src/FOLP/simp.ML
author wenzelm
Sun Jul 05 16:39:25 2015 +0200 (2015-07-05)
changeset 60644 4af8b9c2b52f
parent 59621 291934bac95e
child 60645 2affe7e97a34
permissions -rw-r--r--
clarified context;
     1 (*  Title:      FOLP/simp.ML
     2     Author:     Tobias Nipkow
     3     Copyright   1993  University of Cambridge
     4 
     5 FOLP version of...
     6 
     7 Generic simplifier, suitable for most logics.  (from Provers)
     8 
     9 This version allows instantiation of Vars in the subgoal, since the proof
    10 term must change.
    11 *)
    12 
    13 signature SIMP_DATA =
    14 sig
    15   val case_splits  : (thm * string) list
    16   val dest_red     : term -> term * term * term
    17   val mk_rew_rules : thm -> thm list
    18   val norm_thms    : (thm*thm) list (* [(?x>>norm(?x), norm(?x)>>?x), ...] *)
    19   val red1         : thm        (*  ?P>>?Q  ==>  ?P  ==>  ?Q  *)
    20   val red2         : thm        (*  ?P>>?Q  ==>  ?Q  ==>  ?P  *)
    21   val refl_thms    : thm list
    22   val subst_thms   : thm list   (* [ ?a>>?b ==> ?P(?a) ==> ?P(?b), ...] *)
    23   val trans_thms   : thm list
    24 end;
    25 
    26 
    27 infix 4 addcongs delrews delcongs setauto;
    28 
    29 signature SIMP =
    30 sig
    31   type simpset
    32   val empty_ss  : simpset
    33   val addcongs  : simpset * thm list -> simpset
    34   val addrew    : Proof.context -> thm -> simpset -> simpset
    35   val delcongs  : simpset * thm list -> simpset
    36   val delrews   : simpset * thm list -> simpset
    37   val dest_ss   : simpset -> thm list * thm list
    38   val print_ss  : simpset -> unit
    39   val setauto   : simpset * (int -> tactic) -> simpset
    40   val ASM_SIMP_CASE_TAC : simpset -> int -> tactic
    41   val ASM_SIMP_TAC      : simpset -> int -> tactic
    42   val CASE_TAC          : simpset -> int -> tactic
    43   val SIMP_CASE2_TAC    : simpset -> int -> tactic
    44   val SIMP_THM          : simpset -> thm -> thm
    45   val SIMP_TAC          : simpset -> int -> tactic
    46   val SIMP_CASE_TAC     : simpset -> int -> tactic
    47   val mk_congs          : theory -> string list -> thm list
    48   val mk_typed_congs    : theory -> (string * string) list -> thm list
    49 (* temporarily disabled:
    50   val extract_free_congs        : unit -> thm list
    51 *)
    52   val tracing   : bool Unsynchronized.ref
    53 end;
    54 
    55 functor SimpFun (Simp_data: SIMP_DATA) : SIMP =
    56 struct
    57 
    58 local open Simp_data in
    59 
    60 (*For taking apart reductions into left, right hand sides*)
    61 val lhs_of = #2 o dest_red;
    62 val rhs_of = #3 o dest_red;
    63 
    64 (*** Indexing and filtering of theorems ***)
    65 
    66 fun eq_brl ((b1 : bool, th1), (b2, th2)) = b1 = b2 andalso Thm.eq_thm_prop (th1, th2);
    67 
    68 (*insert a thm in a discrimination net by its lhs*)
    69 fun lhs_insert_thm th net =
    70     Net.insert_term eq_brl (lhs_of (Thm.concl_of th), (false,th)) net
    71     handle  Net.INSERT => net;
    72 
    73 (*match subgoal i against possible theorems in the net.
    74   Similar to match_from_nat_tac, but the net does not contain numbers;
    75   rewrite rules are not ordered.*)
    76 fun net_tac net =
    77   SUBGOAL(fn (prem,i) =>
    78           resolve0_tac (Net.unify_term net (Logic.strip_assums_concl prem)) i);
    79 
    80 (*match subgoal i against possible theorems indexed by lhs in the net*)
    81 fun lhs_net_tac net =
    82   SUBGOAL(fn (prem,i) =>
    83           biresolve0_tac (Net.unify_term net
    84                        (lhs_of (Logic.strip_assums_concl prem))) i);
    85 
    86 fun nth_subgoal i thm = nth (Thm.prems_of thm) (i - 1);
    87 
    88 fun goal_concl i thm = Logic.strip_assums_concl (nth_subgoal i thm);
    89 
    90 fun lhs_of_eq i thm = lhs_of(goal_concl i thm)
    91 and rhs_of_eq i thm = rhs_of(goal_concl i thm);
    92 
    93 fun var_lhs(thm,i) =
    94 let fun var(Var _) = true
    95       | var(Abs(_,_,t)) = var t
    96       | var(f$_) = var f
    97       | var _ = false;
    98 in var(lhs_of_eq i thm) end;
    99 
   100 fun contains_op opns =
   101     let fun contains(Const(s,_)) = member (op =) opns s |
   102             contains(s$t) = contains s orelse contains t |
   103             contains(Abs(_,_,t)) = contains t |
   104             contains _ = false;
   105     in contains end;
   106 
   107 fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i;
   108 
   109 val (normI_thms,normE_thms) = split_list norm_thms;
   110 
   111 (*Get the norm constants from norm_thms*)
   112 val norms =
   113   let fun norm thm =
   114       case lhs_of (Thm.concl_of thm) of
   115           Const(n,_)$_ => n
   116         | _ => error "No constant in lhs of a norm_thm"
   117   in map norm normE_thms end;
   118 
   119 fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
   120         Const(s,_)$_ => member (op =) norms s | _ => false;
   121 
   122 val refl_tac = resolve0_tac refl_thms;
   123 
   124 fun find_res thms thm =
   125     let fun find [] = error "Check Simp_Data"
   126           | find(th::thms) = thm RS th handle THM _ => find thms
   127     in find thms end;
   128 
   129 val mk_trans = find_res trans_thms;
   130 
   131 fun mk_trans2 thm =
   132 let fun mk[] = error"Check transitivity"
   133       | mk(t::ts) = (thm RSN (2,t))  handle THM _  => mk ts
   134 in mk trans_thms end;
   135 
   136 (*Applies tactic and returns the first resulting state, FAILS if none!*)
   137 fun one_result(tac,thm) = case Seq.pull(tac thm) of
   138         SOME(thm',_) => thm'
   139       | NONE => raise THM("Simplifier: could not continue", 0, [thm]);
   140 
   141 fun res1(thm,thms,i) = one_result(resolve0_tac thms i,thm);
   142 
   143 
   144 (**** Adding "NORM" tags ****)
   145 
   146 (*get name of the constant from conclusion of a congruence rule*)
   147 fun cong_const cong =
   148     case head_of (lhs_of (Thm.concl_of cong)) of
   149         Const(c,_) => c
   150       | _ => ""                 (*a placeholder distinct from const names*);
   151 
   152 (*true if the term is an atomic proposition (no ==> signs) *)
   153 val atomic = null o Logic.strip_assums_hyp;
   154 
   155 (*ccs contains the names of the constants possessing congruence rules*)
   156 fun add_hidden_vars ccs =
   157   let fun add_hvars tm hvars = case tm of
   158               Abs(_,_,body) => Misc_Legacy.add_term_vars(body,hvars)
   159             | _$_ => let val (f,args) = strip_comb tm
   160                      in case f of
   161                             Const(c,T) =>
   162                                 if member (op =) ccs c
   163                                 then fold_rev add_hvars args hvars
   164                                 else Misc_Legacy.add_term_vars (tm, hvars)
   165                           | _ => Misc_Legacy.add_term_vars (tm, hvars)
   166                      end
   167             | _ => hvars;
   168   in add_hvars end;
   169 
   170 fun add_new_asm_vars new_asms =
   171     let fun itf (tm, at) vars =
   172                 if at then vars else Misc_Legacy.add_term_vars(tm,vars)
   173         fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
   174                 in if length(tml)=length(al)
   175                    then fold_rev itf (tml ~~ al) vars
   176                    else vars
   177                 end
   178         fun add_vars (tm,vars) = case tm of
   179                   Abs (_,_,body) => add_vars(body,vars)
   180                 | r$s => (case head_of tm of
   181                           Const(c,T) => (case AList.lookup (op =) new_asms c of
   182                                   NONE => add_vars(r,add_vars(s,vars))
   183                                 | SOME(al) => add_list(tm,al,vars))
   184                         | _ => add_vars(r,add_vars(s,vars)))
   185                 | _ => vars
   186     in add_vars end;
   187 
   188 
   189 fun add_norms(congs,ccs,new_asms) thm =
   190 let val thm' = mk_trans2 thm;
   191 (* thm': [?z -> l; Prems; r -> ?t] ==> ?z -> ?t *)
   192     val nops = Thm.nprems_of thm'
   193     val lhs = rhs_of_eq 1 thm'
   194     val rhs = lhs_of_eq nops thm'
   195     val asms = tl(rev(tl(Thm.prems_of thm')))
   196     val hvars = fold_rev (add_hidden_vars ccs) (lhs::rhs::asms) []
   197     val hvars = add_new_asm_vars new_asms (rhs,hvars)
   198     fun it_asms asm hvars =
   199         if atomic asm then add_new_asm_vars new_asms (asm,hvars)
   200         else Misc_Legacy.add_term_frees(asm,hvars)
   201     val hvars = fold_rev it_asms asms hvars
   202     val hvs = map (#1 o dest_Var) hvars
   203     val refl1_tac = refl_tac 1
   204     fun norm_step_tac st = st |>
   205          (case head_of(rhs_of_eq 1 st) of
   206             Var(ixn,_) => if member (op =) hvs ixn then refl1_tac
   207                           else resolve0_tac normI_thms 1 ORELSE refl1_tac
   208           | Const _ => resolve0_tac normI_thms 1 ORELSE
   209                        resolve0_tac congs 1 ORELSE refl1_tac
   210           | Free _ => resolve0_tac congs 1 ORELSE refl1_tac
   211           | _ => refl1_tac)
   212     val add_norm_tac = DEPTH_FIRST (has_fewer_prems nops) norm_step_tac
   213     val SOME(thm'',_) = Seq.pull(add_norm_tac thm')
   214 in thm'' end;
   215 
   216 fun add_norm_tags congs =
   217     let val ccs = map cong_const congs
   218         val new_asms = filter (exists not o #2)
   219                 (ccs ~~ (map (map atomic o Thm.prems_of) congs));
   220     in add_norms(congs,ccs,new_asms) end;
   221 
   222 fun normed_rews congs =
   223   let
   224     val add_norms = add_norm_tags congs
   225     fun normed ctxt thm =
   226       let
   227         val ctxt' = Variable.declare_thm thm ctxt;
   228       in Variable.tradeT (K (map (add_norms o mk_trans) o maps mk_rew_rules)) ctxt [thm] end
   229   in normed end;
   230 
   231 fun NORM norm_lhs_tac = EVERY'[rtac red2 , norm_lhs_tac, refl_tac];
   232 
   233 val trans_norms = map mk_trans normE_thms;
   234 
   235 
   236 (* SIMPSET *)
   237 
   238 datatype simpset =
   239         SS of {auto_tac: int -> tactic,
   240                congs: thm list,
   241                cong_net: thm Net.net,
   242                mk_simps: Proof.context -> thm -> thm list,
   243                simps: (thm * thm list) list,
   244                simp_net: thm Net.net}
   245 
   246 val empty_ss = SS{auto_tac= K no_tac, congs=[], cong_net=Net.empty,
   247                   mk_simps=normed_rews[], simps=[], simp_net=Net.empty};
   248 
   249 (** Insertion of congruences and rewrites **)
   250 
   251 (*insert a thm in a thm net*)
   252 fun insert_thm_warn th net =
   253   Net.insert_term Thm.eq_thm_prop (Thm.concl_of th, th) net
   254   handle Net.INSERT =>
   255     (writeln ("Duplicate rewrite or congruence rule:\n" ^
   256         Display.string_of_thm_without_context th); net);
   257 
   258 val insert_thms = fold_rev insert_thm_warn;
   259 
   260 fun addrew ctxt thm (SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}) =
   261 let val thms = mk_simps ctxt thm
   262 in SS{auto_tac=auto_tac,congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   263       simps = (thm,thms)::simps, simp_net = insert_thms thms simp_net}
   264 end;
   265 
   266 fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
   267 let val congs' = thms @ congs;
   268 in SS{auto_tac=auto_tac, congs= congs',
   269       cong_net= insert_thms (map mk_trans thms) cong_net,
   270       mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
   271 end;
   272 
   273 (** Deletion of congruences and rewrites **)
   274 
   275 (*delete a thm from a thm net*)
   276 fun delete_thm_warn th net =
   277   Net.delete_term Thm.eq_thm_prop (Thm.concl_of th, th) net
   278   handle Net.DELETE =>
   279     (writeln ("No such rewrite or congruence rule:\n" ^
   280         Display.string_of_thm_without_context th); net);
   281 
   282 val delete_thms = fold_rev delete_thm_warn;
   283 
   284 fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
   285 let val congs' = fold (remove Thm.eq_thm_prop) thms congs
   286 in SS{auto_tac=auto_tac, congs= congs',
   287       cong_net= delete_thms (map mk_trans thms) cong_net,
   288       mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
   289 end;
   290 
   291 fun delrew thm (SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}) =
   292 let fun find((p as (th,ths))::ps',ps) =
   293           if Thm.eq_thm_prop(thm,th) then (ths,ps@ps') else find(ps',p::ps)
   294       | find([],simps') =
   295           (writeln ("No such rewrite or congruence rule:\n" ^
   296               Display.string_of_thm_without_context thm); ([], simps'))
   297     val (thms,simps') = find(simps,[])
   298 in SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   299       simps = simps', simp_net = delete_thms thms simp_net }
   300 end;
   301 
   302 fun ss delrews thms = fold delrew thms ss;
   303 
   304 
   305 fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,...}, auto_tac) =
   306     SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   307        simps=simps, simp_net=simp_net};
   308 
   309 
   310 (** Inspection of a simpset **)
   311 
   312 fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
   313 
   314 fun print_ss(SS{congs,simps,...}) =
   315   writeln (cat_lines
   316    (["Congruences:"] @ map Display.string_of_thm_without_context congs @
   317     ["Rewrite Rules:"] @ map (Display.string_of_thm_without_context o #1) simps));
   318 
   319 
   320 (* Rewriting with conditionals *)
   321 
   322 val (case_thms,case_consts) = split_list case_splits;
   323 val case_rews = map mk_trans case_thms;
   324 
   325 fun if_rewritable ifc i thm =
   326     let val tm = goal_concl i thm
   327         fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
   328           | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
   329           | nobound(Bound n,j,k) = n < k orelse k+j <= n
   330           | nobound(_) = true;
   331         fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
   332         fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
   333           | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
   334                 case f of Const(c,_) => if c=ifc then check_args(al,j)
   335                         else find_if(s,j) orelse find_if(t,j)
   336                 | _ => find_if(s,j) orelse find_if(t,j) end
   337           | find_if(_) = false;
   338     in find_if(tm,0) end;
   339 
   340 fun IF1_TAC cong_tac i =
   341     let fun seq_try (ifth::ifths,ifc::ifcs) thm =
   342                 (COND (if_rewritable ifc i) (DETERM(rtac ifth i))
   343                         (seq_try(ifths,ifcs))) thm
   344               | seq_try([],_) thm = no_tac thm
   345         and try_rew thm = (seq_try(case_rews,case_consts) ORELSE one_subt) thm
   346         and one_subt thm =
   347                 let val test = has_fewer_prems (Thm.nprems_of thm + 1)
   348                     fun loop thm =
   349                         COND test no_tac
   350                           ((try_rew THEN DEPTH_FIRST test (refl_tac i))
   351                            ORELSE (refl_tac i THEN loop)) thm
   352                 in (cong_tac THEN loop) thm end
   353     in COND (may_match(case_consts,i)) try_rew no_tac end;
   354 
   355 fun CASE_TAC (SS{cong_net,...}) i =
   356 let val cong_tac = net_tac cong_net i
   357 in NORM (IF1_TAC cong_tac) i end;
   358 
   359 (* Rewriting Automaton *)
   360 
   361 datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
   362                | PROVE | POP_CS | POP_ARTR | IF;
   363 
   364 fun simp_refl([],_,ss) = ss
   365   | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
   366         else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
   367 
   368 (** Tracing **)
   369 
   370 val tracing = Unsynchronized.ref false;
   371 
   372 (*Replace parameters by Free variables in P*)
   373 fun variants_abs ([],P) = P
   374   | variants_abs ((a,T)::aTs, P) =
   375       variants_abs (aTs, #2 (Syntax_Trans.variant_abs(a,T,P)));
   376 
   377 (*Select subgoal i from proof state; substitute parameters, for printing*)
   378 fun prepare_goal i st =
   379     let val subgi = nth_subgoal i st
   380         val params = rev (Logic.strip_params subgi)
   381     in variants_abs (params, Logic.strip_assums_concl subgi) end;
   382 
   383 (*print lhs of conclusion of subgoal i*)
   384 fun pr_goal_lhs i st =
   385     writeln (Syntax.string_of_term_global (Thm.theory_of_thm st)
   386              (lhs_of (prepare_goal i st)));
   387 
   388 (*print conclusion of subgoal i*)
   389 fun pr_goal_concl i st =
   390     writeln (Syntax.string_of_term_global (Thm.theory_of_thm st) (prepare_goal i st))
   391 
   392 (*print subgoals i to j (inclusive)*)
   393 fun pr_goals (i,j) st =
   394     if i>j then ()
   395     else (pr_goal_concl i st;  pr_goals (i+1,j) st);
   396 
   397 (*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
   398   thm=old state, thm'=new state *)
   399 fun pr_rew (i,n,thm,thm',not_asms) =
   400     if !tracing
   401     then (if not_asms then () else writeln"Assumption used in";
   402           pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
   403           if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
   404           else ();
   405           writeln"" )
   406     else ();
   407 
   408 (* Skip the first n hyps of a goal, and return the rest in generalized form *)
   409 fun strip_varify(Const(@{const_name Pure.imp}, _) $ H $ B, n, vs) =
   410         if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
   411         else strip_varify(B,n-1,vs)
   412   | strip_varify(Const(@{const_name Pure.all},_)$Abs(_,T,t), n, vs) =
   413         strip_varify(t,n,Var(("?",length vs),T)::vs)
   414   | strip_varify  _  = [];
   415 
   416 fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
   417 
   418 fun simp_lhs(thm,ss,anet,ats,cs) =
   419     if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
   420     if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
   421     else case Seq.pull(cong_tac i thm) of
   422             SOME(thm',_) =>
   423                     let val ps = Thm.prems_of thm
   424                         and ps' = Thm.prems_of thm';
   425                         val n = length(ps')-length(ps);
   426                         val a = length(Logic.strip_assums_hyp(nth ps (i - 1)))
   427                         val l = map (length o Logic.strip_assums_hyp) (take n (drop (i-1) ps'));
   428                     in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
   429           | NONE => (REW::ss,thm,anet,ats,cs);
   430 
   431 (*NB: the "Adding rewrites:" trace will look strange because assumptions
   432       are represented by rules, generalized over their parameters*)
   433 fun add_asms(ss,thm,a,anet,ats,cs) =
   434     let val As = strip_varify(nth_subgoal i thm, a, []);
   435         val thms = map (Thm.trivial o Thm.global_cterm_of(Thm.theory_of_thm thm)) As;
   436         val new_rws = maps mk_rew_rules thms;
   437         val rwrls = map mk_trans (maps mk_rew_rules thms);
   438         val anet' = fold_rev lhs_insert_thm rwrls anet;
   439     in  if !tracing andalso not(null new_rws)
   440         then writeln (cat_lines
   441           ("Adding rewrites:" :: map Display.string_of_thm_without_context new_rws))
   442         else ();
   443         (ss,thm,anet',anet::ats,cs)
   444     end;
   445 
   446 fun rew(seq,thm,ss,anet,ats,cs, more) = case Seq.pull seq of
   447       SOME(thm',seq') =>
   448             let val n = (Thm.nprems_of thm') - (Thm.nprems_of thm)
   449             in pr_rew(i,n,thm,thm',more);
   450                if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
   451                else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
   452                      thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
   453             end
   454     | NONE => if more
   455             then rew((lhs_net_tac anet i THEN atac i) thm,
   456                      thm,ss,anet,ats,cs,false)
   457             else (ss,thm,anet,ats,cs);
   458 
   459 fun try_true(thm,ss,anet,ats,cs) =
   460     case Seq.pull(auto_tac i thm) of
   461       SOME(thm',_) => (ss,thm',anet,ats,cs)
   462     | NONE => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
   463               in if !tracing
   464                  then (writeln"*** Failed to prove precondition. Normal form:";
   465                        pr_goal_concl i thm;  writeln"")
   466                  else ();
   467                  rew(seq,thm0,ss0,anet0,ats0,cs0,more)
   468               end;
   469 
   470 fun if_exp(thm,ss,anet,ats,cs) =
   471         case Seq.pull (IF1_TAC (cong_tac i) i thm) of
   472                 SOME(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
   473               | NONE => (ss,thm,anet,ats,cs);
   474 
   475 fun step(s::ss, thm, anet, ats, cs) = case s of
   476           MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
   477         | ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
   478         | SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
   479         | REW => rew(net_tac net i thm,thm,ss,anet,ats,cs,true)
   480         | REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
   481         | TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
   482         | PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
   483                     else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
   484         | POP_ARTR => (ss,thm,hd ats,tl ats,cs)
   485         | POP_CS => (ss,thm,anet,ats,tl cs)
   486         | IF => if_exp(thm,ss,anet,ats,cs);
   487 
   488 fun exec(state as (s::ss, thm, _, _, _)) =
   489         if s=STOP then thm else exec(step(state));
   490 
   491 in exec(ss, thm, Net.empty, [], []) end;
   492 
   493 
   494 fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
   495 let val cong_tac = net_tac cong_net
   496 in fn i =>
   497     (fn thm =>
   498      if i <= 0 orelse Thm.nprems_of thm < i then Seq.empty
   499      else Seq.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
   500     THEN TRY(auto_tac i)
   501 end;
   502 
   503 val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
   504 val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
   505 
   506 val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
   507 val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
   508 
   509 val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
   510 
   511 fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
   512 let val cong_tac = net_tac cong_net
   513 in fn thm => let val state = thm RSN (2,red1)
   514              in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
   515 end;
   516 
   517 val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
   518 
   519 
   520 (* Compute Congruence rules for individual constants using the substition
   521    rules *)
   522 
   523 val subst_thms = map Drule.export_without_context subst_thms;
   524 
   525 
   526 fun exp_app(0,t) = t
   527   | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
   528 
   529 fun exp_abs(Type("fun",[T1,T2]),t,i) =
   530         Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
   531   | exp_abs(T,t,i) = exp_app(i,t);
   532 
   533 fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
   534 
   535 
   536 fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
   537 let fun xn_list(x,n) =
   538         let val ixs = map_range (fn i => (x^(radixstring(26,"a",i)),0)) (n - 1);
   539         in ListPair.map eta_Var (ixs, take (n+1) Ts) end
   540     val lhs = list_comb(f,xn_list("X",k-1))
   541     val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
   542 in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
   543 
   544 fun find_subst sg T =
   545 let fun find (thm::thms) =
   546         let val (Const(_,cT), va, vb) = dest_red(hd(Thm.prems_of thm));
   547             val [P] = subtract (op =) [va, vb] (Misc_Legacy.add_term_vars (Thm.concl_of thm, []));
   548             val eqT::_ = binder_types cT
   549         in if Sign.typ_instance sg (T,eqT) then SOME(thm,va,vb,P)
   550            else find thms
   551         end
   552       | find [] = NONE
   553 in find subst_thms end;
   554 
   555 fun mk_cong sg (f,aTs,rT) (refl,eq) =
   556 let val k = length aTs;
   557     fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
   558         let val ca = Thm.global_cterm_of sg va
   559             and cx = Thm.global_cterm_of sg (eta_Var(("X"^si,0),T))
   560             val cb = Thm.global_cterm_of sg vb
   561             and cy = Thm.global_cterm_of sg (eta_Var(("Y"^si,0),T))
   562             val cP = Thm.global_cterm_of sg P
   563             and cp = Thm.global_cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
   564         in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
   565     fun mk(c,T::Ts,i,yik) =
   566         let val si = radixstring(26,"a",i)
   567         in case find_subst sg T of
   568              NONE => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
   569            | SOME s => let val c' = c RSN (2,ri(s,i,si,T,yik))
   570                        in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
   571         end
   572       | mk(c,[],_,_) = c;
   573 in mk(refl,rev aTs,k-1,[]) end;
   574 
   575 fun mk_cong_type sg (f,T) =
   576 let val (aTs,rT) = strip_type T;
   577     fun find_refl(r::rs) =
   578         let val (Const(eq,eqT),_,_) = dest_red(Thm.concl_of r)
   579         in if Sign.typ_instance sg (rT, hd(binder_types eqT))
   580            then SOME(r,(eq,body_type eqT)) else find_refl rs
   581         end
   582       | find_refl([]) = NONE;
   583 in case find_refl refl_thms of
   584      NONE => []  |  SOME(refl) => [mk_cong sg (f,aTs,rT) refl]
   585 end;
   586 
   587 fun mk_cong_thy thy f =
   588 let val T = case Sign.const_type thy f of
   589                 NONE => error(f^" not declared") | SOME(T) => T;
   590     val T' = Logic.incr_tvar 9 T;
   591 in mk_cong_type thy (Const(f,T'),T') end;
   592 
   593 fun mk_congs thy = maps (mk_cong_thy thy);
   594 
   595 fun mk_typed_congs thy =
   596 let
   597   fun readfT(f,s) =
   598     let
   599       val T = Logic.incr_tvar 9 (Syntax.read_typ_global thy s);
   600       val t = case Sign.const_type thy f of
   601                   SOME(_) => Const(f,T) | NONE => Free(f,T)
   602     in (t,T) end
   603 in maps (mk_cong_type thy o readfT) end;
   604 
   605 end;
   606 end;