src/Pure/pattern.ML
author haftmann
Tue Oct 20 16:13:01 2009 +0200 (2009-10-20)
changeset 33037 b22e44496dc2
parent 32738 15bb09ca0378
child 33038 8f9594c31de4
permissions -rw-r--r--
replaced old_style infixes eq_set, subset, union, inter and variants by generic versions
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(*  Title:      Pure/pattern.ML
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    Author:     Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer, TU Muenchen
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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 Unsynchronized.ref
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  val aeconv: term * term -> bool
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  val eta_long: typ list -> term -> term
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  val match: theory -> term * term -> Type.tyenv * Envir.tenv -> Type.tyenv * Envir.tenv
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  val first_order_match: theory -> term * term
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    -> Type.tyenv * Envir.tenv -> Type.tyenv * Envir.tenv
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  val matches: theory -> term * term -> bool
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  val matchess: theory -> term list * term list -> bool
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  val equiv: theory -> term * term -> bool
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  val matches_subterm: theory -> term * term -> bool
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  val unify: theory -> term * term -> Envir.env -> Envir.env
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  val first_order: term -> bool
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  val pattern: term -> bool
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  val match_rew: theory -> term -> term * term -> (term * term) option
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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 = Unsynchronized.ref false;
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fun string_of_term thy env binders t =
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  Syntax.string_of_term_global thy
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    (Envir.norm_term env (subst_bounds (map Free binders, t)));
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fun bname binders i = fst (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 = Syntax.string_of_typ_global thy (Envir.norm_type tye T)
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           and u = Syntax.string_of_typ_global 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 = Term.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 (subtract (op =) is (loose_bnos t))
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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 = Term.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)$(mpb d u2)
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          | mpb _ atom           = atom
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    in mpb 0 end;
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fun idx [] j     = raise Unif
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  | idx(i::is) j = if (i:int) =j then length is else idx is j;
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fun mkabs (binders,is,t)  =
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    let fun mk(i::is) = let val (x,T) = nth binders i
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                        in Abs(x,T,mk is) end
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          | mk []     = t
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    in mk is end;
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val incr = mapbnd (fn i => i+1);
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fun ints_of []             = []
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  | ints_of (Bound i ::bs) =
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      let val is = ints_of bs
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      in if member (op =) is i then raise Pattern else i::is end
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  | ints_of _              = raise Pattern;
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fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
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fun app (s,(i::is)) = app (s$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 (nth 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 (T, n, is) =
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  let
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    val tyenv = Envir.type_env env;
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    val (Ts, U) = split_type (Envir.norm_type tyenv T, n, []);
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  in map (nth 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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(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
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fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
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  | downto0 ([], n) = n = ~1;
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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 is_some 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 = map_filter 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 gen_subset (op =) (js, 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 = gen_inter (op =) (is, 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 TermOrd.indexname_ord (G,F) = LESS 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 {maxidx, tenv, tyenv}) =
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  if T = U then env
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  else
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    let val (tyenv', maxidx') = Sign.typ_unify thy (U, T) (tyenv, maxidx)
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    in Envir.Envir {maxidx = maxidx', tenv = tenv, tyenv = tyenv'} end
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    handle Type.TUNIFY => (typ_clash thy (tyenv, T, U); raise Unif);
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fun unif thy binders (s,t) env = 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) (ts,tt) env end
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    | (Abs(ns,Ts,ts),t) => unif thy ((ns,Ts)::binders) (ts,(incr t)$Bound(0)) env
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    | (t,Abs(nt,Tt,tt)) => unif thy ((nt,Tt)::binders) ((incr t)$Bound(0),tt) env
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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 env |> unify_types thy (Ta,Tb) |> fold (unif thy binders) (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 fold (unif thy binders) (ss~~ts) env
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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 = unif thy [];
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(* put a term into eta long beta normal form *)
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fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t)
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  | eta_long Ts t = (case strip_comb t of
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      (Abs _, _) => eta_long Ts (Envir.beta_norm t)
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    | (u, ts) =>
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      let
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        val Us = binder_types (fastype_of1 (Ts, t));
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        val i = length Us
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      in list_abs (map (pair "x") Us,
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        list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts))
berghofe@13998
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          (map (incr_boundvars i) ts @ map Bound (i - 1 downto 0))))
berghofe@13998
   292
      end);
berghofe@13998
   293
paulson@2725
   294
nipkow@678
   295
(*Tests whether 2 terms are alpha/eta-convertible and have same type.
nipkow@678
   296
  Note that Consts and Vars may have more than one type.*)
wenzelm@30555
   297
fun t aeconv u = t aconv u orelse
wenzelm@30555
   298
  Envir.eta_contract t aconv Envir.eta_contract u;
nipkow@678
   299
nipkow@678
   300
nipkow@4820
   301
(*** Matching ***)
nipkow@4820
   302
nipkow@4820
   303
exception MATCH;
nipkow@4820
   304
wenzelm@18182
   305
fun typ_match thy TU tyenv = Sign.typ_match thy TU tyenv
wenzelm@16939
   306
  handle Type.TYPE_MATCH => raise MATCH;
nipkow@4820
   307
nipkow@4820
   308
(*First-order matching;
nipkow@4820
   309
  The pattern and object may have variables in common.
nipkow@4820
   310
  Instantiation does not affect the object, so matching ?a with ?a+1 works.
nipkow@4820
   311
  Object is eta-contracted on the fly (by eta-expanding the pattern).
nipkow@4820
   312
  Precondition: the pattern is already eta-contracted!
wenzelm@18182
   313
  Types are matched on the fly*)
wenzelm@18182
   314
fun first_order_match thy =
nipkow@4820
   315
  let
berghofe@25473
   316
    fun mtch k (instsp as (tyinsts,insts)) = fn
nipkow@4820
   317
        (Var(ixn,T), t)  =>
berghofe@25473
   318
          if k > 0 andalso loose_bvar(t,0) then raise MATCH
berghofe@16651
   319
          else (case Envir.lookup' (insts, (ixn, T)) of
wenzelm@18182
   320
                  NONE => (typ_match thy (T, fastype_of t) tyinsts,
wenzelm@17412
   321
                           Vartab.update_new (ixn, (T, t)) insts)
skalberg@15531
   322
                | SOME u => if t aeconv u then instsp else raise MATCH)
nipkow@4820
   323
      | (Free (a,T), Free (b,U)) =>
wenzelm@18182
   324
          if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH
nipkow@4820
   325
      | (Const (a,T), Const (b,U))  =>
wenzelm@18182
   326
          if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH
nipkow@4820
   327
      | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
nipkow@4820
   328
      | (Abs(_,T,t), Abs(_,U,u))  =>
berghofe@25473
   329
          mtch (k + 1) (typ_match thy (T,U) tyinsts, insts) (t,u)
berghofe@25473
   330
      | (f$t, g$u) => mtch k (mtch k instsp (f,g)) (t, u)
berghofe@25473
   331
      | (t, Abs(_,U,u))  =>  mtch (k + 1) instsp ((incr t)$(Bound 0), u)
nipkow@4820
   332
      | _ => raise MATCH
berghofe@25473
   333
  in fn tu => fn env => mtch 0 env tu end;
nipkow@4820
   334
berghofe@8406
   335
nipkow@4820
   336
(* Matching of higher-order patterns *)
nipkow@4820
   337
berghofe@15797
   338
fun match_bind(itms,binders,ixn,T,is,t) =
nipkow@4820
   339
  let val js = loose_bnos t
nipkow@4820
   340
  in if null is
wenzelm@17412
   341
     then if null js then Vartab.update_new (ixn, (T, t)) itms else raise MATCH
haftmann@33037
   342
     else if gen_subset (op =) (js, is)
nipkow@4820
   343
          then let val t' = if downto0(is,length binders - 1) then t
nipkow@4820
   344
                            else mapbnd (idx is) t
wenzelm@17412
   345
               in Vartab.update_new (ixn, (T, mkabs (binders, is, t'))) itms end
nipkow@4820
   346
          else raise MATCH
nipkow@4820
   347
  end;
nipkow@4820
   348
wenzelm@18182
   349
fun match thy (po as (pat,obj)) envir =
nipkow@678
   350
let
nipkow@4820
   351
  (* Pre: pat and obj have same type *)
wenzelm@18182
   352
  fun mtch binders (pat,obj) (env as (iTs,itms)) =
nipkow@4820
   353
    case pat of
nipkow@4820
   354
      Abs(ns,Ts,ts) =>
nipkow@4820
   355
        (case obj of
wenzelm@18182
   356
           Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (ts,tt) env
wenzelm@32035
   357
         | _ => let val Tt = Envir.subst_type iTs Ts
wenzelm@18182
   358
                in mtch((ns,Tt)::binders) (ts,(incr obj)$Bound(0)) env end)
nipkow@4820
   359
    | _ => (case obj of
nipkow@4820
   360
              Abs(nt,Tt,tt) =>
wenzelm@18182
   361
                mtch((nt,Tt)::binders) ((incr pat)$Bound(0),tt) env
nipkow@4820
   362
            | _ => cases(binders,env,pat,obj))
nipkow@678
   363
nipkow@4820
   364
  and cases(binders,env as (iTs,itms),pat,obj) =
nipkow@4820
   365
    let val (ph,pargs) = strip_comb pat
wenzelm@18182
   366
        fun rigrig1(iTs,oargs) = fold (mtch binders) (pargs~~oargs) (iTs,itms)
wenzelm@16668
   367
        fun rigrig2((a:string,Ta),(b,Tb),oargs) =
wenzelm@16668
   368
              if a <> b then raise MATCH
wenzelm@18182
   369
              else rigrig1(typ_match thy (Ta,Tb) iTs, oargs)
nipkow@4820
   370
    in case ph of
berghofe@15797
   371
         Var(ixn,T) =>
nipkow@4820
   372
           let val is = ints_of pargs
berghofe@16651
   373
           in case Envir.lookup' (itms, (ixn, T)) of
berghofe@15797
   374
                NONE => (iTs,match_bind(itms,binders,ixn,T,is,obj))
skalberg@15531
   375
              | SOME u => if obj aeconv (red u is []) then env
nipkow@4820
   376
                          else raise MATCH
nipkow@4820
   377
           end
nipkow@4820
   378
       | _ =>
nipkow@4820
   379
           let val (oh,oargs) = strip_comb obj
nipkow@4820
   380
           in case (ph,oh) of
nipkow@4820
   381
                (Const c,Const d) => rigrig2(c,d,oargs)
nipkow@4820
   382
              | (Free f,Free g)   => rigrig2(f,g,oargs)
nipkow@4820
   383
              | (Bound i,Bound j) => if i<>j then raise MATCH
nipkow@4820
   384
                                     else rigrig1(iTs,oargs)
nipkow@4820
   385
              | (Abs _, _)        => raise Pattern
nipkow@4820
   386
              | (_, Abs _)        => raise Pattern
nipkow@4820
   387
              | _                 => raise MATCH
nipkow@4820
   388
           end
nipkow@4820
   389
    end;
nipkow@678
   390
nipkow@4820
   391
  val pT = fastype_of pat
nipkow@4820
   392
  and oT = fastype_of obj
wenzelm@18182
   393
  val envir' = apfst (typ_match thy (pT, oT)) envir;
wenzelm@18182
   394
in mtch [] po envir' handle Pattern => first_order_match thy po envir' end;
clasohm@0
   395
wenzelm@18182
   396
fun matches thy po = (match thy po (Vartab.empty, Vartab.empty); true) handle MATCH => false;
wenzelm@18182
   397
haftmann@28348
   398
fun matchess thy pos = (fold (match thy) (op ~~ pos) (Vartab.empty, Vartab.empty); true) handle MATCH => false;
haftmann@28348
   399
wenzelm@19880
   400
fun equiv thy (t, u) = matches thy (t, u) andalso matches thy (u, t);
wenzelm@19880
   401
clasohm@0
   402
nipkow@4667
   403
(* Does pat match a subterm of obj? *)
wenzelm@22255
   404
fun matches_subterm thy (pat, obj) =
wenzelm@22255
   405
  let
wenzelm@22255
   406
    fun msub bounds obj = matches thy (pat, obj) orelse
wenzelm@22255
   407
      (case obj of
wenzelm@22255
   408
        Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
wenzelm@22255
   409
      | t $ u => msub bounds t orelse msub bounds u
wenzelm@22255
   410
      | _ => false)
wenzelm@22255
   411
  in msub 0 obj end;
nipkow@4667
   412
nipkow@4820
   413
fun first_order(Abs(_,_,t)) = first_order t
nipkow@4820
   414
  | first_order(t $ u) = first_order t andalso first_order u andalso
nipkow@4820
   415
                         not(is_Var t)
nipkow@4820
   416
  | first_order _ = true;
nipkow@4820
   417
wenzelm@20672
   418
fun pattern (Abs (_, _, t)) = pattern t
wenzelm@20672
   419
  | pattern t =
wenzelm@20672
   420
      let val (head, args) = strip_comb t in
wenzelm@20672
   421
        if is_Var head then
wenzelm@20672
   422
          forall is_Bound args andalso not (has_duplicates (op aconv) args)
wenzelm@20672
   423
        else forall pattern args
wenzelm@20672
   424
      end;
nipkow@4820
   425
wenzelm@12784
   426
wenzelm@12784
   427
(* rewriting -- simple but fast *)
wenzelm@12784
   428
wenzelm@30565
   429
fun match_rew thy tm (tm1, tm2) =
wenzelm@30565
   430
  let val rtm = the_default tm2 (Term.rename_abs tm1 tm tm2) in
wenzelm@32035
   431
    SOME (Envir.subst_term (match thy (tm1, tm) (Vartab.empty, Vartab.empty)) rtm, rtm)
wenzelm@30565
   432
      handle MATCH => NONE
wenzelm@30565
   433
  end;
wenzelm@30565
   434
wenzelm@17203
   435
fun rewrite_term thy rules procs tm =
wenzelm@12784
   436
  let
berghofe@13195
   437
    val skel0 = Bound 0;
berghofe@13195
   438
wenzelm@16939
   439
    fun variant_absfree bounds (x, T, t) =
wenzelm@12797
   440
      let
wenzelm@20079
   441
        val (x', t') = Term.dest_abs (Name.bound bounds, T, t);
wenzelm@16939
   442
        fun abs u = Abs (x, T, abstract_over (Free (x', T), u));
wenzelm@16939
   443
      in (abs, t') end;
wenzelm@12797
   444
skalberg@15531
   445
    fun rew (Abs (_, _, body) $ t) = SOME (subst_bound (t, body), skel0)
wenzelm@30565
   446
      | rew tm =
wenzelm@30565
   447
          (case get_first (match_rew thy tm) rules of
wenzelm@30565
   448
            NONE => Option.map (rpair skel0) (get_first (fn p => p tm) procs)
wenzelm@30565
   449
          | x => x);
berghofe@13195
   450
wenzelm@16939
   451
    fun rew1 bounds (Var _) _ = NONE
wenzelm@16939
   452
      | rew1 bounds skel tm = (case rew2 bounds skel tm of
skalberg@15531
   453
          SOME tm1 => (case rew tm1 of
wenzelm@18940
   454
              SOME (tm2, skel') => SOME (the_default tm2 (rew1 bounds skel' tm2))
skalberg@15531
   455
            | NONE => SOME tm1)
skalberg@15531
   456
        | NONE => (case rew tm of
wenzelm@18940
   457
              SOME (tm1, skel') => SOME (the_default tm1 (rew1 bounds skel' tm1))
skalberg@15531
   458
            | NONE => NONE))
wenzelm@12784
   459
wenzelm@16939
   460
    and rew2 bounds skel (tm1 $ tm2) = (case tm1 of
wenzelm@12784
   461
            Abs (_, _, body) =>
wenzelm@12784
   462
              let val tm' = subst_bound (tm2, body)
wenzelm@18940
   463
              in SOME (the_default tm' (rew2 bounds skel0 tm')) end
wenzelm@14787
   464
          | _ =>
berghofe@13195
   465
            let val (skel1, skel2) = (case skel of
berghofe@13195
   466
                skel1 $ skel2 => (skel1, skel2)
berghofe@13195
   467
              | _ => (skel0, skel0))
wenzelm@16939
   468
            in case rew1 bounds skel1 tm1 of
wenzelm@16939
   469
                SOME tm1' => (case rew1 bounds skel2 tm2 of
skalberg@15531
   470
                    SOME tm2' => SOME (tm1' $ tm2')
skalberg@15531
   471
                  | NONE => SOME (tm1' $ tm2))
wenzelm@16939
   472
              | NONE => (case rew1 bounds skel2 tm2 of
skalberg@15531
   473
                    SOME tm2' => SOME (tm1 $ tm2')
skalberg@15531
   474
                  | NONE => NONE)
berghofe@13195
   475
            end)
wenzelm@16939
   476
      | rew2 bounds skel (Abs body) =
berghofe@13195
   477
          let
wenzelm@16939
   478
            val (abs, tm') = variant_absfree bounds body;
berghofe@13195
   479
            val skel' = (case skel of Abs (_, _, skel') => skel' | _ => skel0)
wenzelm@16939
   480
          in case rew1 (bounds + 1) skel' tm' of
skalberg@15531
   481
              SOME tm'' => SOME (abs tm'')
skalberg@15531
   482
            | NONE => NONE
wenzelm@12797
   483
          end
wenzelm@16939
   484
      | rew2 _ _ _ = NONE;
wenzelm@12784
   485
wenzelm@18940
   486
  in the_default tm (rew1 0 skel0 tm) end;
wenzelm@12784
   487
clasohm@0
   488
end;
nipkow@13642
   489
nipkow@13642
   490
val trace_unify_fail = Pattern.trace_unify_fail;