src/Pure/pattern.ML
author wenzelm
Fri Jan 18 18:36:19 2002 +0100 (2002-01-18)
changeset 12817 fcbb6ad5c790
parent 12797 4de06a8f67ef
child 12826 dfb214fa310b
permissions -rw-r--r--
rewrite_term: removed rew0, so no on-the-fly eta-contraction;
     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   type type_sig
    20   type sg
    21   type env
    22   val aeconv            : term * term -> bool
    23   val eta_contract      : term -> term
    24   val beta_eta_contract : term -> term
    25   val eta_contract_atom : term -> term
    26   val match             : type_sig -> term * term
    27                           -> (indexname*typ)list * (indexname*term)list
    28   val first_order_match : type_sig -> term * term
    29                           -> (indexname*typ)list * (indexname*term)list
    30   val matches           : type_sig -> term * term -> bool
    31   val matches_subterm   : type_sig -> term * term -> bool
    32   val unify             : sg * env * (term * term)list -> env
    33   val first_order       : term -> bool
    34   val pattern           : term -> bool
    35   val rewrite_term      : type_sig -> (term * term) list -> term -> term
    36   exception Unif
    37   exception MATCH
    38   exception Pattern
    39   end;
    40 
    41 structure Pattern : PATTERN =
    42 struct
    43 
    44 type type_sig = Type.type_sig
    45 type sg = Sign.sg
    46 type env = Envir.env
    47 
    48 exception Unif;
    49 exception Pattern;
    50 
    51 fun occurs(F,t,env) =
    52     let fun occ(Var(G,_))   = (case Envir.lookup(env,G) of
    53                                  Some(t) => occ t
    54                                | None    => F=G)
    55           | occ(t1$t2)      = occ t1 orelse occ t2
    56           | occ(Abs(_,_,t)) = occ t
    57           | occ _           = false
    58     in occ t end;
    59 
    60 
    61 fun mapbnd f =
    62     let fun mpb d (Bound(i))     = if i < d then Bound(i) else Bound(f(i-d)+d)
    63           | mpb d (Abs(s,T,t))   = Abs(s,T,mpb(d+1) t)
    64           | mpb d ((u1 $ u2))    = (mpb d u1)$(mpb d u2)
    65           | mpb _ atom           = atom
    66     in mpb 0 end;
    67 
    68 fun idx [] j     = ~10000
    69   | idx(i::is) j = if i=j then length is else idx is j;
    70 
    71 fun at xs i = nth_elem (i,xs);
    72 
    73 fun mkabs (binders,is,t)  =
    74     let fun mk(i::is) = let val (x,T) = nth_elem(i,binders)
    75                         in Abs(x,T,mk is) end
    76           | mk []     = t
    77     in mk is end;
    78 
    79 val incr = mapbnd (fn i => i+1);
    80 
    81 fun ints_of []             = []
    82   | ints_of (Bound i ::bs) =
    83       let val is = ints_of bs
    84       in if i mem_int is then raise Pattern else i::is end
    85   | ints_of _              = raise Pattern;
    86 
    87 fun ints_of' env ts = ints_of (map (Envir.head_norm env) ts);
    88 
    89 
    90 fun app (s,(i::is)) = app (s$Bound(i),is)
    91   | app (s,[])      = s;
    92 
    93 fun red (Abs(_,_,s)) (i::is) js = red s is (i::js)
    94   | red t            []      [] = t
    95   | red t            is      jn = app (mapbnd (at jn) t,is);
    96 
    97 
    98 (* split_type ([T1,....,Tn]---> T,n,[]) = ([Tn,...,T1],T) *)
    99 fun split_type (T,0,Ts)                    = (Ts,T)
   100   | split_type (Type ("fun",[T1,T2]),n,Ts) = split_type (T2,n-1,T1::Ts)
   101   | split_type _                           = error("split_type");
   102 
   103 fun type_of_G (T,n,is) =
   104   let val (Ts,U) = split_type(T,n,[]) in map(at Ts)is ---> U end;
   105 
   106 fun mkhnf (binders,is,G,js) = mkabs (binders, is, app(G,js));
   107 
   108 fun mknewhnf(env,binders,is,F as (a,_),T,js) =
   109   let val (env',G) = Envir.genvar a (env,type_of_G(T,length is,js))
   110   in Envir.update((F,mkhnf(binders,is,G,js)),env') end;
   111 
   112 
   113 (* mk_proj_list(is) = [ |is| - k | 1 <= k <= |is| and is[k] >= 0 ] *)
   114 fun mk_proj_list is =
   115     let fun mk(i::is,j) = if i >= 0 then j :: mk(is,j-1) else mk(is,j-1)
   116           | mk([],_)    = []
   117     in mk(is,length is - 1) end;
   118 
   119 fun proj(s,env,binders,is) =
   120     let fun trans d i = if i<d then i else (idx is (i-d))+d;
   121         fun pr(s,env,d,binders) = (case Envir.head_norm env s of
   122               Abs(a,T,t) => let val (t',env') = pr(t,env,d+1,((a,T)::binders))
   123                             in (Abs(a,T,t'),env') end
   124             | t => (case strip_comb t of
   125                 (c as Const _,ts) =>
   126                          let val (ts',env') = prs(ts,env,d,binders)
   127                          in (list_comb(c,ts'),env') end
   128                  | (f as Free _,ts) =>
   129                          let val (ts',env') = prs(ts,env,d,binders)
   130                          in (list_comb(f,ts'),env') end
   131                  | (Bound(i),ts) =>
   132                          let val j = trans d i
   133                          in if j < 0 then raise Unif
   134                             else let val (ts',env') = prs(ts,env,d,binders)
   135                                  in (list_comb(Bound j,ts'),env') end
   136                          end
   137                  | (Var(F as (a,_),Fty),ts) =>
   138                       let val js = ints_of' env ts;
   139                           val js' = map (trans d) js;
   140                           val ks = mk_proj_list js';
   141                           val ls = filter (fn i => i >= 0) js'
   142                           val Hty = type_of_G(Fty,length js,ks)
   143                           val (env',H) = Envir.genvar a (env,Hty)
   144                           val env'' =
   145                                 Envir.update((F,mkhnf(binders,js,H,ks)),env')
   146                       in (app(H,ls),env'') end
   147                  | _  => raise Pattern))
   148         and prs(s::ss,env,d,binders) =
   149               let val (s',env1) = pr(s,env,d,binders)
   150                   val (ss',env2) = prs(ss,env1,d,binders)
   151               in (s'::ss',env2) end
   152           | prs([],env,_,_) = ([],env)
   153    in if downto0(is,length binders - 1) then (s,env)
   154       else pr(s,env,0,binders)
   155    end;
   156 
   157 
   158 (* mk_ff_list(is,js) = [ length(is) - k | 1 <= k <= |is| and is[k] = js[k] ] *)
   159 fun mk_ff_list(is,js) =
   160     let fun mk([],[],_)        = []
   161           | mk(i::is,j::js, k) = if i=j then k :: mk(is,js,k-1)
   162                                         else mk(is,js,k-1)
   163           | mk _               = error"mk_ff_list"
   164     in mk(is,js,length is-1) end;
   165 
   166 fun flexflex1(env,binders,F,Fty,is,js) =
   167   if is=js then env
   168   else let val ks = mk_ff_list(is,js)
   169        in mknewhnf(env,binders,is,F,Fty,ks) end;
   170 
   171 fun flexflex2(env,binders,F,Fty,is,G,Gty,js) =
   172   let fun ff(F,Fty,is,G as (a,_),Gty,js) =
   173             if js subset_int is
   174             then let val t= mkabs(binders,is,app(Var(G,Gty),map (idx is) js))
   175                  in Envir.update((F,t),env) end
   176             else let val ks = is inter_int js
   177                      val Hty = type_of_G(Fty,length is,map (idx is) ks)
   178                      val (env',H) = Envir.genvar a (env,Hty)
   179                      fun lam(is) = mkabs(binders,is,app(H,map (idx is) ks));
   180                  in Envir.update((G,lam js), Envir.update((F,lam is),env'))
   181                  end;
   182   in if xless(G,F) then ff(F,Fty,is,G,Gty,js) else ff(G,Gty,js,F,Fty,is) end
   183 
   184 val tsgr = ref(Type.tsig0);
   185 
   186 fun unify_types(T,U, env as Envir.Envir{asol,iTs,maxidx}) =
   187   if T=U then env
   188   else let val (iTs',maxidx') = Type.unify (!tsgr) (iTs, maxidx) (U, T)
   189        in Envir.Envir{asol=asol,maxidx=maxidx',iTs=iTs'} end
   190        handle Type.TUNIFY => raise Unif;
   191 
   192 fun unif binders (env,(s,t)) = case (Envir.head_norm env s, Envir.head_norm env t) of
   193       (Abs(ns,Ts,ts),Abs(nt,Tt,tt)) =>
   194          let val name = if ns = "" then nt else ns
   195          in unif ((name,Ts)::binders) (env,(ts,tt)) end
   196     | (Abs(ns,Ts,ts),t) => unif ((ns,Ts)::binders) (env,(ts,(incr t)$Bound(0)))
   197     | (t,Abs(nt,Tt,tt)) => unif ((nt,Tt)::binders) (env,((incr t)$Bound(0),tt))
   198     | p => cases(binders,env,p)
   199 
   200 and cases(binders,env,(s,t)) = case (strip_comb s,strip_comb t) of
   201        ((Var(F,Fty),ss),(Var(G,Gty),ts)) =>
   202          if F = G then flexflex1(env,binders,F,Fty,ints_of' env ss,ints_of' env ts)
   203                   else flexflex2(env,binders,F,Fty,ints_of' env ss,G,Gty,ints_of' env ts)
   204       | ((Var(F,_),ss),_)             => flexrigid(env,binders,F,ints_of' env ss,t)
   205       | (_,(Var(F,_),ts))             => flexrigid(env,binders,F,ints_of' env ts,s)
   206       | ((Const c,ss),(Const d,ts))   => rigidrigid(env,binders,c,d,ss,ts)
   207       | ((Free(f),ss),(Free(g),ts))   => rigidrigid(env,binders,f,g,ss,ts)
   208       | ((Bound(i),ss),(Bound(j),ts)) => rigidrigidB (env,binders,i,j,ss,ts)
   209       | ((Abs(_),_),_)                => raise Pattern
   210       | (_,(Abs(_),_))                => raise Pattern
   211       | _                             => raise Unif
   212 
   213 and rigidrigid (env,binders,(a,Ta),(b,Tb),ss,ts) =
   214       if a<>b then raise Unif
   215       else foldl (unif binders) (unify_types(Ta,Tb,env), ss~~ts)
   216 
   217 and rigidrigidB (env,binders,i,j,ss,ts) =
   218      if i <> j then raise Unif else foldl (unif binders) (env ,ss~~ts)
   219 
   220 and flexrigid (env,binders,F,is,t) =
   221       if occurs(F,t,env) then raise Unif
   222       else let val (u,env') = proj(t,env,binders,is)
   223            in Envir.update((F,mkabs(binders,is,u)),env') end;
   224 
   225 fun unify(sg,env,tus) = (tsgr := #tsig(Sign.rep_sg sg);
   226                          foldl (unif []) (env,tus));
   227 
   228 
   229 (*Eta-contract a term (fully)*)
   230 
   231 fun eta_contract t =
   232   let
   233     exception SAME;
   234     fun eta (Abs (a, T, body)) = 
   235       ((case eta body of
   236           body' as (f $ Bound 0) => 
   237 	    if loose_bvar1 (f, 0) then Abs(a, T, body')
   238 	    else incr_boundvars ~1 f
   239         | body' => Abs (a, T, body')) handle SAME =>
   240        (case body of
   241           (f $ Bound 0) => 
   242 	    if loose_bvar1 (f, 0) then raise SAME
   243 	    else incr_boundvars ~1 f
   244         | _ => raise SAME))
   245       | eta (f $ t) =
   246           (let val f' = eta f
   247            in f' $ etah t end handle SAME => f $ eta t)
   248       | eta _ = raise SAME
   249     and etah t = (eta t handle SAME => t)
   250   in etah t end;
   251 
   252 val beta_eta_contract = eta_contract o Envir.beta_norm;
   253 
   254 (*Eta-contract a term from outside: just enough to reduce it to an atom
   255 DOESN'T QUITE WORK!
   256 *)
   257 fun eta_contract_atom (t0 as Abs(a, T, body)) =
   258       (case  eta_contract2 body  of
   259         body' as (f $ Bound 0) =>
   260             if loose_bvar1(f,0) then Abs(a,T,body')
   261             else eta_contract_atom (incr_boundvars ~1 f)
   262       | _ => t0)
   263   | eta_contract_atom t = t
   264 and eta_contract2 (f$t) = f $ eta_contract_atom t
   265   | eta_contract2 t     = eta_contract_atom t;
   266 
   267 
   268 (*Tests whether 2 terms are alpha/eta-convertible and have same type.
   269   Note that Consts and Vars may have more than one type.*)
   270 fun t aeconv u = aconv_aux (eta_contract_atom t, eta_contract_atom u)
   271 and aconv_aux (Const(a,T), Const(b,U)) = a=b  andalso  T=U
   272   | aconv_aux (Free(a,T),  Free(b,U))  = a=b  andalso  T=U
   273   | aconv_aux (Var(v,T),   Var(w,U))   = eq_ix(v,w) andalso  T=U
   274   | aconv_aux (Bound i,    Bound j)    = i=j
   275   | aconv_aux (Abs(_,T,t), Abs(_,U,u)) = (t aeconv u)  andalso  T=U
   276   | aconv_aux (f$t,        g$u)        = (f aeconv g)  andalso (t aeconv u)
   277   | aconv_aux _ =  false;
   278 
   279 
   280 (*** Matching ***)
   281 
   282 exception MATCH;
   283 
   284 fun typ_match tsig args = (Type.typ_match tsig args)
   285                           handle Type.TYPE_MATCH => raise MATCH;
   286 
   287 (*First-order matching;
   288   fomatch tsig (pattern, object) returns a (tyvar,typ)list and (var,term)list.
   289   The pattern and object may have variables in common.
   290   Instantiation does not affect the object, so matching ?a with ?a+1 works.
   291   Object is eta-contracted on the fly (by eta-expanding the pattern).
   292   Precondition: the pattern is already eta-contracted!
   293   Note: types are matched on the fly *)
   294 fun fomatch tsig =
   295   let
   296     fun mtch (instsp as (tyinsts,insts)) = fn
   297         (Var(ixn,T), t)  =>
   298           if loose_bvar(t,0) then raise MATCH
   299           else (case assoc_string_int(insts,ixn) of
   300                   None => (typ_match tsig (tyinsts, (T, fastype_of t)),
   301                            (ixn,t)::insts)
   302                 | Some u => if t aeconv u then instsp else raise MATCH)
   303       | (Free (a,T), Free (b,U)) =>
   304           if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
   305       | (Const (a,T), Const (b,U))  =>
   306           if a=b then (typ_match tsig (tyinsts,(T,U)), insts) else raise MATCH
   307       | (Bound i, Bound j)  =>  if  i=j  then  instsp  else raise MATCH
   308       | (Abs(_,T,t), Abs(_,U,u))  =>
   309           mtch (typ_match tsig (tyinsts,(T,U)),insts) (t,u)
   310       | (f$t, g$u) => mtch (mtch instsp (f,g)) (t, u)
   311       | (t, Abs(_,U,u))  =>  mtch instsp ((incr t)$(Bound 0), u)
   312       | _ => raise MATCH
   313   in mtch end;
   314 
   315 fun first_order_match tsig = apfst Vartab.dest o fomatch tsig (Vartab.empty, []);
   316 
   317 (* Matching of higher-order patterns *)
   318 
   319 fun match_bind(itms,binders,ixn,is,t) =
   320   let val js = loose_bnos t
   321   in if null is
   322      then if null js then (ixn,t)::itms else raise MATCH
   323      else if js subset_int is
   324           then let val t' = if downto0(is,length binders - 1) then t
   325                             else mapbnd (idx is) t
   326                in (ixn, mkabs(binders,is,t')) :: itms end
   327           else raise MATCH
   328   end;
   329 
   330 fun match tsg (po as (pat,obj)) =
   331 let
   332   (* Pre: pat and obj have same type *)
   333   fun mtch binders (env as (iTs,itms),(pat,obj)) =
   334     case pat of
   335       Abs(ns,Ts,ts) =>
   336         (case obj of
   337            Abs(nt,Tt,tt) => mtch ((nt,Tt)::binders) (env,(ts,tt))
   338          | _ => let val Tt = typ_subst_TVars_Vartab iTs Ts
   339                 in mtch((ns,Tt)::binders)(env,(ts,(incr obj)$Bound(0))) end)
   340     | _ => (case obj of
   341               Abs(nt,Tt,tt) =>
   342                 mtch((nt,Tt)::binders)(env,((incr pat)$Bound(0),tt))
   343             | _ => cases(binders,env,pat,obj))
   344 
   345   and cases(binders,env as (iTs,itms),pat,obj) =
   346     let val (ph,pargs) = strip_comb pat
   347         fun rigrig1(iTs,oargs) =
   348               foldl (mtch binders) ((iTs,itms), pargs~~oargs)
   349         fun rigrig2((a,Ta),(b,Tb),oargs) =
   350               if a<> b then raise MATCH
   351               else rigrig1(typ_match tsg (iTs,(Ta,Tb)), oargs)
   352     in case ph of
   353          Var(ixn,_) =>
   354            let val is = ints_of pargs
   355            in case assoc_string_int(itms,ixn) of
   356                 None => (iTs,match_bind(itms,binders,ixn,is,obj))
   357               | Some u => if obj aeconv (red u is []) then env
   358                           else raise MATCH
   359            end
   360        | _ =>
   361            let val (oh,oargs) = strip_comb obj
   362            in case (ph,oh) of
   363                 (Const c,Const d) => rigrig2(c,d,oargs)
   364               | (Free f,Free g)   => rigrig2(f,g,oargs)
   365               | (Bound i,Bound j) => if i<>j then raise MATCH
   366                                      else rigrig1(iTs,oargs)
   367               | (Abs _, _)        => raise Pattern
   368               | (_, Abs _)        => raise Pattern
   369               | _                 => raise MATCH
   370            end
   371     end;
   372 
   373   val pT = fastype_of pat
   374   and oT = fastype_of obj
   375   val iTs = typ_match tsg (Vartab.empty, (pT,oT))
   376   val insts2 = (iTs,[])
   377 
   378 in apfst Vartab.dest (mtch [] (insts2, po)
   379    handle Pattern => fomatch tsg insts2 po)
   380 end;
   381 
   382 (*Predicate: does the pattern match the object?*)
   383 fun matches tsig po = (match tsig po; true) handle MATCH => false;
   384 
   385 (* Does pat match a subterm of obj? *)
   386 fun matches_subterm tsig (pat,obj) =
   387   let fun msub(bounds,obj) = matches tsig (pat,obj) orelse
   388             case obj of
   389               Abs(x,T,t) => let val y = variant bounds x
   390                                 val f = Free(":" ^ y,T)
   391                             in msub(x::bounds,subst_bound(f,t)) end
   392             | s$t => msub(bounds,s) orelse msub(bounds,t)
   393             | _ => false
   394   in msub([],obj) end;
   395 
   396 fun first_order(Abs(_,_,t)) = first_order t
   397   | first_order(t $ u) = first_order t andalso first_order u andalso
   398                          not(is_Var t)
   399   | first_order _ = true;
   400 
   401 fun pattern(Abs(_,_,t)) = pattern t
   402   | pattern(t) = let val (head,args) = strip_comb t
   403                  in if is_Var head
   404                     then let val _ = ints_of args in true end
   405                          handle Pattern => false
   406                     else forall pattern args
   407                  end;
   408 
   409 
   410 (* rewriting -- simple but fast *)
   411 
   412 fun rewrite_term tsig rules tm =
   413   let
   414     val rhs_names =
   415       foldr (fn ((_, rhs), names) => add_term_free_names (rhs, names)) (rules, []);
   416     fun variant_absfree (x, T, t) =
   417       let
   418         val x' = variant (add_term_free_names (t, rhs_names)) x;
   419         val t' = subst_bound (Free (x', T), t);
   420       in (fn u => Abs (x, T, abstract_over (Free (x', T), u)), t') end;
   421 
   422     fun match_rew tm (tm1, tm2) =
   423       Some (subst_vars (match tsig (tm1, tm)) tm2) handle MATCH => None;
   424     fun rew (Abs (_, _, body) $ t) = Some (subst_bound (t, body))
   425       | rew tm = get_first (match_rew tm) rules;
   426 
   427     fun rew1 tm = (case rew2 tm of
   428           Some tm1 => (case rew tm1 of
   429               Some tm2 => Some (if_none (rew1 tm2) tm2)
   430             | None => Some tm1)
   431         | None => (case rew tm of
   432               Some tm1 => Some (if_none (rew1 tm1) tm1)
   433             | None => None))
   434 
   435     and rew2 (tm1 $ tm2) = (case tm1 of
   436             Abs (_, _, body) =>
   437               let val tm' = subst_bound (tm2, body)
   438               in Some (if_none (rew2 tm') tm') end
   439           | _ => (case rew1 tm1 of
   440               Some tm1' => (case rew1 tm2 of
   441                   Some tm2' => Some (tm1' $ tm2')
   442                 | None => Some (tm1' $ tm2))
   443             | None => (case rew1 tm2 of
   444                   Some tm2' => Some (tm1 $ tm2')
   445                 | None => None)))
   446       | rew2 (Abs (x, T, tm)) =
   447           let val (abs, tm') = variant_absfree (x, T, tm) in
   448             (case rew1 tm' of
   449               Some tm'' => Some (abs tm'')
   450             | None => None)
   451           end
   452       | rew2 _ = None
   453 
   454   in if_none (timeap_msg "FIXME: rewrite_term" rew1 tm) tm end;
   455 
   456 end;