src/Pure/pattern.ML
author wenzelm
Fri Jul 17 23:11:40 2009 +0200 (2009-07-17)
changeset 32035 8e77b6a250d5
parent 32032 a6a6e8031c14
child 32738 15bb09ca0378
permissions -rw-r--r--
tuned/modernized Envir.subst_XXX;
     1 (*  Title:      Pure/pattern.ML
     2     Author:     Tobias Nipkow, Christine Heinzelmann, and Stefan Berghofer, TU Muenchen
     3 
     4 Unification of Higher-Order Patterns.
     5 
     6 See also:
     7 Tobias Nipkow. Functional Unification of Higher-Order Patterns.
     8 In Proceedings of the 8th IEEE Symposium Logic in Computer Science, 1993.
     9 
    10 TODO: optimize red by special-casing it
    11 *)
    12 
    13 infix aeconv;
    14 
    15 signature PATTERN =
    16 sig
    17   val trace_unify_fail: bool ref
    18   val aeconv: term * term -> bool
    19   val eta_long: typ list -> term -> term
    20   val match: theory -> term * term -> Type.tyenv * Envir.tenv -> Type.tyenv * Envir.tenv
    21   val first_order_match: theory -> term * term
    22     -> Type.tyenv * Envir.tenv -> Type.tyenv * Envir.tenv
    23   val matches: theory -> term * term -> bool
    24   val matchess: theory -> term list * term list -> bool
    25   val equiv: theory -> term * term -> bool
    26   val matches_subterm: theory -> term * term -> bool
    27   val unify: theory -> term * term -> Envir.env -> Envir.env
    28   val first_order: term -> bool
    29   val pattern: term -> bool
    30   val match_rew: theory -> term -> term * term -> (term * term) option
    31   val rewrite_term: theory -> (term * term) list -> (term -> term option) list -> term -> term
    32   exception Unif
    33   exception MATCH
    34   exception Pattern
    35 end;
    36 
    37 structure Pattern: PATTERN =
    38 struct
    39 
    40 exception Unif;
    41 exception Pattern;
    42 
    43 val trace_unify_fail = ref false;
    44 
    45 fun string_of_term thy env binders t =
    46   Syntax.string_of_term_global thy
    47     (Envir.norm_term env (subst_bounds (map Free binders, t)));
    48 
    49 fun bname binders i = fst (nth binders i);
    50 fun bnames binders is = space_implode " " (map (bname binders) is);
    51 
    52 fun typ_clash thy (tye,T,U) =
    53   if !trace_unify_fail
    54   then let val t = Syntax.string_of_typ_global thy (Envir.norm_type tye T)
    55            and u = Syntax.string_of_typ_global thy (Envir.norm_type tye U)
    56        in tracing("The following types do not unify:\n" ^ t ^ "\n" ^ u) end
    57   else ()
    58 
    59 fun clash a b =
    60   if !trace_unify_fail then tracing("Clash: " ^ a ^ " =/= " ^ b) else ()
    61 
    62 fun boundVar binders i =
    63   "bound variable " ^ bname binders i ^ " (depth " ^ string_of_int i ^ ")";
    64 
    65 fun clashBB binders i j =
    66   if !trace_unify_fail then clash (boundVar binders i) (boundVar binders j)
    67   else ()
    68 
    69 fun clashB binders i s =
    70   if !trace_unify_fail then clash (boundVar binders i) s
    71   else ()
    72 
    73 fun proj_fail thy (env,binders,F,_,is,t) =
    74   if !trace_unify_fail
    75   then let val f = Term.string_of_vname F
    76            val xs = bnames binders is
    77            val u = string_of_term thy env binders t
    78            val ys = bnames binders (subtract (op =) is (loose_bnos t))
    79        in tracing("Cannot unify variable " ^ f ^
    80                " (depending on bound variables " ^ xs ^ ")\nwith term " ^ u ^
    81                "\nTerm contains additional bound variable(s) " ^ ys)
    82        end
    83   else ()
    84 
    85 fun ocheck_fail thy (F,t,binders,env) =
    86   if !trace_unify_fail
    87   then let val f = Term.string_of_vname F
    88            val u = string_of_term thy env binders t
    89        in tracing("Variable " ^ f ^ " occurs in term\n" ^ u ^
    90                   "\nCannot unify!\n")
    91        end
    92   else ()
    93 
    94 fun occurs(F,t,env) =
    95     let fun occ(Var (G, T))   = (case Envir.lookup (env, (G, T)) of
    96                                  SOME(t) => occ t
    97                                | NONE    => F=G)
    98           | occ(t1$t2)      = occ t1 orelse occ t2
    99           | occ(Abs(_,_,t)) = occ t
   100           | occ _           = false
   101     in occ t end;
   102 
   103 
   104 fun mapbnd f =
   105     let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
   106           | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
   107           | mpb d ((u1 $ u2))    = (mpb d u1)$(mpb d u2)
   108           | mpb _ atom           = atom
   109     in mpb 0 end;
   110 
   111 fun idx [] j     = raise Unif
   112   | idx(i::is) j = if (i:int) =j then length is else idx is j;
   113 
   114 fun mkabs (binders,is,t)  =
   115     let fun mk(i::is) = let val (x,T) = nth binders i
   116                         in Abs(x,T,mk is) end
   117           | mk []     = t
   118     in mk is end;
   119 
   120 val incr = mapbnd (fn i => i+1);
   121 
   122 fun ints_of []             = []
   123   | ints_of (Bound i ::bs) =
   124       let val is = ints_of bs
   125       in if member (op =) is i then raise Pattern else i::is end
   126   | ints_of _              = raise Pattern;
   127 
   128 fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
   129 
   130 
   131 fun app (s,(i::is)) = app (s$Bound(i),is)
   132   | app (s,[])      = s;
   133 
   134 fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
   135   | red t            []      [] = t
   136   | red t            is      jn = app (mapbnd (nth jn) t,is);
   137 
   138 
   139 (* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
   140 fun split_type (T,0,Ts)                    = (Ts,T)
   141   | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
   142   | split_type _                           = error("split_type");
   143 
   144 fun type_of_G env (T, n, is) =
   145   let
   146     val tyenv = Envir.type_env env;
   147     val (Ts, U) = split_type (Envir.norm_type tyenv T, n, []);
   148   in map (nth Ts) is ---> U end;
   149 
   150 fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));
   151 
   152 fun mknewhnf(env,binders,is,F as (a,_),T,js) =
   153   let val (env',G) = Envir.genvar a (env,type_of_G env (T,length is,js))
   154   in Envir.update (((F, T), mkhnf (binders, is, G, js)), env') end;
   155 
   156 
   157 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
   158 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
   159   | downto0 ([], n) = n = ~1;
   160 
   161 (*mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ]*)
   162 fun mk_proj_list is =
   163     let fun mk(i::is,j) = if is_some i then j :: mk(is,j-1) else mk(is,j-1)
   164           | mk([],_)    = []
   165     in mk(is,length is - 1) end;
   166 
   167 fun proj(s,env,binders,is) =
   168     let fun trans d i = if i<d then i else (idx is (i-d))+d;
   169         fun pr(s,env,d,binders) = (case Envir.head_norm env s of
   170               Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
   171                             in (Abs(a,T,t'),env') end
   172             | t => (case strip_comb t of
   173                 (c as Const _,ts) =>
   174                          let val (ts',env') = prs(ts,env,d,binders)
   175                          in (list_comb(c,ts'),env') end
   176                  | (f as Free _,ts) =>
   177                          let val (ts',env') = prs(ts,env,d,binders)
   178                          in (list_comb(f,ts'),env') end
   179                  | (Bound(i),ts) =>
   180                          let val j = trans d i
   181                              val (ts',env') = prs(ts,env,d,binders)
   182                          in (list_comb(Bound j,ts'),env') end
   183                  | (Var(F as (a,_),Fty),ts) =>
   184                       let val js = ints_of' env ts;
   185                           val js' = map (try (trans d)) js;
   186                           val ks = mk_proj_list js';
   187                           val ls = map_filter I js'
   188                           val Hty = type_of_G env (Fty,length js,ks)
   189                           val (env',H) = Envir.genvar a (env,Hty)
   190                           val env'' =
   191                             Envir.update (((F, Fty), mkhnf (binders, js, H, ks)), env')
   192                       in (app(H,ls),env'') end
   193                  | _  => raise Pattern))
   194         and prs(s::ss,env,d,binders) =
   195               let val (s',env1) = pr(s,env,d,binders)
   196                   val (ss',env2) = prs(ss,env1,d,binders)
   197               in (s'::ss',env2) end
   198           | prs([],env,_,_) = ([],env)
   199    in if downto0(is,length binders - 1) then (s,env)
   200       else pr(s,env,0,binders)
   201    end;
   202 
   203 
   204 (* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
   205 fun mk_ff_list(is,js) =
   206     let fun mk([],[],_)        = []
   207           | mk(i::is,j::js, k) = if (i:int) = j then k :: mk(is,js,k-1)
   208                                         else mk(is,js,k-1)
   209           | mk _               = error"mk_ff_list"
   210     in mk(is,js,length is-1) end;
   211 
   212 fun flexflex1(env,binders,F,Fty,is,js) =
   213   if is=js then env
   214   else let val ks = mk_ff_list(is,js)
   215        in mknewhnf(env,binders,is,F,Fty,ks) end;
   216 
   217 fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
   218   let fun ff(F,Fty,is,G as (a,_),Gty,js) =
   219             if js subset_int is
   220             then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
   221                  in Envir.update (((F, Fty), t), env) end
   222             else let val ks = is inter_int js
   223                      val Hty = type_of_G env (Fty,length is,map (idx is) ks)
   224                      val (env',H) = Envir.genvar a (env,Hty)
   225                      fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
   226                  in Envir.update (((G, Gty), lam js), Envir.update (((F, Fty), lam is), env'))
   227                  end;
   228   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
   229 
   230 fun unify_types thy (T, U) (env as Envir.Envir {maxidx, tenv, tyenv}) =
   231   if T = U then env
   232   else
   233     let val (tyenv', maxidx') = Sign.typ_unify thy (U, T) (tyenv, maxidx)
   234     in Envir.Envir {maxidx = maxidx', tenv = tenv, tyenv = tyenv'} end
   235     handle Type.TUNIFY => (typ_clash thy (tyenv, T, U); raise Unif);
   236 
   237 fun unif thy binders (s,t) env = case (Envir.head_norm env s, Envir.head_norm env t) of
   238       (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
   239          let val name = if ns = "" then nt else ns
   240          in unif thy ((name,Ts)::binders) (ts,tt) env end
   241     | (Abs(ns,Ts,ts),t) => unif thy ((ns,Ts)::binders) (ts,(incr t)$Bound(0)) env
   242     | (t,Abs(nt,Tt,tt)) => unif thy ((nt,Tt)::binders) ((incr t)$Bound(0),tt) env
   243     | p => cases thy (binders,env,p)
   244 
   245 and cases thy (binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
   246        ((Var(F,Fty),ss),(Var(G,Gty),ts)) =>
   247          if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts)
   248                   else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts)
   249       | ((Var(F,Fty),ss),_)           => flexrigid thy (env,binders,F,Fty,ints_of' env ss,t)
   250       | (_,(Var(F,Fty),ts))           => flexrigid thy (env,binders,F,Fty,ints_of' env ts,s)
   251       | ((Const c,ss),(Const d,ts))   => rigidrigid thy (env,binders,c,d,ss,ts)
   252       | ((Free(f),ss),(Free(g),ts))   => rigidrigid thy (env,binders,f,g,ss,ts)
   253       | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB thy (env,binders,i,j,ss,ts)
   254       | ((Abs(_),_),_)                => raise Pattern
   255       | (_,(Abs(_),_))                => raise Pattern
   256       | ((Const(c,_),_),(Free(f,_),_)) => (clash c f; raise Unif)
   257       | ((Const(c,_),_),(Bound i,_))   => (clashB binders i c; raise Unif)
   258       | ((Free(f,_),_),(Const(c,_),_)) => (clash f c; raise Unif)
   259       | ((Free(f,_),_),(Bound i,_))    => (clashB binders i f; raise Unif)
   260       | ((Bound i,_),(Const(c,_),_))   => (clashB binders i c; raise Unif)
   261       | ((Bound i,_),(Free(f,_),_))    => (clashB binders i f; raise Unif)
   262 
   263 
   264 and rigidrigid thy (env,binders,(a,Ta),(b,Tb),ss,ts) =
   265       if a<>b then (clash a b; raise Unif)
   266       else env |> unify_types thy (Ta,Tb) |> fold (unif thy binders) (ss~~ts)
   267 
   268 and rigidrigidB thy (env,binders,i,j,ss,ts) =
   269      if i <> j then (clashBB binders i j; raise Unif)
   270      else fold (unif thy binders) (ss~~ts) env
   271 
   272 and flexrigid thy (params as (env,binders,F,Fty,is,t)) =
   273       if occurs(F,t,env) then (ocheck_fail thy (F,t,binders,env); raise Unif)
   274       else (let val (u,env') = proj(t,env,binders,is)
   275             in Envir.update (((F, Fty), mkabs (binders, is, u)), env') end
   276             handle Unif => (proj_fail thy params; raise Unif));
   277 
   278 fun unify thy = unif thy [];
   279 
   280 
   281 (* put a term into eta long beta normal form *)
   282 fun eta_long Ts (Abs (s, T, t)) = Abs (s, T, eta_long (T :: Ts) t)
   283   | eta_long Ts t = (case strip_comb t of
   284       (Abs _, _) => eta_long Ts (Envir.beta_norm t)
   285     | (u, ts) =>
   286       let
   287         val Us = binder_types (fastype_of1 (Ts, t));
   288         val i = length Us
   289       in list_abs (map (pair "x") Us,
   290         list_comb (incr_boundvars i u, map (eta_long (rev Us @ Ts))
   291           (map (incr_boundvars i) ts @ map Bound (i - 1 downto 0))))
   292       end);
   293 
   294 
   295 (*Tests whether 2 terms are alpha/eta-convertible and have same type.
   296   Note that Consts and Vars may have more than one type.*)
   297 fun t aeconv u = t aconv u orelse
   298   Envir.eta_contract t aconv Envir.eta_contract u;
   299 
   300 
   301 (*** Matching ***)
   302 
   303 exception MATCH;
   304 
   305 fun typ_match thy TU tyenv = Sign.typ_match thy TU tyenv
   306   handle Type.TYPE_MATCH => raise MATCH;
   307 
   308 (*First-order matching;
   309   The pattern and object may have variables in common.
   310   Instantiation does not affect the object, so matching ?a with ?a+1 works.
   311   Object is eta-contracted on the fly (by eta-expanding the pattern).
   312   Precondition: the pattern is already eta-contracted!
   313   Types are matched on the fly*)
   314 fun first_order_match thy =
   315   let
   316     fun mtch k (instsp as (tyinsts,insts)) = fn
   317         (Var(ixn,T), t)  =>
   318           if k > 0 andalso loose_bvar(t,0) then raise MATCH
   319           else (case Envir.lookup' (insts, (ixn, T)) of
   320                   NONE => (typ_match thy (T, fastype_of t) tyinsts,
   321                            Vartab.update_new (ixn, (T, t)) insts)
   322                 | SOME u => if t aeconv u then instsp else raise MATCH)
   323       | (Free (a,T), Free (b,U)) =>
   324           if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH
   325       | (Const (a,T), Const (b,U))  =>
   326           if a=b then (typ_match thy (T,U) tyinsts, insts) else raise MATCH
   327       | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
   328       | (Abs(_,T,t), Abs(_,U,u))  =>
   329           mtch (k + 1) (typ_match thy (T,U) tyinsts, insts) (t,u)
   330       | (f$t, g$u) => mtch k (mtch k instsp (f,g)) (t, u)
   331       | (t, Abs(_,U,u))  =>  mtch (k + 1) instsp ((incr t)$(Bound 0), u)
   332       | _ => raise MATCH
   333   in fn tu => fn env => mtch 0 env tu end;
   334 
   335 
   336 (* Matching of higher-order patterns *)
   337 
   338 fun match_bind(itms,binders,ixn,T,is,t) =
   339   let val js = loose_bnos t
   340   in if null is
   341      then if null js then Vartab.update_new (ixn, (T, t)) itms else raise MATCH
   342      else if js subset_int is
   343           then let val t' = if downto0(is,length binders - 1) then t
   344                             else mapbnd (idx is) t
   345                in Vartab.update_new (ixn, (T, mkabs (binders, is, t'))) itms end
   346           else raise MATCH
   347   end;
   348 
   349 fun match thy (po as (pat,obj)) envir =
   350 let
   351   (* Pre: pat and obj have same type *)
   352   fun mtch binders (pat,obj) (env as (iTs,itms)) =
   353     case pat of
   354       Abs(ns,Ts,ts) =>
   355         (case obj of
   356            Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (ts,tt) env
   357          | _ => let val Tt = Envir.subst_type iTs Ts
   358                 in mtch((ns,Tt)::binders) (ts,(incr obj)$Bound(0)) env end)
   359     | _ => (case obj of
   360               Abs(nt,Tt,tt) =>
   361                 mtch((nt,Tt)::binders) ((incr pat)$Bound(0),tt) env
   362             | _ => cases(binders,env,pat,obj))
   363 
   364   and cases(binders,env as (iTs,itms),pat,obj) =
   365     let val (ph,pargs) = strip_comb pat
   366         fun rigrig1(iTs,oargs) = fold (mtch binders) (pargs~~oargs) (iTs,itms)
   367         fun rigrig2((a:string,Ta),(b,Tb),oargs) =
   368               if a <> b then raise MATCH
   369               else rigrig1(typ_match thy (Ta,Tb) iTs, oargs)
   370     in case ph of
   371          Var(ixn,T) =>
   372            let val is = ints_of pargs
   373            in case Envir.lookup' (itms, (ixn, T)) of
   374                 NONE => (iTs,match_bind(itms,binders,ixn,T,is,obj))
   375               | SOME u => if obj aeconv (red u is []) then env
   376                           else raise MATCH
   377            end
   378        | _ =>
   379            let val (oh,oargs) = strip_comb obj
   380            in case (ph,oh) of
   381                 (Const c,Const d) => rigrig2(c,d,oargs)
   382               | (Free f,Free g)   => rigrig2(f,g,oargs)
   383               | (Bound i,Bound j) => if i<>j then raise MATCH
   384                                      else rigrig1(iTs,oargs)
   385               | (Abs _, _)        => raise Pattern
   386               | (_, Abs _)        => raise Pattern
   387               | _                 => raise MATCH
   388            end
   389     end;
   390 
   391   val pT = fastype_of pat
   392   and oT = fastype_of obj
   393   val envir' = apfst (typ_match thy (pT, oT)) envir;
   394 in mtch [] po envir' handle Pattern => first_order_match thy po envir' end;
   395 
   396 fun matches thy po = (match thy po (Vartab.empty, Vartab.empty); true) handle MATCH => false;
   397 
   398 fun matchess thy pos = (fold (match thy) (op ~~ pos) (Vartab.empty, Vartab.empty); true) handle MATCH => false;
   399 
   400 fun equiv thy (t, u) = matches thy (t, u) andalso matches thy (u, t);
   401 
   402 
   403 (* Does pat match a subterm of obj? *)
   404 fun matches_subterm thy (pat, obj) =
   405   let
   406     fun msub bounds obj = matches thy (pat, obj) orelse
   407       (case obj of
   408         Abs (x, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t)))
   409       | t $ u => msub bounds t orelse msub bounds u
   410       | _ => false)
   411   in msub 0 obj end;
   412 
   413 fun first_order(Abs(_,_,t)) = first_order t
   414   | first_order(t $ u) = first_order t andalso first_order u andalso
   415                          not(is_Var t)
   416   | first_order _ = true;
   417 
   418 fun pattern (Abs (_, _, t)) = pattern t
   419   | pattern t =
   420       let val (head, args) = strip_comb t in
   421         if is_Var head then
   422           forall is_Bound args andalso not (has_duplicates (op aconv) args)
   423         else forall pattern args
   424       end;
   425 
   426 
   427 (* rewriting -- simple but fast *)
   428 
   429 fun match_rew thy tm (tm1, tm2) =
   430   let val rtm = the_default tm2 (Term.rename_abs tm1 tm tm2) in
   431     SOME (Envir.subst_term (match thy (tm1, tm) (Vartab.empty, Vartab.empty)) rtm, rtm)
   432       handle MATCH => NONE
   433   end;
   434 
   435 fun rewrite_term thy rules procs tm =
   436   let
   437     val skel0 = Bound 0;
   438 
   439     fun variant_absfree bounds (x, T, t) =
   440       let
   441         val (x', t') = Term.dest_abs (Name.bound bounds, T, t);
   442         fun abs u = Abs (x, T, abstract_over (Free (x', T), u));
   443       in (abs, t') end;
   444 
   445     fun rew (Abs (_, _, body) $ t) = SOME (subst_bound (t, body), skel0)
   446       | rew tm =
   447           (case get_first (match_rew thy tm) rules of
   448             NONE => Option.map (rpair skel0) (get_first (fn p => p tm) procs)
   449           | x => x);
   450 
   451     fun rew1 bounds (Var _) _ = NONE
   452       | rew1 bounds skel tm = (case rew2 bounds skel tm of
   453           SOME tm1 => (case rew tm1 of
   454               SOME (tm2, skel') => SOME (the_default tm2 (rew1 bounds skel' tm2))
   455             | NONE => SOME tm1)
   456         | NONE => (case rew tm of
   457               SOME (tm1, skel') => SOME (the_default tm1 (rew1 bounds skel' tm1))
   458             | NONE => NONE))
   459 
   460     and rew2 bounds skel (tm1 $ tm2) = (case tm1 of
   461             Abs (_, _, body) =>
   462               let val tm' = subst_bound (tm2, body)
   463               in SOME (the_default tm' (rew2 bounds skel0 tm')) end
   464           | _ =>
   465             let val (skel1, skel2) = (case skel of
   466                 skel1 $ skel2 => (skel1, skel2)
   467               | _ => (skel0, skel0))
   468             in case rew1 bounds skel1 tm1 of
   469                 SOME tm1' => (case rew1 bounds skel2 tm2 of
   470                     SOME tm2' => SOME (tm1' $ tm2')
   471                   | NONE => SOME (tm1' $ tm2))
   472               | NONE => (case rew1 bounds skel2 tm2 of
   473                     SOME tm2' => SOME (tm1 $ tm2')
   474                   | NONE => NONE)
   475             end)
   476       | rew2 bounds skel (Abs body) =
   477           let
   478             val (abs, tm') = variant_absfree bounds body;
   479             val skel' = (case skel of Abs (_, _, skel') => skel' | _ => skel0)
   480           in case rew1 (bounds + 1) skel' tm' of
   481               SOME tm'' => SOME (abs tm'')
   482             | NONE => NONE
   483           end
   484       | rew2 _ _ _ = NONE;
   485 
   486   in the_default tm (rew1 0 skel0 tm) end;
   487 
   488 end;
   489 
   490 val trace_unify_fail = Pattern.trace_unify_fail;