src/Pure/pattern.ML
author wenzelm
Thu Jan 17 21:00:38 2002 +0100 (2002-01-17)
changeset 12797 4de06a8f67ef
parent 12784 bab3b002cbbb
child 12817 fcbb6ad5c790
permissions -rw-r--r--
eta_contract with sharing (by berghofe);
rewrite_term: proper handling of Abs cong;
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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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  type type_sig
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  type sg
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  type env
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  val aeconv            : term * term -> bool
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  val eta_contract      : 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             : type_sig -> term * term
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                          -> (indexname*typ)list * (indexname*term)list
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  val first_order_match : type_sig -> term * term
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                          -> (indexname*typ)list * (indexname*term)list
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  val matches           : type_sig -> term * term -> bool
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  val matches_subterm   : type_sig -> term * term -> bool
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  val unify             : sg * env * (term * term)list -> 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      : type_sig -> (term * term) 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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type type_sig = Type.type_sig
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type sg = Sign.sg
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type env = Envir.env
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exception Unif;
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exception Pattern;
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fun occurs(F,t,env) =
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    let fun occ(Var(G,_))   = (case Envir.lookup(env,G) 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)$(mpb d u2)
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          | mpb _ atom           = atom
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    in mpb 0 end;
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fun idx [] j     = ~10000
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  | idx(i::is) j = if i=j then length is else idx is j;
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fun at xs i = nth_elem (i,xs);
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fun mkabs (binders,is,t)  =
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    let fun mk(i::is) = let val (x,T) = nth_elem(i,binders)
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                        in Abs(x,T,mk is) end
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          | mk []     = t
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    in mk is end;
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val incr = mapbnd (fn i => i+1);
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fun ints_of []             = []
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  | ints_of (Bound i ::bs) =
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      let val is = ints_of bs
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      in if i mem_int is then raise Pattern else i::is end
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  | ints_of _              = raise Pattern;
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fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
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fun app (s,(i::is)) = app (s$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 (T,n,is) =
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  let val (Ts,U) = split_type(T,n,[]) 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(T,length is,js))
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  in Envir.update((F,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 i >= 0 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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                         in if j < 0 then raise Unif
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                            else let val (ts',env') = prs(ts,env,d,binders)
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                                 in (list_comb(Bound j,ts'),env') end
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                         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 (trans d) js;
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                          val ks = mk_proj_list js';
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                          val ls = filter (fn i => i >= 0) js'
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                          val Hty = type_of_G(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,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=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,t),env) end
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            else let val ks = is inter_int js
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                     val Hty = type_of_G(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,lam js), Envir.update((F,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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val tsgr = ref(Type.tsig0);
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fun unify_types(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') = Type.unify (!tsgr) (iTs, maxidx) (U, T)
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       in Envir.Envir{asol=asol,maxidx=maxidx',iTs=iTs'} end
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       handle Type.TUNIFY => raise Unif;
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fun unif 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 ((name,Ts)::binders) (env,(ts,tt)) end
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    | (Abs(ns,Ts,ts),t) => unif ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
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    | (t,Abs(nt,Tt,tt)) => unif ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
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    | p => cases(binders,env,p)
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and cases(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,_),ss),_)             => flexrigid(env,binders,F,ints_of' env ss,t)
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      | (_,(Var(F,_),ts))             => flexrigid(env,binders,F,ints_of' env ts,s)
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      | ((Const c,ss),(Const d,ts))   => rigidrigid(env,binders,c,d,ss,ts)
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      | ((Free(f),ss),(Free(g),ts))   => rigidrigid(env,binders,f,g,ss,ts)
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      | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB (env,binders,i,j,ss,ts)
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      | ((Abs(_),_),_)                => raise Pattern
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      | (_,(Abs(_),_))                => raise Pattern
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      | _                             => raise Unif
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and rigidrigid (env,binders,(a,Ta),(b,Tb),ss,ts) =
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      if a<>b then raise Unif
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      else foldl (unif binders) (unify_types(Ta,Tb,env), ss~~ts)
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and rigidrigidB (env,binders,i,j,ss,ts) =
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     if i <> j then raise Unif else foldl (unif binders) (env ,ss~~ts)
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and flexrigid (env,binders,F,is,t) =
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      if occurs(F,t,env) then raise Unif
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      else let val (u,env') = proj(t,env,binders,is)
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           in Envir.update((F,mkabs(binders,is,u)),env') end;
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fun unify(sg,env,tus) = (tsgr := #tsig(Sign.rep_sg sg);
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                         foldl (unif []) (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;
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val beta_eta_contract = eta_contract o Envir.beta_norm;
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(*Eta-contract a term from outside: just enough to reduce it to an atom
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DOESN'T QUITE WORK!
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*)
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fun eta_contract_atom (t0 as Abs(a, T, body)) =
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      (case  eta_contract2 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 eta_contract_atom (incr_boundvars ~1 f)
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      | _ => t0)
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  | eta_contract_atom t = t
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and eta_contract2 (f$t) = f $ eta_contract_atom t
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  | eta_contract2 t     = eta_contract_atom t;
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(*Tests whether 2 terms are alpha/eta-convertible and have same type.
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  Note that Consts and Vars may have more than one type.*)
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fun t aeconv u = aconv_aux (eta_contract_atom t, eta_contract_atom u)
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and aconv_aux (Const(a,T), Const(b,U)) = a=b  andalso  T=U
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  | aconv_aux (Free(a,T),  Free(b,U))  = a=b  andalso  T=U
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  | aconv_aux (Var(v,T),   Var(w,U))   = eq_ix(v,w) andalso  T=U
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  | aconv_aux (Bound i,    Bound j)    = i=j
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  | aconv_aux (Abs(_,T,t), Abs(_,U,u)) = (t aeconv u)  andalso  T=U
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  | aconv_aux (f$t,        g$u)        = (f aeconv g)  andalso (t aeconv u)
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  | aconv_aux _ =  false;
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(*** Matching ***)
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exception MATCH;
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fun typ_match tsig args = (Type.typ_match tsig args)
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                          handle Type.TYPE_MATCH => raise MATCH;
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(*First-order matching;
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  fomatch tsig (pattern, object) returns a (tyvar,typ)list and (var,term)list.
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  The pattern and object may have variables in common.
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  Instantiation does not affect the object, so matching ?a with ?a+1 works.
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  Object is eta-contracted on the fly (by eta-expanding the pattern).
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  Precondition: the pattern is already eta-contracted!
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  Note: types are matched on the fly *)
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fun fomatch tsig =
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  let
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    fun mtch (instsp as (tyinsts,insts)) = fn
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        (Var(ixn,T), t)  =>
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          if loose_bvar(t,0) then raise MATCH
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          else (case assoc_string_int(insts,ixn) of
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                  None => (typ_match tsig (tyinsts, (T, fastype_of t)),
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                           (ixn,t)::insts)
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                | Some u => if t aeconv u then instsp else raise MATCH)
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      | (Free (a,T), Free (b,U)) =>
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          if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
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      | (Const (a,T), Const (b,U))  =>
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          if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
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      | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
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      | (Abs(_,T,t), Abs(_,U,u))  =>
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          mtch (typ_match tsig (tyinsts,(T,U)),insts) (t,u)
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      | (f$t, g$u) => mtch (mtch instsp (f,g)) (t, u)
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      | (t, Abs(_,U,u))  =>  mtch instsp ((incr t)$(Bound 0), u)
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      | _ => raise MATCH
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  in mtch end;
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berghofe@8406
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fun first_order_match tsig = apfst Vartab.dest o fomatch tsig (Vartab.empty, []);
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(* Matching of higher-order patterns *)
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fun match_bind(itms,binders,ixn,is,t) =
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  let val js = loose_bnos t
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  in if null is
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     then if null js then (ixn,t)::itms else raise MATCH
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     else if js subset_int is
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          then let val t' = if downto0(is,length binders - 1) then t
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                            else mapbnd (idx is) t
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               in (ixn, mkabs(binders,is,t')) :: itms end
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          else raise MATCH
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  end;
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   330
fun match tsg (po as (pat,obj)) =
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let
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  (* Pre: pat and obj have same type *)
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  fun mtch binders (env as (iTs,itms),(pat,obj)) =
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    case pat of
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      Abs(ns,Ts,ts) =>
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        (case obj of
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           Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (env,(ts,tt))
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         | _ => let val Tt = typ_subst_TVars_Vartab iTs Ts
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   339
                in mtch((ns,Tt)::binders)(env,(ts,(incr obj)$Bound(0))) end)
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   340
    | _ => (case obj of
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   341
              Abs(nt,Tt,tt) =>
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   342
                mtch((nt,Tt)::binders)(env,((incr pat)$Bound(0),tt))
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   343
            | _ => cases(binders,env,pat,obj))
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   344
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   345
  and cases(binders,env as (iTs,itms),pat,obj) =
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    let val (ph,pargs) = strip_comb pat
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        fun rigrig1(iTs,oargs) =
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              foldl (mtch binders) ((iTs,itms), pargs~~oargs)
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        fun rigrig2((a,Ta),(b,Tb),oargs) =
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              if a<> b then raise MATCH
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              else rigrig1(typ_match tsg (iTs,(Ta,Tb)), oargs)
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   352
    in case ph of
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         Var(ixn,_) =>
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   354
           let val is = ints_of pargs
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   355
           in case assoc_string_int(itms,ixn) of
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   356
                None => (iTs,match_bind(itms,binders,ixn,is,obj))
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   357
              | Some u => if obj aeconv (red u is []) then env
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   358
                          else raise MATCH
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   359
           end
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   360
       | _ =>
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   361
           let val (oh,oargs) = strip_comb obj
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   362
           in case (ph,oh) of
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   363
                (Const c,Const d) => rigrig2(c,d,oargs)
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   364
              | (Free f,Free g)   => rigrig2(f,g,oargs)
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   365
              | (Bound i,Bound j) => if i<>j then raise MATCH
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   366
                                     else rigrig1(iTs,oargs)
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   367
              | (Abs _, _)        => raise Pattern
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   368
              | (_, Abs _)        => raise Pattern
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   369
              | _                 => raise MATCH
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   370
           end
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   371
    end;
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   372
nipkow@4820
   373
  val pT = fastype_of pat
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   374
  and oT = fastype_of obj
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   375
  val iTs = typ_match tsg (Vartab.empty, (pT,oT))
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   376
  val insts2 = (iTs,[])
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   377
berghofe@8406
   378
in apfst Vartab.dest (mtch [] (insts2, po)
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   379
   handle Pattern => fomatch tsg insts2 po)
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   380
end;
clasohm@0
   381
clasohm@0
   382
(*Predicate: does the pattern match the object?*)
nipkow@678
   383
fun matches tsig po = (match tsig po; true) handle MATCH => false;
clasohm@0
   384
nipkow@4667
   385
(* Does pat match a subterm of obj? *)
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   386
fun matches_subterm tsig (pat,obj) =
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   387
  let fun msub(bounds,obj) = matches tsig (pat,obj) orelse
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   388
            case obj of
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   389
              Abs(x,T,t) => let val y = variant bounds x
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   390
                                val f = Free(":" ^ y,T)
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   391
                            in msub(x::bounds,subst_bound(f,t)) end
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   392
            | s$t => msub(bounds,s) orelse msub(bounds,t)
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   393
            | _ => false
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   394
  in msub([],obj) end;
nipkow@4667
   395
nipkow@4820
   396
fun first_order(Abs(_,_,t)) = first_order t
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   397
  | first_order(t $ u) = first_order t andalso first_order u andalso
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   398
                         not(is_Var t)
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   399
  | first_order _ = true;
nipkow@4820
   400
nipkow@4820
   401
fun pattern(Abs(_,_,t)) = pattern t
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   402
  | pattern(t) = let val (head,args) = strip_comb t
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   403
                 in if is_Var head
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   404
                    then let val _ = ints_of args in true end
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   405
                         handle Pattern => false
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   406
                    else forall pattern args
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   407
                 end;
nipkow@4820
   408
wenzelm@12784
   409
wenzelm@12784
   410
(* rewriting -- simple but fast *)
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   411
wenzelm@12784
   412
fun rewrite_term tsig rules tm =
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   413
  let
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   414
    val rhs_names =
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   415
      foldr (fn ((_, rhs), names) => add_term_free_names (rhs, names)) (rules, []);
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   416
    fun variant_absfree (x, T, t) =
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   417
      let
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   418
        val x' = variant (add_term_free_names (t, rhs_names)) x;
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   419
        val t' = subst_bound (Free (x', T), t);
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   420
      in (fn u => Abs (x, T, abstract_over (Free (x', T), u)), t') end;
wenzelm@12797
   421
wenzelm@12784
   422
    fun match_rew tm (tm1, tm2) =
wenzelm@12784
   423
      Some (subst_vars (match tsig (tm1, tm)) tm2) handle MATCH => None;
wenzelm@12784
   424
    fun rew (Abs (_, _, body) $ t) = Some (subst_bound (t, body))
wenzelm@12784
   425
      | rew tm = get_first (match_rew tm) rules;
wenzelm@12784
   426
wenzelm@12784
   427
    fun rew0 (tm as Abs (_, _, tm' $ Bound 0)) =
wenzelm@12784
   428
          if loose_bvar1 (tm', 0) then rew tm
wenzelm@12784
   429
          else
wenzelm@12784
   430
            let val tm'' = incr_boundvars ~1 tm'
wenzelm@12784
   431
            in Some (if_none (rew tm'') tm'') end
wenzelm@12784
   432
      | rew0 tm = rew tm;
wenzelm@12784
   433
wenzelm@12784
   434
    fun rew1 tm = (case rew2 tm of
wenzelm@12784
   435
          Some tm1 => (case rew0 tm1 of
wenzelm@12784
   436
              Some tm2 => Some (if_none (rew1 tm2) tm2)
wenzelm@12784
   437
            | None => Some tm1)
wenzelm@12784
   438
        | None => (case rew0 tm of
wenzelm@12784
   439
              Some tm1 => Some (if_none (rew1 tm1) tm1)
wenzelm@12784
   440
            | None => None))
wenzelm@12784
   441
wenzelm@12784
   442
    and rew2 (tm1 $ tm2) = (case tm1 of
wenzelm@12784
   443
            Abs (_, _, body) =>
wenzelm@12784
   444
              let val tm' = subst_bound (tm2, body)
wenzelm@12784
   445
              in Some (if_none (rew2 tm') tm') end
wenzelm@12784
   446
          | _ => (case rew1 tm1 of
wenzelm@12784
   447
              Some tm1' => (case rew1 tm2 of
wenzelm@12784
   448
                  Some tm2' => Some (tm1' $ tm2')
wenzelm@12784
   449
                | None => Some (tm1' $ tm2))
wenzelm@12784
   450
            | None => (case rew1 tm2 of
wenzelm@12784
   451
                  Some tm2' => Some (tm1 $ tm2')
wenzelm@12784
   452
                | None => None)))
wenzelm@12797
   453
      | rew2 (Abs (x, T, tm)) =
wenzelm@12797
   454
          let val (abs, tm') = variant_absfree (x, T, tm) in
wenzelm@12797
   455
            (case rew1 tm' of
wenzelm@12797
   456
              Some tm'' => Some (abs tm'')
wenzelm@12797
   457
            | None => None)
wenzelm@12797
   458
          end
wenzelm@12784
   459
      | rew2 _ = None
wenzelm@12784
   460
wenzelm@12797
   461
  in if_none (timeap_msg "FIXME: rewrite_term" rew1 tm) tm end;
wenzelm@12784
   462
clasohm@0
   463
end;