (term * term)list -> Envir.env
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  val first_order: term -> bool
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  val pattern: term -> bool
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  val rewrite_term: theory -> (term * term) list -> (term -> term option) list -> term -> term
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  exception Unif
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  exception MATCH
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  exception Pattern
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end;
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structure Pattern: PATTERN =
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struct
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exception Unif;
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exception Pattern;
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val trace_unify_fail = ref false;
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fun string_of_term thy env binders t = Sign.string_of_term thy
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  (Envir.norm_term env (subst_bounds(map Free binders,t)));
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fun bname binders i = fst(List.nth(binders,i));
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fun bnames binders is = space_implode " " (map (bname binders) is);
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fun typ_clash thy (tye,T,U) =
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  if !trace_unify_fail
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  then let val t = Sign.string_of_typ thy (Envir.norm_type tye T)
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           and u = Sign.string_of_typ thy (Envir.norm_type tye U)
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       in tracing("The following types do not unify:\n" ^ t ^ "\n" ^ u) end
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  else ()
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fun clash a b =
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  if !trace_unify_fail then tracing("Clash: " ^ a ^ " =/= " ^ b) else ()
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fun boundVar binders i =
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  "bound variable " ^ bname binders i ^ " (depth " ^ string_of_int i ^ ")";
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fun clashBB binders i j =
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  if !trace_unify_fail then clash (boundVar binders i) (boundVar binders j)
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  else ()
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fun clashB binders i s =
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  if !trace_unify_fail then clash (boundVar binders i) s
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  else ()
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fun proj_fail thy (env,binders,F,_,is,t) =
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  if !trace_unify_fail
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  then let val f = Syntax.string_of_vname F
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           val xs = bnames binders is
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           val u = string_of_term thy env binders t
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           val ys = bnames binders (loose_bnos t \\ is)
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       in tracing("Cannot unify variable " ^ f ^
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               " (depending on bound variables " ^ xs ^ ")\nwith term " ^ u ^
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               "\nTerm contains additional bound variable(s) " ^ ys)
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       end
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  else ()
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fun ocheck_fail thy (F,t,binders,env) =
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  if !trace_unify_fail
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  then let val f = Syntax.string_of_vname F
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           val u = string_of_term thy env binders t
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       in tracing("Variable " ^ f ^ " occurs in term\n" ^ u ^
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                  "\nCannot unify!\n")
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       end
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  else ()
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fun occurs(F,t,env) =
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    let fun occ(Var (G, T))   = (case Envir.lookup (env, (G, T)) of
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                                 SOME(t) => occ t
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                               | NONE    => F=G)
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          | occ(t1$t2)      = occ t1 orelse occ t2
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          | occ(Abs(_,_,t)) = occ t
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          | occ _           = false
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    in occ t end;
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fun mapbnd f =
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    let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
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          | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
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          | mpb d ((u1 $ u2))    = (mpb d u1)$(mpb d u2)
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          | mpb _ atom           = atom
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    in mpb 0 end;
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fun idx [] j     = raise Unif
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  | idx(i::is) j = if (i:int) =j then length is else idx is j;
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fun at xs i = List.nth (xs,i);
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fun mkabs (binders,is,t)  =
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    let fun mk(i::is) = let val (x,T) = List.nth(binders,i)
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                        in Abs(x,T,mk is) end
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          | mk []     = t
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    in mk is end;
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val incr = mapbnd (fn i => i+1);
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fun ints_of []             = []
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  | ints_of (Bound i ::bs) =
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      let val is = ints_of bs
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      in if i mem_int is then raise Pattern else i::is end
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  | ints_of _              = raise Pattern;
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fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
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fun app (s,(i::is)) = app (s$Bound(i),is)
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  | app (s,[])      = s;
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fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
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  | red t            []      [] = t
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  | red t            is      jn = app (mapbnd (at jn) t,is);
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(* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
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fun split_type (T,0,Ts)                    = (Ts,T)
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  | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
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  | split_type _                           = error("split_type");
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fun type_of_G (env as Envir.Envir {iTs, ...}) (T,n,is) =
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  let val (Ts, U) = split_type (Envir.norm_type iTs T, n, [])
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  in map (at Ts) is ---> U end;
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fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));
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fun mknewhnf(env,binders,is,F as (a,_),T,js) =
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  let val (env',G) = Envir.genvar a (env,type_of_G env (T,length is,js))
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  in Envir.update (((F, T), mkhnf (binders, is, G, js)), env') end;
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(* mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ] *)
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fun mk_proj_list is =
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    let fun mk(i::is,j) = if isSome i then j :: mk(is,j-1) else mk(is,j-1)
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          | mk([],_)    = []
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    in mk(is,length is - 1) end;
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fun proj(s,env,binders,is) =
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    let fun trans d i = if i<d then i else (idx is (i-d))+d;
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        fun pr(s,env,d,binders) = (case Envir.head_norm env s of
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              Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
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                            in (Abs(a,T,t'),env') end
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            | t => (case strip_comb t of
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                (c as Const _,ts) =>
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                         let val (ts',env') = prs(ts,env,d,binders)
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                         in (list_comb(c,ts'),env') end
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                 | (f as Free _,ts) =>
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                         let val (ts',env') = prs(ts,env,d,binders)
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                         in (list_comb(f,ts'),env') end
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                 | (Bound(i),ts) =>
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                         let val j = trans d i
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                             val (ts',env') = prs(ts,env,d,binders)
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                         in (list_comb(Bound j,ts'),env') end
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                 | (Var(F as (a,_),Fty),ts) =>
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                      let val js = ints_of' env ts;
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                          val js' = map (try (trans d)) js;
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                          val ks = mk_proj_list js';
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                          val ls = List.mapPartial I js'
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                          val Hty = type_of_G env (Fty,length js,ks)
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                          val (env',H) = Envir.genvar a (env,Hty)
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                          val env'' =
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                            Envir.update (((F, Fty), mkhnf (binders, js, H, ks)), env')
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                      in (app(H,ls),env'') end
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                 | _  => raise Pattern))
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        and prs(s::ss,env,d,binders) =
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              let val (s',env1) = pr(s,env,d,binders)
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                  val (ss',env2) = prs(ss,env1,d,binders)
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              in (s'::ss',env2) end
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          | prs([],env,_,_) = ([],env)
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   in if downto0(is,length binders - 1) then (s,env)
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      else pr(s,env,0,binders)
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   end;
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(* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
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fun mk_ff_list(is,js) =
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    let fun mk([],[],_)        = []
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          | mk(i::is,j::js, k) = if (i:int) = j then k :: mk(is,js,k-1)
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                                        else mk(is,js,k-1)
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          | mk _               = error"mk_ff_list"
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    in mk(is,js,length is-1) end;
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fun flexflex1(env,binders,F,Fty,is,js) =
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  if is=js then env
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  else let val ks = mk_ff_list(is,js)
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       in mknewhnf(env,binders,is,F,Fty,ks) end;
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fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
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  let fun ff(F,Fty,is,G as (a,_),Gty,js) =
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            if js subset_int is
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            then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
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                 in Envir.update (((F, Fty), t), env) end
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            else let val ks = is inter_int js
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                     val Hty = type_of_G env (Fty,length is,map (idx is) ks)
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                     val (env',H) = Envir.genvar a (env,Hty)
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                     fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
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                 in Envir.update (((G, Gty), lam js), Envir.update (((F, Fty), lam is), env'))
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                 end;
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  in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end
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fun unify_types thy (T,U, env as Envir.Envir{asol,iTs,maxidx}) =
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  if T=U then env
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  else let val (iTs',maxidx') = Sign.typ_unify thy (U, T) (iTs, maxidx)
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       in Envir.Envir{asol=asol,maxidx=maxidx',iTs=iTs'} end
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       handle Type.TUNIFY => (typ_clash thy (iTs,T,U); raise Unif);
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fun unif thy binders (env,(s,t)) = case (Envir.head_norm env s, Envir.head_norm env t) of
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      (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
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         let val name = if ns = "" then nt else ns
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         in unif thy ((name,Ts)::binders) (env,(ts,tt)) end
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    | (Abs(ns,Ts,ts),t) => unif thy ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
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    | (t,Abs(nt,Tt,tt)) => unif thy ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
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    | p => cases thy (binders,env,p)
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and cases thy (binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
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       ((Var(F,Fty),ss),(Var(G,Gty),ts)) =>
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         if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts)
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                  else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts)
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      | ((Var(F,Fty),ss),_)           => flexrigid thy (env,binders,F,Fty,ints_of' env ss,t)
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      | (_,(Var(F,Fty),ts))           => flexrigid thy (env,binders,F,Fty,ints_of' env ts,s)
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      | ((Const c,ss),(Const d,ts))   => rigidrigid thy (env,binders,c,d,ss,ts)
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      | ((Free(f),ss),(Free(g),ts))   => rigidrigid thy (env,binders,f,g,ss,ts)
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      | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB thy (env,binders,i,j,ss,ts)
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      | ((Abs(_),_),_)                => raise Pattern
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      | (_,(Abs(_),_))                => raise Pattern
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      | ((Const(c,_),_),(Free(f,_),_)) => (clash c f; raise Unif)
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      | ((Const(c,_),_),(Bound i,_))   => (clashB binders i c; raise Unif)
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      | ((Free(f,_),_),(Const(c,_),_)) => (clash f c; raise Unif)
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      | ((Free(f,_),_),(Bound i,_))    => (clashB binders i f; raise Unif)
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      | ((Bound i,_),(Const(c,_),_))   => (clashB binders i c; raise Unif)
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      | ((Bound i,_),(Free(f,_),_))    => (clashB binders i f; raise Unif)
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and rigidrigid thy (env,binders,(a,Ta),(b,Tb),ss,ts) =
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      if a<>b then (clash a b; raise Unif)
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      else Library.foldl (unif thy binders) (unify_types thy (Ta,Tb,env), ss~~ts)
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and rigidrigidB thy (env,binders,i,j,ss,ts) =
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     if i <> j then (clashBB binders i j; raise Unif)
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     else Library.foldl (unif thy binders) (env ,ss~~ts)
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and flexrigid thy (params as (env,binders,F,Fty,is,t)) =
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      if occurs(F,t,env) then (ocheck_fail thy (F,t,binders,env); raise Unif)
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      else (let val (u,env') = proj(t,env,binders,is)
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            in Envir.update (((F, Fty), mkabs (binders, is, u)), env') end
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            handle Unif => (proj_fail thy params; raise Unif));
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fun unify(thy,env,tus) = Library.foldl (unif thy []) (env,tus);
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(*Eta-contract a term (fully)*)
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fun eta_contract t =
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  let
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    exception SAME;
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    fun eta (Abs (a, T, body)) =
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      ((case eta body of
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          body' as (f $ Bound 0) =>
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            if loose_bvar1 (f, 0) then Abs(a, T, body')
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            else incr_boundvars ~1 f
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        | body' => Abs (a, T, body')) handle SAME =>
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       (case body of
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          (f $ Bound 0) =>
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            if loose_bvar1 (f, 0) then raise SAME
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            else incr_boundvars ~1 f
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        | _ => raise SAME))
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      | eta (f $ t) =
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          (let val f' = eta f
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           in f' $ etah t end handle SAME => f $ eta t)
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      | eta _ = raise SAME
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    and etah t = (eta t handle SAME => t)
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  in etah t end;
clasohm@0
   297
wenzelm@12781
   298
val beta_eta_contract = eta_contract o Envir.beta_norm;
wenzelm@12781
   299
nipkow@6539
   300
(*Eta-contract a term from outside: just enough to reduce it to an atom
nipkow@6539
   301
DOESN'T QUITE WORK!
nipkow@6539
   302
*)
wenzelm@12784
   303
fun eta_contract_atom (t0 as Abs(a, T, body)) =
paulson@2725
   304
      (case  eta_contract2 body  of
wenzelm@12784
   305
        body' as (f $ Bound 0) =>
wenzelm@12784
   306
            if loose_bvar1(f,0) then Abs(a,T,body')
wenzelm@12784
   307
            else eta_contract_atom (incr_boundvars ~1 f)
paulson@2725
   308
      | _ => t0)
paulson@2725
   309
  | eta_contract_atom t = t
paulson@2725
   310
and eta_contract2 (f$t) = f $ eta_contract_atom t
paulson@2725
   311
  | eta_contract2 t     = eta_contract_atom t;
paulson@2725
   312
berghofe@13998
   313
(* put a term into eta long beta normal form *)
berghofe@13998
   314
fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t)
berghofe@13998
   315
  | eta_long Ts t = (case strip_comb t of
berghofe@13998
   316
      (Abs _, _) => eta_long Ts (Envir.beta_norm t)
wenzelm@14787
   317
    | (u, ts) =>
berghofe@13998
   318
      let
berghofe@13998
   319
        val Us = binder_types (fastype_of1 (Ts, t));
berghofe@13998
   320
        val i = length Us
berghofe@13998
   321
      in list_abs (map (pair "x") Us,
berghofe@13998
   322
        list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts))
berghofe@13998
   323
          (map (incr_boundvars i) ts @ map Bound (i - 1 downto 0))))
berghofe@13998
   324
      end);
berghofe@13998
   325
paulson@2725
   326
nipkow@678
   327
(*Tests whether 2 terms are alpha/eta-convertible and have same type.
nipkow@678
   328
  Note that Consts and Vars may have more than one type.*)
paulson@2751
   329
fun t aeconv u = aconv_aux (eta_contract_atom t, eta_contract_atom u)
paulson@2751
   330
and aconv_aux (Const(a,T), Const(b,U)) = a=b  andalso  T=U
paulson@2751
   331
  | aconv_aux (Free(a,T),  Free(b,U))  = a=b  andalso  T=U
paulson@2751
   332
  | aconv_aux (Var(v,T),   Var(w,U))   = eq_ix(v,w) andalso  T=U
wenzelm@12784
   333
  | aconv_aux (Bound i,    Bound j)    = i=j
paulson@2751
   334
  | aconv_aux (Abs(_,T,t), Abs(_,U,u)) = (t aeconv u)  andalso  T=U
wenzelm@12784
   335
  | aconv_aux (f$t,        g$u)        = (f aeconv g)  andalso (t aeconv u)
paulson@2751
   336
  | aconv_aux _ =  false;
nipkow@678
   337
nipkow@678
   338
nipkow@4820
   339
(*** Matching ***)
nipkow@4820
   340
nipkow@4820
   341
exception MATCH;
nipkow@4820
   342
wenzelm@17203
   343
fun typ_match thy (tyenv, TU) = Sign.typ_match thy TU tyenv
wenzelm@16939
   344
  handle Type.TYPE_MATCH => raise MATCH;
nipkow@4820
   345
nipkow@4820
   346
(*First-order matching;
wenzelm@17203
   347
  fomatch thy (pattern, object) returns a (tyvar,typ)list and (var,term)list.
nipkow@4820
   348
  The pattern and object may have variables in common.
nipkow@4820
   349
  Instantiation does not affect the object, so matching ?a with ?a+1 works.
nipkow@4820
   350
  Object is eta-contracted on the fly (by eta-expanding the pattern).
nipkow@4820
   351
  Precondition: the pattern is already eta-contracted!
nipkow@4820
   352
  Note: types are matched on the fly *)
wenzelm@17203
   353
fun fomatch thy =
nipkow@4820
   354
  let
nipkow@4820
   355
    fun mtch (instsp as (tyinsts,insts)) = fn
nipkow@4820
   356
        (Var(ixn,T), t)  =>
wenzelm@12784
   357
          if loose_bvar(t,0) then raise MATCH
berghofe@16651
   358
          else (case Envir.lookup' (insts, (ixn, T)) of
wenzelm@17203
   359
                  NONE => (typ_match thy (tyinsts, (T, fastype_of t)),
wenzelm@17221
   360
                           Vartab.curried_update_new (ixn, (T, t)) insts)
skalberg@15531
   361
                | SOME u => if t aeconv u then instsp else raise MATCH)
nipkow@4820
   362
      | (Free (a,T), Free (b,U)) =>
wenzelm@17203
   363
          if a=b then (typ_match thy (tyinsts,(T,U)), insts) else raise MATCH
nipkow@4820
   364
      | (Const (a,T), Const (b,U))  =>
wenzelm@17203
   365
          if a=b then (typ_match thy (tyinsts,(T,U)), insts) else raise MATCH
nipkow@4820
   366
      | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
nipkow@4820
   367
      | (Abs(_,T,t), Abs(_,U,u))  =>
wenzelm@17203
   368
          mtch (typ_match thy (tyinsts,(T,U)),insts) (t,u)
nipkow@4820
   369
      | (f$t, g$u) => mtch (mtch instsp (f,g)) (t, u)
nipkow@4820
   370
      | (t, Abs(_,U,u))  =>  mtch instsp ((incr t)$(Bound 0), u)
nipkow@4820
   371
      | _ => raise MATCH
nipkow@4820
   372
  in mtch end;
nipkow@4820
   373
wenzelm@17203
   374
fun first_order_match thy = fomatch thy (Vartab.empty, Vartab.empty);
berghofe@8406
   375
nipkow@4820
   376
(* Matching of higher-order patterns *)
nipkow@4820
   377
berghofe@15797
   378
fun match_bind(itms,binders,ixn,T,is,t) =
nipkow@4820
   379
  let val js = loose_bnos t
nipkow@4820
   380
  in if null is
wenzelm@17221
   381
     then if null js then Vartab.curried_update_new (ixn, (T, t)) itms else raise MATCH
nipkow@4820
   382
     else if js subset_int is
nipkow@4820
   383
          then let val t' = if downto0(is,length binders - 1) then t
nipkow@4820
   384
                            else mapbnd (idx is) t
wenzelm@17221
   385
               in Vartab.curried_update_new (ixn, (T, mkabs (binders, is, t'))) itms end
nipkow@4820
   386
          else raise MATCH
nipkow@4820
   387
  end;
nipkow@4820
   388
wenzelm@17203
   389
fun match thy (po as (pat,obj)) =
nipkow@678
   390
let
nipkow@4820
   391
  (* Pre: pat and obj have same type *)
nipkow@4820
   392
  fun mtch binders (env as (iTs,itms),(pat,obj)) =
nipkow@4820
   393
    case pat of
nipkow@4820
   394
      Abs(ns,Ts,ts) =>
nipkow@4820
   395
        (case obj of
nipkow@4820
   396
           Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (env,(ts,tt))
berghofe@15797
   397
         | _ => let val Tt = Envir.typ_subst_TVars iTs Ts
nipkow@4820
   398
                in mtch((ns,Tt)::binders)(env,(ts,(incr obj)$Bound(0))) end)
nipkow@4820
   399
    | _ => (case obj of
nipkow@4820
   400
              Abs(nt,Tt,tt) =>
nipkow@4820
   401
                mtch((nt,Tt)::binders)(env,((incr pat)$Bound(0),tt))
nipkow@4820
   402
            | _ => cases(binders,env,pat,obj))
nipkow@678
   403
nipkow@4820
   404
  and cases(binders,env as (iTs,itms),pat,obj) =
nipkow@4820
   405
    let val (ph,pargs) = strip_comb pat
nipkow@4820
   406
        fun rigrig1(iTs,oargs) =
skalberg@15570
   407
              Library.foldl (mtch binders) ((iTs,itms), pargs~~oargs)
wenzelm@16668
   408
        fun rigrig2((a:string,Ta),(b,Tb),oargs) =
wenzelm@16668
   409
              if a <> b then raise MATCH
wenzelm@17203
   410
              else rigrig1(typ_match thy (iTs,(Ta,Tb)), oargs)
nipkow@4820
   411
    in case ph of
berghofe@15797
   412
         Var(ixn,T) =>
nipkow@4820
   413
           let val is = ints_of pargs
berghofe@16651
   414
           in case Envir.lookup' (itms, (ixn, T)) of
berghofe@15797
   415
                NONE => (iTs,match_bind(itms,binders,ixn,T,is,obj))
skalberg@15531
   416
              | SOME u => if obj aeconv (red u is []) then env
nipkow@4820
   417
                          else raise MATCH
nipkow@4820
   418
           end
nipkow@4820
   419
       | _ =>
nipkow@4820
   420
           let val (oh,oargs) = strip_comb obj
nipkow@4820
   421
           in case (ph,oh) of
nipkow@4820
   422
                (Const c,Const d) => rigrig2(c,d,oargs)
nipkow@4820
   423
              | (Free f,Free g)   => rigrig2(f,g,oargs)
nipkow@4820
   424
              | (Bound i,Bound j) => if i<>j then raise MATCH
nipkow@4820
   425
                                     else rigrig1(iTs,oargs)
nipkow@4820
   426
              | (Abs _, _)        => raise Pattern
nipkow@4820
   427
              | (_, Abs _)        => raise Pattern
nipkow@4820
   428
              | _                 => raise MATCH
nipkow@4820
   429
           end
nipkow@4820
   430
    end;
nipkow@678
   431
nipkow@4820
   432
  val pT = fastype_of pat
nipkow@4820
   433
  and oT = fastype_of obj
wenzelm@17203
   434
  val iTs = typ_match thy (Vartab.empty, (pT,oT))
berghofe@15797
   435
  val insts2 = (iTs, Vartab.empty)
nipkow@678
   436
berghofe@15797
   437
in mtch [] (insts2, po)
wenzelm@17203
   438
   handle Pattern => fomatch thy insts2 po
nipkow@678
   439
end;
clasohm@0
   440
clasohm@0
   441
(*Predicate: does the pattern match the object?*)
wenzelm@17203
   442
fun matches thy po = (match thy po; true) handle MATCH => false;
clasohm@0
   443
nipkow@4667
   444
(* Does pat match a subterm of obj? *)
wenzelm@17203
   445
fun matches_subterm thy (pat,obj) =
wenzelm@17203
   446
  let fun msub(bounds,obj) = matches thy (pat,obj) orelse
nipkow@4667
   447
            case obj of
nipkow@4667
   448
              Abs(x,T,t) => let val y = variant bounds x
nipkow@4667
   449
                                val f = Free(":" ^ y,T)
nipkow@4667
   450
                            in msub(x::bounds,subst_bound(f,t)) end
nipkow@4667
   451
            | s$t => msub(bounds,s) orelse msub(bounds,t)
nipkow@4667
   452
            | _ => false
nipkow@4667
   453
  in msub([],obj) end;
nipkow@4667
   454
nipkow@4820
   455
fun first_order(Abs(_,_,t)) = first_order t
nipkow@4820
   456
  | first_order(t $ u) = first_order t andalso first_order u andalso
nipkow@4820
   457
                         not(is_Var t)
nipkow@4820
   458
  | first_order _ = true;
nipkow@4820
   459
nipkow@4820
   460
fun pattern(Abs(_,_,t)) = pattern t
nipkow@4820
   461
  | pattern(t) = let val (head,args) = strip_comb t
nipkow@4820
   462
                 in if is_Var head
nipkow@4820
   463
                    then let val _ = ints_of args in true end
nipkow@4820
   464
                         handle Pattern => false
nipkow@4820
   465
                    else forall pattern args
nipkow@4820
   466
                 end;
nipkow@4820
   467
wenzelm@12784
   468
wenzelm@12784
   469
(* rewriting -- simple but fast *)
wenzelm@12784
   470
wenzelm@17203
   471
fun rewrite_term thy rules procs tm =
wenzelm@12784
   472
  let
berghofe@13195
   473
    val skel0 = Bound 0;
berghofe@13195
   474
wenzelm@16939
   475
    fun variant_absfree bounds (x, T, t) =
wenzelm@12797
   476
      let
wenzelm@16986
   477
        val (x', t') = Term.dest_abs (Term.bound bounds, T, t);
wenzelm@16939
   478
        fun abs u = Abs (x, T, abstract_over (Free (x', T), u));
wenzelm@16939
   479
      in (abs, t') end;
wenzelm@12797
   480
wenzelm@12784
   481
    fun match_rew tm (tm1, tm2) =
wenzelm@16939
   482
      let val rtm = if_none (Term.rename_abs tm1 tm tm2) tm2 in
wenzelm@17203
   483
        SOME (Envir.subst_vars (match thy (tm1, tm)) rtm, rtm)
wenzelm@16939
   484
          handle MATCH => NONE
berghofe@13195
   485
      end;
wenzelm@12784
   486
skalberg@15531
   487
    fun rew (Abs (_, _, body) $ t) = SOME (subst_bound (t, body), skel0)
berghofe@13195
   488
      | rew tm = (case get_first (match_rew tm) rules of
skalberg@15570
   489
          NONE => Option.map (rpair skel0) (get_first (fn p => p tm) procs)
berghofe@13195
   490
        | x => x);
berghofe@13195
   491
wenzelm@16939
   492
    fun rew1 bounds (Var _) _ = NONE
wenzelm@16939
   493
      | rew1 bounds skel tm = (case rew2 bounds skel tm of
skalberg@15531
   494
          SOME tm1 => (case rew tm1 of
wenzelm@16939
   495
              SOME (tm2, skel') => SOME (if_none (rew1 bounds skel' tm2) tm2)
skalberg@15531
   496
            | NONE => SOME tm1)
skalberg@15531
   497
        | NONE => (case rew tm of
wenzelm@16939
   498
              SOME (tm1, skel') => SOME (if_none (rew1 bounds skel' tm1) tm1)
skalberg@15531
   499
            | NONE => NONE))
wenzelm@12784
   500
wenzelm@16939
   501
    and rew2 bounds skel (tm1 $ tm2) = (case tm1 of
wenzelm@12784
   502
            Abs (_, _, body) =>
wenzelm@12784
   503
              let val tm' = subst_bound (tm2, body)
wenzelm@16939
   504
              in SOME (if_none (rew2 bounds skel0 tm') tm') end
wenzelm@14787
   505
          | _ =>
berghofe@13195
   506
            let val (skel1, skel2) = (case skel of
berghofe@13195
   507
                skel1 $ skel2 => (skel1, skel2)
berghofe@13195
   508
              | _ => (skel0, skel0))
wenzelm@16939
   509
            in case rew1 bounds skel1 tm1 of
wenzelm@16939
   510
                SOME tm1' => (case rew1 bounds skel2 tm2 of
skalberg@15531
   511
                    SOME tm2' => SOME (tm1' $ tm2')
skalberg@15531
   512
                  | NONE => SOME (tm1' $ tm2))
wenzelm@16939
   513
              | NONE => (case rew1 bounds skel2 tm2 of
skalberg@15531
   514
                    SOME tm2' => SOME (tm1 $ tm2')
skalberg@15531
   515
                  | NONE => NONE)
berghofe@13195
   516
            end)
wenzelm@16939
   517
      | rew2 bounds skel (Abs body) =
berghofe@13195
   518
          let
wenzelm@16939
   519
            val (abs, tm') = variant_absfree bounds body;
berghofe@13195
   520
            val skel' = (case skel of Abs (_, _, skel') => skel' | _ => skel0)
wenzelm@16939
   521
          in case rew1 (bounds + 1) skel' tm' of
skalberg@15531
   522
              SOME tm'' => SOME (abs tm'')
skalberg@15531
   523
            | NONE => NONE
wenzelm@12797
   524
          end
wenzelm@16939
   525
      | rew2 _ _ _ = NONE;
wenzelm@12784
   526
wenzelm@16939
   527
  in if_none (rew1 0 skel0 tm) tm end;
wenzelm@12784
   528
clasohm@0
   529
end;
nipkow@13642
   530
nipkow@13642
   531
val trace_unify_fail = Pattern.trace_unify_fail;