src/Pure/pattern.ML
author wenzelm
Fri May 21 21:24:22 2004 +0200 (2004-05-21)
changeset 14787 724ce6e574e3
parent 14643 130076a81b84
child 14861 ca5cae7fb65a
permissions -rw-r--r--
adapted tsig interface;
     1 (*  Title:      Pure/pattern.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer
     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 Unification of Higher-Order Patterns.
     7 
     8 See also:
     9 Tobias Nipkow. Functional Unification of Higher-Order Patterns.
    10 In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993.
    11 
    12 TODO: optimize red by special-casing it
    13 *)
    14 
    15 infix aeconv;
    16 
    17 signature PATTERN =
    18 sig
    19   val trace_unify_fail  : bool ref
    20   val aeconv            : term * term -> bool
    21   val eta_contract      : term -> term
    22   val eta_long          : typ list -> term -> term
    23   val beta_eta_contract : term -> term
    24   val eta_contract_atom : term -> term
    25   val match             : Type.tsig -> term * term
    26                           -> (indexname*typ)list * (indexname*term)list
    27   val first_order_match : Type.tsig -> term * term
    28                           -> (indexname*typ)list * (indexname*term)list
    29   val matches           : Type.tsig -> term * term -> bool
    30   val matches_subterm   : Type.tsig -> term * term -> bool
    31   val unify             : Sign.sg * Envir.env * (term * term)list -> Envir.env
    32   val first_order       : term -> bool
    33   val pattern           : term -> bool
    34   val rewrite_term      : Type.tsig -> (term * term) list -> (term -> term option) list
    35                           -> term -> term
    36   exception Unif
    37   exception MATCH
    38   exception Pattern
    39 end;
    40 
    41 structure Pattern : PATTERN =
    42 struct
    43 
    44 exception Unif;
    45 exception Pattern;
    46 
    47 val trace_unify_fail = ref false;
    48 
    49 (* Only for communication between unification and error message printing *)
    50 val sgr = ref Sign.pre_pure
    51 
    52 fun string_of_term env binders t = Sign.string_of_term (!sgr)
    53   (Envir.norm_term env (subst_bounds(map Free binders,t)));
    54 
    55 fun bname binders i = fst(nth_elem(i,binders));
    56 fun bnames binders is = space_implode " " (map (bname binders) is);
    57 
    58 fun typ_clash(tye,T,U) =
    59   if !trace_unify_fail
    60   then let val t = Sign.string_of_typ (!sgr) (Envir.norm_type tye T)
    61            and u = Sign.string_of_typ (!sgr) (Envir.norm_type tye U)
    62        in tracing("The following types do not unify:\n" ^ t ^ "\n" ^ u) end
    63   else ()
    64 
    65 fun clash a b =
    66   if !trace_unify_fail then tracing("Clash: " ^ a ^ " =/= " ^ b) else ()
    67 
    68 fun boundVar binders i =
    69   "bound variable " ^ bname binders i ^ " (depth " ^ string_of_int i ^ ")";
    70 
    71 fun clashBB binders i j =
    72   if !trace_unify_fail then clash (boundVar binders i) (boundVar binders j)
    73   else ()
    74 
    75 fun clashB binders i s =
    76   if !trace_unify_fail then clash (boundVar binders i) s
    77   else ()
    78 
    79 fun proj_fail(env,binders,F,is,t) =
    80   if !trace_unify_fail
    81   then let val f = Syntax.string_of_vname F
    82            val xs = bnames binders is
    83            val u = string_of_term env binders t
    84            val ys = bnames binders (loose_bnos t \\ is)
    85        in tracing("Cannot unify variable " ^ f ^
    86                " (depending on bound variables " ^ xs ^ ")\nwith term " ^ u ^
    87                "\nTerm contains additional bound variable(s) " ^ ys)
    88        end
    89   else ()
    90 
    91 fun ocheck_fail(F,t,binders,env) =
    92   if !trace_unify_fail
    93   then let val f = Syntax.string_of_vname F
    94            val u = string_of_term env binders t
    95        in tracing("Variable " ^ f ^ " occurs in term\n" ^ u ^
    96                   "\nCannot unify!\n")
    97        end
    98   else ()
    99 
   100 fun occurs(F,t,env) =
   101     let fun occ(Var(G,_))   = (case Envir.lookup(env,G) of
   102                                  Some(t) => occ t
   103                                | None    => F=G)
   104           | occ(t1$t2)      = occ t1 orelse occ t2
   105           | occ(Abs(_,_,t)) = occ t
   106           | occ _           = false
   107     in occ t end;
   108 
   109 
   110 fun mapbnd f =
   111     let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
   112           | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
   113           | mpb d ((u1 $ u2))    = (mpb d u1)$(mpb d u2)
   114           | mpb _ atom           = atom
   115     in mpb 0 end;
   116 
   117 fun idx [] j     = ~10000
   118   | idx(i::is) j = if i=j then length is else idx is j;
   119 
   120 fun at xs i = nth_elem (i,xs);
   121 
   122 fun mkabs (binders,is,t)  =
   123     let fun mk(i::is) = let val (x,T) = nth_elem(i,binders)
   124                         in Abs(x,T,mk is) end
   125           | mk []     = t
   126     in mk is end;
   127 
   128 val incr = mapbnd (fn i => i+1);
   129 
   130 fun ints_of []             = []
   131   | ints_of (Bound i ::bs) =
   132       let val is = ints_of bs
   133       in if i mem_int is then raise Pattern else i::is end
   134   | ints_of _              = raise Pattern;
   135 
   136 fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
   137 
   138 
   139 fun app (s,(i::is)) = app (s$Bound(i),is)
   140   | app (s,[])      = s;
   141 
   142 fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
   143   | red t            []      [] = t
   144   | red t            is      jn = app (mapbnd (at jn) t,is);
   145 
   146 
   147 (* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
   148 fun split_type (T,0,Ts)                    = (Ts,T)
   149   | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
   150   | split_type _                           = error("split_type");
   151 
   152 fun type_of_G (env as Envir.Envir {iTs, ...}) (T,n,is) =
   153   let val (Ts, U) = split_type (Envir.norm_type iTs T, n, [])
   154   in map (at Ts) is ---> U end;
   155 
   156 fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));
   157 
   158 fun mknewhnf(env,binders,is,F as (a,_),T,js) =
   159   let val (env',G) = Envir.genvar a (env,type_of_G env (T,length is,js))
   160   in Envir.update((F,mkhnf(binders,is,G,js)),env') end;
   161 
   162 
   163 (* mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ] *)
   164 fun mk_proj_list is =
   165     let fun mk(i::is,j) = if i >= 0 then j :: mk(is,j-1) else mk(is,j-1)
   166           | mk([],_)    = []
   167     in mk(is,length is - 1) end;
   168 
   169 fun proj(s,env,binders,is) =
   170     let fun trans d i = if i<d then i else (idx is (i-d))+d;
   171         fun pr(s,env,d,binders) = (case Envir.head_norm env s of
   172               Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
   173                             in (Abs(a,T,t'),env') end
   174             | t => (case strip_comb t of
   175                 (c as Const _,ts) =>
   176                          let val (ts',env') = prs(ts,env,d,binders)
   177                          in (list_comb(c,ts'),env') end
   178                  | (f as Free _,ts) =>
   179                          let val (ts',env') = prs(ts,env,d,binders)
   180                          in (list_comb(f,ts'),env') end
   181                  | (Bound(i),ts) =>
   182                          let val j = trans d i
   183                          in if j < 0 then raise Unif
   184                             else let val (ts',env') = prs(ts,env,d,binders)
   185                                  in (list_comb(Bound j,ts'),env') end
   186                          end
   187                  | (Var(F as (a,_),Fty),ts) =>
   188                       let val js = ints_of' env ts;
   189                           val js' = map (trans d) js;
   190                           val ks = mk_proj_list js';
   191                           val ls = filter (fn i => i >= 0) js'
   192                           val Hty = type_of_G env (Fty,length js,ks)
   193                           val (env',H) = Envir.genvar a (env,Hty)
   194                           val env'' =
   195                                 Envir.update((F,mkhnf(binders,js,H,ks)),env')
   196                       in (app(H,ls),env'') end
   197                  | _  => raise Pattern))
   198         and prs(s::ss,env,d,binders) =
   199               let val (s',env1) = pr(s,env,d,binders)
   200                   val (ss',env2) = prs(ss,env1,d,binders)
   201               in (s'::ss',env2) end
   202           | prs([],env,_,_) = ([],env)
   203    in if downto0(is,length binders - 1) then (s,env)
   204       else pr(s,env,0,binders)
   205    end;
   206 
   207 
   208 (* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
   209 fun mk_ff_list(is,js) =
   210     let fun mk([],[],_)        = []
   211           | mk(i::is,j::js, k) = if i=j then k :: mk(is,js,k-1)
   212                                         else mk(is,js,k-1)
   213           | mk _               = error"mk_ff_list"
   214     in mk(is,js,length is-1) end;
   215 
   216 fun flexflex1(env,binders,F,Fty,is,js) =
   217   if is=js then env
   218   else let val ks = mk_ff_list(is,js)
   219        in mknewhnf(env,binders,is,F,Fty,ks) end;
   220 
   221 fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
   222   let fun ff(F,Fty,is,G as (a,_),Gty,js) =
   223             if js subset_int is
   224             then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
   225                  in Envir.update((F,t),env) end
   226             else let val ks = is inter_int js
   227                      val Hty = type_of_G env (Fty,length is,map (idx is) ks)
   228                      val (env',H) = Envir.genvar a (env,Hty)
   229                      fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
   230                  in Envir.update((G,lam js), Envir.update((F,lam is),env'))
   231                  end;
   232   in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end
   233 
   234 val tsgr = ref(Type.empty_tsig);
   235 
   236 fun unify_types(T,U, env as Envir.Envir{asol,iTs,maxidx}) =
   237   if T=U then env
   238   else let val (iTs',maxidx') = Type.unify (!tsgr) (iTs, maxidx) (U, T)
   239        in Envir.Envir{asol=asol,maxidx=maxidx',iTs=iTs'} end
   240        handle Type.TUNIFY => (typ_clash(iTs,T,U); raise Unif);
   241 
   242 fun unif binders (env,(s,t)) = case (Envir.head_norm env s, Envir.head_norm env t) of
   243       (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
   244          let val name = if ns = "" then nt else ns
   245          in unif ((name,Ts)::binders) (env,(ts,tt)) end
   246     | (Abs(ns,Ts,ts),t) => unif ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
   247     | (t,Abs(nt,Tt,tt)) => unif ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
   248     | p => cases(binders,env,p)
   249 
   250 and cases(binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
   251        ((Var(F,Fty),ss),(Var(G,Gty),ts)) =>
   252          if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts)
   253                   else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts)
   254       | ((Var(F,_),ss),_)             => flexrigid(env,binders,F,ints_of' env ss,t)
   255       | (_,(Var(F,_),ts))             => flexrigid(env,binders,F,ints_of' env ts,s)
   256       | ((Const c,ss),(Const d,ts))   => rigidrigid(env,binders,c,d,ss,ts)
   257       | ((Free(f),ss),(Free(g),ts))   => rigidrigid(env,binders,f,g,ss,ts)
   258       | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB (env,binders,i,j,ss,ts)
   259       | ((Abs(_),_),_)                => raise Pattern
   260       | (_,(Abs(_),_))                => raise Pattern
   261       | ((Const(c,_),_),(Free(f,_),_)) => (clash c f; raise Unif)
   262       | ((Const(c,_),_),(Bound i,_))   => (clashB binders i c; raise Unif)
   263       | ((Free(f,_),_),(Const(c,_),_)) => (clash f c; raise Unif)
   264       | ((Free(f,_),_),(Bound i,_))    => (clashB binders i f; raise Unif)
   265       | ((Bound i,_),(Const(c,_),_))   => (clashB binders i c; raise Unif)
   266       | ((Bound i,_),(Free(f,_),_))    => (clashB binders i f; raise Unif)
   267 
   268 
   269 and rigidrigid (env,binders,(a,Ta),(b,Tb),ss,ts) =
   270       if a<>b then (clash a b; raise Unif)
   271       else foldl (unif binders) (unify_types(Ta,Tb,env), ss~~ts)
   272 
   273 and rigidrigidB (env,binders,i,j,ss,ts) =
   274      if i <> j then (clashBB binders i j; raise Unif)
   275      else foldl (unif binders) (env ,ss~~ts)
   276 
   277 and flexrigid (params as (env,binders,F,is,t)) =
   278       if occurs(F,t,env) then (ocheck_fail(F,t,binders,env); raise Unif)
   279       else (let val (u,env') = proj(t,env,binders,is)
   280             in Envir.update((F,mkabs(binders,is,u)),env') end
   281             handle Unif => (proj_fail params; raise Unif));
   282 
   283 fun unify(sg,env,tus) = (sgr := sg; tsgr := Sign.tsig_of sg;
   284                          foldl (unif []) (env,tus));
   285 
   286 
   287 (*Eta-contract a term (fully)*)
   288 
   289 fun eta_contract t =
   290   let
   291     exception SAME;
   292     fun eta (Abs (a, T, body)) =
   293       ((case eta body of
   294           body' as (f $ Bound 0) =>
   295             if loose_bvar1 (f, 0) then Abs(a, T, body')
   296             else incr_boundvars ~1 f
   297         | body' => Abs (a, T, body')) handle SAME =>
   298        (case body of
   299           (f $ Bound 0) =>
   300             if loose_bvar1 (f, 0) then raise SAME
   301             else incr_boundvars ~1 f
   302         | _ => raise SAME))
   303       | eta (f $ t) =
   304           (let val f' = eta f
   305            in f' $ etah t end handle SAME => f $ eta t)
   306       | eta _ = raise SAME
   307     and etah t = (eta t handle SAME => t)
   308   in etah t end;
   309 
   310 val beta_eta_contract = eta_contract o Envir.beta_norm;
   311 
   312 (*Eta-contract a term from outside: just enough to reduce it to an atom
   313 DOESN'T QUITE WORK!
   314 *)
   315 fun eta_contract_atom (t0 as Abs(a, T, body)) =
   316       (case  eta_contract2 body  of
   317         body' as (f $ Bound 0) =>
   318             if loose_bvar1(f,0) then Abs(a,T,body')
   319             else eta_contract_atom (incr_boundvars ~1 f)
   320       | _ => t0)
   321   | eta_contract_atom t = t
   322 and eta_contract2 (f$t) = f $ eta_contract_atom t
   323   | eta_contract2 t     = eta_contract_atom t;
   324 
   325 (* put a term into eta long beta normal form *)
   326 fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t)
   327   | eta_long Ts t = (case strip_comb t of
   328       (Abs _, _) => eta_long Ts (Envir.beta_norm t)
   329     | (u, ts) =>
   330       let
   331         val Us = binder_types (fastype_of1 (Ts, t));
   332         val i = length Us
   333       in list_abs (map (pair "x") Us,
   334         list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts))
   335           (map (incr_boundvars i) ts @ map Bound (i - 1 downto 0))))
   336       end);
   337 
   338 
   339 (*Tests whether 2 terms are alpha/eta-convertible and have same type.
   340   Note that Consts and Vars may have more than one type.*)
   341 fun t aeconv u = aconv_aux (eta_contract_atom t, eta_contract_atom u)
   342 and aconv_aux (Const(a,T), Const(b,U)) = a=b  andalso  T=U
   343   | aconv_aux (Free(a,T),  Free(b,U))  = a=b  andalso  T=U
   344   | aconv_aux (Var(v,T),   Var(w,U))   = eq_ix(v,w) andalso  T=U
   345   | aconv_aux (Bound i,    Bound j)    = i=j
   346   | aconv_aux (Abs(_,T,t), Abs(_,U,u)) = (t aeconv u)  andalso  T=U
   347   | aconv_aux (f$t,        g$u)        = (f aeconv g)  andalso (t aeconv u)
   348   | aconv_aux _ =  false;
   349 
   350 
   351 (*** Matching ***)
   352 
   353 exception MATCH;
   354 
   355 fun typ_match tsig args = (Type.typ_match tsig args)
   356                           handle Type.TYPE_MATCH => raise MATCH;
   357 
   358 (*First-order matching;
   359   fomatch tsig (pattern, object) returns a (tyvar,typ)list and (var,term)list.
   360   The pattern and object may have variables in common.
   361   Instantiation does not affect the object, so matching ?a with ?a+1 works.
   362   Object is eta-contracted on the fly (by eta-expanding the pattern).
   363   Precondition: the pattern is already eta-contracted!
   364   Note: types are matched on the fly *)
   365 fun fomatch tsig =
   366   let
   367     fun mtch (instsp as (tyinsts,insts)) = fn
   368         (Var(ixn,T), t)  =>
   369           if loose_bvar(t,0) then raise MATCH
   370           else (case assoc_string_int(insts,ixn) of
   371                   None => (typ_match tsig (tyinsts, (T, fastype_of t)),
   372                            (ixn,t)::insts)
   373                 | Some u => if t aeconv u then instsp else raise MATCH)
   374       | (Free (a,T), Free (b,U)) =>
   375           if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
   376       | (Const (a,T), Const (b,U))  =>
   377           if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
   378       | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
   379       | (Abs(_,T,t), Abs(_,U,u))  =>
   380           mtch (typ_match tsig (tyinsts,(T,U)),insts) (t,u)
   381       | (f$t, g$u) => mtch (mtch instsp (f,g)) (t, u)
   382       | (t, Abs(_,U,u))  =>  mtch instsp ((incr t)$(Bound 0), u)
   383       | _ => raise MATCH
   384   in mtch end;
   385 
   386 fun first_order_match tsig = apfst Vartab.dest o fomatch tsig (Vartab.empty, []);
   387 
   388 (* Matching of higher-order patterns *)
   389 
   390 fun match_bind(itms,binders,ixn,is,t) =
   391   let val js = loose_bnos t
   392   in if null is
   393      then if null js then (ixn,t)::itms else raise MATCH
   394      else if js subset_int is
   395           then let val t' = if downto0(is,length binders - 1) then t
   396                             else mapbnd (idx is) t
   397                in (ixn, mkabs(binders,is,t')) :: itms end
   398           else raise MATCH
   399   end;
   400 
   401 fun match tsg (po as (pat,obj)) =
   402 let
   403   (* Pre: pat and obj have same type *)
   404   fun mtch binders (env as (iTs,itms),(pat,obj)) =
   405     case pat of
   406       Abs(ns,Ts,ts) =>
   407         (case obj of
   408            Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (env,(ts,tt))
   409          | _ => let val Tt = typ_subst_TVars_Vartab iTs Ts
   410                 in mtch((ns,Tt)::binders)(env,(ts,(incr obj)$Bound(0))) end)
   411     | _ => (case obj of
   412               Abs(nt,Tt,tt) =>
   413                 mtch((nt,Tt)::binders)(env,((incr pat)$Bound(0),tt))
   414             | _ => cases(binders,env,pat,obj))
   415 
   416   and cases(binders,env as (iTs,itms),pat,obj) =
   417     let val (ph,pargs) = strip_comb pat
   418         fun rigrig1(iTs,oargs) =
   419               foldl (mtch binders) ((iTs,itms), pargs~~oargs)
   420         fun rigrig2((a,Ta),(b,Tb),oargs) =
   421               if a<> b then raise MATCH
   422               else rigrig1(typ_match tsg (iTs,(Ta,Tb)), oargs)
   423     in case ph of
   424          Var(ixn,_) =>
   425            let val is = ints_of pargs
   426            in case assoc_string_int(itms,ixn) of
   427                 None => (iTs,match_bind(itms,binders,ixn,is,obj))
   428               | Some u => if obj aeconv (red u is []) then env
   429                           else raise MATCH
   430            end
   431        | _ =>
   432            let val (oh,oargs) = strip_comb obj
   433            in case (ph,oh) of
   434                 (Const c,Const d) => rigrig2(c,d,oargs)
   435               | (Free f,Free g)   => rigrig2(f,g,oargs)
   436               | (Bound i,Bound j) => if i<>j then raise MATCH
   437                                      else rigrig1(iTs,oargs)
   438               | (Abs _, _)        => raise Pattern
   439               | (_, Abs _)        => raise Pattern
   440               | _                 => raise MATCH
   441            end
   442     end;
   443 
   444   val pT = fastype_of pat
   445   and oT = fastype_of obj
   446   val iTs = typ_match tsg (Vartab.empty, (pT,oT))
   447   val insts2 = (iTs,[])
   448 
   449 in apfst Vartab.dest (mtch [] (insts2, po)
   450    handle Pattern => fomatch tsg insts2 po)
   451 end;
   452 
   453 (*Predicate: does the pattern match the object?*)
   454 fun matches tsig po = (match tsig po; true) handle MATCH => false;
   455 
   456 (* Does pat match a subterm of obj? *)
   457 fun matches_subterm tsig (pat,obj) =
   458   let fun msub(bounds,obj) = matches tsig (pat,obj) orelse
   459             case obj of
   460               Abs(x,T,t) => let val y = variant bounds x
   461                                 val f = Free(":" ^ y,T)
   462                             in msub(x::bounds,subst_bound(f,t)) end
   463             | s$t => msub(bounds,s) orelse msub(bounds,t)
   464             | _ => false
   465   in msub([],obj) end;
   466 
   467 fun first_order(Abs(_,_,t)) = first_order t
   468   | first_order(t $ u) = first_order t andalso first_order u andalso
   469                          not(is_Var t)
   470   | first_order _ = true;
   471 
   472 fun pattern(Abs(_,_,t)) = pattern t
   473   | pattern(t) = let val (head,args) = strip_comb t
   474                  in if is_Var head
   475                     then let val _ = ints_of args in true end
   476                          handle Pattern => false
   477                     else forall pattern args
   478                  end;
   479 
   480 
   481 (* rewriting -- simple but fast *)
   482 
   483 fun rewrite_term tsig rules procs tm =
   484   let
   485     val skel0 = Bound 0;
   486 
   487     val rhs_names =
   488       foldr (fn ((_, rhs), names) => add_term_free_names (rhs, names)) (rules, []);
   489 
   490     fun variant_absfree (x, T, t) =
   491       let
   492         val x' = variant (add_term_free_names (t, rhs_names)) x;
   493         val t' = subst_bound (Free (x', T), t);
   494       in (fn u => Abs (x, T, abstract_over (Free (x', T), u)), t') end;
   495 
   496     fun match_rew tm (tm1, tm2) =
   497       let val rtm = if_none (Term.rename_abs tm1 tm tm2) tm2
   498       in Some (subst_vars (match tsig (tm1, tm)) rtm, rtm)
   499         handle MATCH => None
   500       end;
   501 
   502     fun rew (Abs (_, _, body) $ t) = Some (subst_bound (t, body), skel0)
   503       | rew tm = (case get_first (match_rew tm) rules of
   504           None => apsome (rpair skel0) (get_first (fn p => p tm) procs)
   505         | x => x);
   506 
   507     fun rew1 (Var _) _ = None
   508       | rew1 skel tm = (case rew2 skel tm of
   509           Some tm1 => (case rew tm1 of
   510               Some (tm2, skel') => Some (if_none (rew1 skel' tm2) tm2)
   511             | None => Some tm1)
   512         | None => (case rew tm of
   513               Some (tm1, skel') => Some (if_none (rew1 skel' tm1) tm1)
   514             | None => None))
   515 
   516     and rew2 skel (tm1 $ tm2) = (case tm1 of
   517             Abs (_, _, body) =>
   518               let val tm' = subst_bound (tm2, body)
   519               in Some (if_none (rew2 skel0 tm') tm') end
   520           | _ =>
   521             let val (skel1, skel2) = (case skel of
   522                 skel1 $ skel2 => (skel1, skel2)
   523               | _ => (skel0, skel0))
   524             in case rew1 skel1 tm1 of
   525                 Some tm1' => (case rew1 skel2 tm2 of
   526                     Some tm2' => Some (tm1' $ tm2')
   527                   | None => Some (tm1' $ tm2))
   528               | None => (case rew1 skel2 tm2 of
   529                     Some tm2' => Some (tm1 $ tm2')
   530                   | None => None)
   531             end)
   532       | rew2 skel (Abs (x, T, tm)) =
   533           let
   534             val (abs, tm') = variant_absfree (x, T, tm);
   535             val skel' = (case skel of Abs (_, _, skel') => skel' | _ => skel0)
   536           in case rew1 skel' tm' of
   537               Some tm'' => Some (abs tm'')
   538             | None => None
   539           end
   540       | rew2 _ _ = None
   541 
   542   in if_none (rew1 skel0 tm) tm end;
   543 
   544 end;
   545 
   546 val trace_unify_fail = Pattern.trace_unify_fail;