src/FOLP/simp.ML
author lcp
Tue Jan 18 16:37:12 1994 +0100 (1994-01-18)
changeset 231 cb6a24451544
parent 0 a5a9c433f639
child 611 11098f505bfe
permissions -rw-r--r--
Updated refs to old Sign functions
     1 (*  Title:      FOLP/simp
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1993  University of Cambridge
     5 
     6 FOLP version of...
     7 
     8 Generic simplifier, suitable for most logics.  (from Provers)
     9 
    10 This version allows instantiation of Vars in the subgoal, since the proof
    11 term must change.
    12 *)
    13 
    14 signature SIMP_DATA =
    15 sig
    16   val case_splits  : (thm * string) list
    17   val dest_red     : term -> term * term * term
    18   val mk_rew_rules : thm -> thm list
    19   val norm_thms    : (thm*thm) list (* [(?x>>norm(?x), norm(?x)>>?x), ...] *)
    20   val red1         : thm        (*  ?P>>?Q  ==>  ?P  ==>  ?Q  *)
    21   val red2         : thm        (*  ?P>>?Q  ==>  ?Q  ==>  ?P  *)
    22   val refl_thms    : thm list
    23   val subst_thms   : thm list   (* [ ?a>>?b ==> ?P(?a) ==> ?P(?b), ...] *)
    24   val trans_thms   : thm list
    25 end;
    26 
    27 
    28 infix 4 addrews addcongs delrews delcongs setauto;
    29 
    30 signature SIMP =
    31 sig
    32   type simpset
    33   val empty_ss  : simpset
    34   val addcongs  : simpset * thm list -> simpset
    35   val addrews   : simpset * thm list -> simpset
    36   val delcongs  : simpset * thm list -> simpset
    37   val delrews   : simpset * thm list -> simpset
    38   val dest_ss   : simpset -> thm list * thm list
    39   val print_ss  : simpset -> unit
    40   val setauto   : simpset * (int -> tactic) -> simpset
    41   val ASM_SIMP_CASE_TAC : simpset -> int -> tactic
    42   val ASM_SIMP_TAC      : simpset -> int -> tactic
    43   val CASE_TAC          : simpset -> int -> tactic
    44   val SIMP_CASE2_TAC    : simpset -> int -> tactic
    45   val SIMP_THM          : simpset -> thm -> thm
    46   val SIMP_TAC          : simpset -> int -> tactic
    47   val SIMP_CASE_TAC     : simpset -> int -> tactic
    48   val mk_congs          : theory -> string list -> thm list
    49   val mk_typed_congs    : theory -> (string * string) list -> thm list
    50 (* temporarily disabled:
    51   val extract_free_congs        : unit -> thm list
    52 *)
    53   val tracing   : bool ref
    54 end;
    55 
    56 functor SimpFun (Simp_data: SIMP_DATA) : SIMP = 
    57 struct
    58 
    59 local open Simp_data Logic in
    60 
    61 (*For taking apart reductions into left, right hand sides*)
    62 val lhs_of = #2 o dest_red;
    63 val rhs_of = #3 o dest_red;
    64 
    65 (*** Indexing and filtering of theorems ***)
    66 
    67 fun eq_brl ((b1,th1),(b2,th2)) = b1=b2 andalso eq_thm(th1,th2);
    68 
    69 (*insert a thm in a discrimination net by its lhs*)
    70 fun lhs_insert_thm (th,net) =
    71     Net.insert_term((lhs_of (concl_of th), (false,th)), net, eq_brl)
    72     handle  Net.INSERT => net;
    73 
    74 (*match subgoal i against possible theorems in the net.
    75   Similar to match_from_nat_tac, but the net does not contain numbers;
    76   rewrite rules are not ordered.*)
    77 fun net_tac net =
    78   SUBGOAL(fn (prem,i) => 
    79 	  resolve_tac (Net.unify_term net (strip_assums_concl prem)) i);
    80 
    81 (*match subgoal i against possible theorems indexed by lhs in the net*)
    82 fun lhs_net_tac net =
    83   SUBGOAL(fn (prem,i) => 
    84 	  biresolve_tac (Net.unify_term net
    85 		       (lhs_of (strip_assums_concl prem))) i);
    86 
    87 fun nth_subgoal i thm = nth_elem(i-1,prems_of thm);
    88 
    89 fun goal_concl i thm = strip_assums_concl(nth_subgoal i thm);
    90 
    91 fun lhs_of_eq i thm = lhs_of(goal_concl i thm)
    92 and rhs_of_eq i thm = rhs_of(goal_concl i thm);
    93 
    94 fun var_lhs(thm,i) =
    95 let fun var(Var _) = true
    96       | var(Abs(_,_,t)) = var t
    97       | var(f$_) = var f
    98       | var _ = false;
    99 in var(lhs_of_eq i thm) end;
   100 
   101 fun contains_op opns =
   102     let fun contains(Const(s,_)) = s mem opns |
   103             contains(s$t) = contains s orelse contains t |
   104             contains(Abs(_,_,t)) = contains t |
   105             contains _ = false;
   106     in contains end;
   107 
   108 fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i;
   109 
   110 val (normI_thms,normE_thms) = split_list norm_thms;
   111 
   112 (*Get the norm constants from norm_thms*)
   113 val norms =
   114   let fun norm thm = 
   115       case lhs_of(concl_of thm) of
   116 	  Const(n,_)$_ => n
   117 	| _ => (prths normE_thms; error"No constant in lhs of a norm_thm")
   118   in map norm normE_thms end;
   119 
   120 fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
   121 	Const(s,_)$_ => s mem norms | _ => false;
   122 
   123 val refl_tac = resolve_tac refl_thms;
   124 
   125 fun find_res thms thm =
   126     let fun find [] = (prths thms; error"Check Simp_Data")
   127           | find(th::thms) = thm RS th handle _ => find thms
   128     in find thms end;
   129 
   130 val mk_trans = find_res trans_thms;
   131 
   132 fun mk_trans2 thm =
   133 let fun mk[] = error"Check transitivity"
   134       | mk(t::ts) = (thm RSN (2,t))  handle _  => mk ts
   135 in mk trans_thms end;
   136 
   137 (*Applies tactic and returns the first resulting state, FAILS if none!*)
   138 fun one_result(tac,thm) = case Sequence.pull(tapply(tac,thm)) of
   139 	Some(thm',_) => thm'
   140       | None => raise THM("Simplifier: could not continue", 0, [thm]);
   141 
   142 fun res1(thm,thms,i) = one_result(resolve_tac thms i,thm);
   143 
   144 
   145 (**** Adding "NORM" tags ****)
   146 
   147 (*get name of the constant from conclusion of a congruence rule*)
   148 fun cong_const cong = 
   149     case head_of (lhs_of (concl_of cong)) of
   150 	Const(c,_) => c
   151       | _ => ""			(*a placeholder distinct from const names*);
   152 
   153 (*true if the term is an atomic proposition (no ==> signs) *)
   154 val atomic = null o strip_assums_hyp;
   155 
   156 (*ccs contains the names of the constants possessing congruence rules*)
   157 fun add_hidden_vars ccs =
   158   let fun add_hvars(tm,hvars) = case tm of
   159 	      Abs(_,_,body) => add_term_vars(body,hvars)
   160 	    | _$_ => let val (f,args) = strip_comb tm 
   161 		     in case f of
   162 			    Const(c,T) => 
   163 				if c mem ccs
   164 				then foldr add_hvars (args,hvars)
   165 				else add_term_vars(tm,hvars)
   166 			  | _ => add_term_vars(tm,hvars)
   167 		     end
   168 	    | _ => hvars;
   169   in add_hvars end;
   170 
   171 fun add_new_asm_vars new_asms =
   172     let fun itf((tm,at),vars) =
   173 		if at then vars else add_term_vars(tm,vars)
   174 	fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
   175 		in if length(tml)=length(al)
   176 		   then foldr itf (tml~~al,vars)
   177 		   else vars
   178 		end
   179 	fun add_vars (tm,vars) = case tm of
   180 		  Abs (_,_,body) => add_vars(body,vars)
   181 		| r$s => (case head_of tm of
   182 			  Const(c,T) => (case assoc(new_asms,c) of
   183 				  None => add_vars(r,add_vars(s,vars))
   184 				| Some(al) => add_list(tm,al,vars))
   185 			| _ => add_vars(r,add_vars(s,vars)))
   186 		| _ => vars
   187     in add_vars end;
   188 
   189 
   190 fun add_norms(congs,ccs,new_asms) thm =
   191 let val thm' = mk_trans2 thm;
   192 (* thm': [?z -> l; Prems; r -> ?t] ==> ?z -> ?t *)
   193     val nops = nprems_of thm'
   194     val lhs = rhs_of_eq 1 thm'
   195     val rhs = lhs_of_eq nops thm'
   196     val asms = tl(rev(tl(prems_of thm')))
   197     val hvars = foldr (add_hidden_vars ccs) (lhs::rhs::asms,[])
   198     val hvars = add_new_asm_vars new_asms (rhs,hvars)
   199     fun it_asms (asm,hvars) =
   200 	if atomic asm then add_new_asm_vars new_asms (asm,hvars)
   201 	else add_term_frees(asm,hvars)
   202     val hvars = foldr it_asms (asms,hvars)
   203     val hvs = map (#1 o dest_Var) hvars
   204     val refl1_tac = refl_tac 1
   205     val add_norm_tac = DEPTH_FIRST (has_fewer_prems nops)
   206 	      (STATE(fn thm =>
   207 		case head_of(rhs_of_eq 1 thm) of
   208 		  Var(ixn,_) => if ixn mem hvs then refl1_tac
   209 				else resolve_tac normI_thms 1 ORELSE refl1_tac
   210 		| Const _ => resolve_tac normI_thms 1 ORELSE
   211 			     resolve_tac congs 1 ORELSE refl1_tac
   212 		| Free _ => resolve_tac congs 1 ORELSE refl1_tac
   213 		| _ => refl1_tac))
   214     val Some(thm'',_) = Sequence.pull(tapply(add_norm_tac,thm'))
   215 in thm'' end;
   216 
   217 fun add_norm_tags congs =
   218     let val ccs = map cong_const congs
   219 	val new_asms = filter (exists not o #2)
   220 		(ccs ~~ (map (map atomic o prems_of) congs));
   221     in add_norms(congs,ccs,new_asms) end;
   222 
   223 fun normed_rews congs =
   224   let val add_norms = add_norm_tags congs;
   225   in fn thm => map (varifyT o add_norms o mk_trans) (mk_rew_rules(freezeT thm))
   226   end;
   227 
   228 fun NORM norm_lhs_tac = EVERY'[resolve_tac [red2], norm_lhs_tac, refl_tac];
   229 
   230 val trans_norms = map mk_trans normE_thms;
   231 
   232 
   233 (* SIMPSET *)
   234 
   235 datatype simpset =
   236 	SS of {auto_tac: int -> tactic,
   237 	       congs: thm list,
   238 	       cong_net: thm Net.net,
   239 	       mk_simps: thm -> thm list,
   240 	       simps: (thm * thm list) list,
   241 	       simp_net: thm Net.net}
   242 
   243 val empty_ss = SS{auto_tac= K no_tac, congs=[], cong_net=Net.empty,
   244 		  mk_simps=normed_rews[], simps=[], simp_net=Net.empty};
   245 
   246 (** Insertion of congruences and rewrites **)
   247 
   248 (*insert a thm in a thm net*)
   249 fun insert_thm_warn (th,net) = 
   250   Net.insert_term((concl_of th, th), net, eq_thm)
   251   handle Net.INSERT => 
   252     (writeln"\nDuplicate rewrite or congruence rule:"; print_thm th;
   253      net);
   254 
   255 val insert_thms = foldr insert_thm_warn;
   256 
   257 fun addrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
   258 let val thms = mk_simps thm
   259 in SS{auto_tac=auto_tac,congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   260       simps = (thm,thms)::simps, simp_net = insert_thms(thms,simp_net)}
   261 end;
   262 
   263 val op addrews = foldl addrew;
   264 
   265 fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
   266 let val congs' = thms @ congs;
   267 in SS{auto_tac=auto_tac, congs= congs',
   268       cong_net= insert_thms (map mk_trans thms,cong_net),
   269       mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
   270 end;
   271 
   272 (** Deletion of congruences and rewrites **)
   273 
   274 (*delete a thm from a thm net*)
   275 fun delete_thm_warn (th,net) = 
   276   Net.delete_term((concl_of th, th), net, eq_thm)
   277   handle Net.DELETE => 
   278     (writeln"\nNo such rewrite or congruence rule:";  print_thm th;
   279      net);
   280 
   281 val delete_thms = foldr delete_thm_warn;
   282 
   283 fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
   284 let val congs' = foldl (gen_rem eq_thm) (congs,thms)
   285 in SS{auto_tac=auto_tac, congs= congs',
   286       cong_net= delete_thms(map mk_trans thms,cong_net),
   287       mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
   288 end;
   289 
   290 fun delrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
   291 let fun find((p as (th,ths))::ps',ps) =
   292 	  if eq_thm(thm,th) then (ths,ps@ps') else find(ps',p::ps)
   293       | find([],simps') = (writeln"\nNo such rewrite or congruence rule:";
   294 			   print_thm thm;
   295 			   ([],simps'))
   296     val (thms,simps') = find(simps,[])
   297 in SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   298       simps = simps', simp_net = delete_thms(thms,simp_net)}
   299 end;
   300 
   301 val op delrews = foldl delrew;
   302 
   303 
   304 fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,...}, auto_tac) =
   305     SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
   306        simps=simps, simp_net=simp_net};
   307 
   308 
   309 (** Inspection of a simpset **)
   310 
   311 fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
   312 
   313 fun print_ss(SS{congs,simps,...}) =
   314 	(writeln"Congruences:"; prths congs;
   315 	 writeln"Rewrite Rules:"; prths (map #1 simps); ());
   316 
   317 
   318 (* Rewriting with conditionals *)
   319 
   320 val (case_thms,case_consts) = split_list case_splits;
   321 val case_rews = map mk_trans case_thms;
   322 
   323 fun if_rewritable ifc i thm =
   324     let val tm = goal_concl i thm
   325 	fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
   326 	  | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
   327 	  | nobound(Bound n,j,k) = n < k orelse k+j <= n
   328 	  | nobound(_) = true;
   329 	fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
   330 	fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
   331 	  | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
   332 		case f of Const(c,_) =>	if c=ifc then check_args(al,j)
   333 			else find_if(s,j) orelse find_if(t,j)
   334 		| _ => find_if(s,j) orelse find_if(t,j) end
   335 	  | find_if(_) = false;
   336     in find_if(tm,0) end;
   337 
   338 fun IF1_TAC cong_tac i =
   339     let fun seq_try (ifth::ifths,ifc::ifcs) thm = tapply(
   340 		COND (if_rewritable ifc i) (DETERM(resolve_tac[ifth]i))
   341 			(Tactic(seq_try(ifths,ifcs))), thm)
   342 	      | seq_try([],_) thm = tapply(no_tac,thm)
   343 	and try_rew thm = tapply(Tactic(seq_try(case_rews,case_consts))
   344 				 ORELSE Tactic one_subt, thm)
   345 	and one_subt thm =
   346 		let val test = has_fewer_prems (nprems_of thm + 1)
   347 		    fun loop thm = tapply(COND test no_tac
   348 			((Tactic try_rew THEN DEPTH_FIRST test (refl_tac i))
   349 			 ORELSE (refl_tac i THEN Tactic loop)), thm)
   350 		in tapply(cong_tac THEN Tactic loop, thm) end
   351     in COND (may_match(case_consts,i)) (Tactic try_rew) no_tac end;
   352 
   353 fun CASE_TAC (SS{cong_net,...}) i =
   354 let val cong_tac = net_tac cong_net i
   355 in NORM (IF1_TAC cong_tac) i end;
   356 
   357 (* Rewriting Automaton *)
   358 
   359 datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
   360 	       | PROVE | POP_CS | POP_ARTR | IF;
   361 (*
   362 fun pr_cntrl c = case c of STOP => prs("STOP") | MK_EQ => prs("MK_EQ") |
   363 ASMS i => print_int i | POP_ARTR => prs("POP_ARTR") |
   364 SIMP_LHS => prs("SIMP_LHS") | REW => prs("REW") | REFL => prs("REFL") |
   365 TRUE => prs("TRUE") | PROVE => prs("PROVE") | POP_CS => prs("POP_CS") | IF
   366 => prs("IF");
   367 *)
   368 fun simp_refl([],_,ss) = ss
   369   | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
   370 	else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
   371 
   372 (** Tracing **)
   373 
   374 val tracing = ref false;
   375 
   376 (*Replace parameters by Free variables in P*)
   377 fun variants_abs ([],P) = P
   378   | variants_abs ((a,T)::aTs, P) =
   379       variants_abs (aTs, #2 (variant_abs(a,T,P)));
   380 
   381 (*Select subgoal i from proof state; substitute parameters, for printing*)
   382 fun prepare_goal i st =
   383     let val subgi = nth_subgoal i st
   384 	val params = rev(strip_params subgi)
   385     in variants_abs (params, strip_assums_concl subgi) end;
   386 
   387 (*print lhs of conclusion of subgoal i*)
   388 fun pr_goal_lhs i st =
   389     writeln (Sign.string_of_term (#sign(rep_thm st)) 
   390 	     (lhs_of (prepare_goal i st)));
   391 
   392 (*print conclusion of subgoal i*)
   393 fun pr_goal_concl i st =
   394     writeln (Sign.string_of_term (#sign(rep_thm st)) (prepare_goal i st)) 
   395 
   396 (*print subgoals i to j (inclusive)*)
   397 fun pr_goals (i,j) st =
   398     if i>j then ()
   399     else (pr_goal_concl i st;  pr_goals (i+1,j) st);
   400 
   401 (*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
   402   thm=old state, thm'=new state *)
   403 fun pr_rew (i,n,thm,thm',not_asms) =
   404     if !tracing
   405     then (if not_asms then () else writeln"Assumption used in";
   406           pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
   407 	  if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
   408           else ();
   409           writeln"" )
   410     else ();
   411 
   412 (* Skip the first n hyps of a goal, and return the rest in generalized form *)
   413 fun strip_varify(Const("==>", _) $ H $ B, n, vs) =
   414 	if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
   415 	else strip_varify(B,n-1,vs)
   416   | strip_varify(Const("all",_)$Abs(_,T,t), n, vs) =
   417 	strip_varify(t,n,Var(("?",length vs),T)::vs)
   418   | strip_varify  _  = [];
   419 
   420 fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
   421 
   422 fun simp_lhs(thm,ss,anet,ats,cs) =
   423     if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
   424     if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
   425     else case Sequence.pull(tapply(cong_tac i,thm)) of
   426 	    Some(thm',_) =>
   427 		    let val ps = prems_of thm and ps' = prems_of thm';
   428 			val n = length(ps')-length(ps);
   429 			val a = length(strip_assums_hyp(nth_elem(i-1,ps)))
   430 			val l = map (fn p => length(strip_assums_hyp(p)))
   431 				    (take(n,drop(i-1,ps')));
   432 		    in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
   433 	  | None => (REW::ss,thm,anet,ats,cs);
   434 
   435 (*NB: the "Adding rewrites:" trace will look strange because assumptions
   436       are represented by rules, generalized over their parameters*)
   437 fun add_asms(ss,thm,a,anet,ats,cs) =
   438     let val As = strip_varify(nth_subgoal i thm, a, []);
   439 	val thms = map (trivial o cterm_of(#sign(rep_thm(thm))))As;
   440 	val new_rws = flat(map mk_rew_rules thms);
   441 	val rwrls = map mk_trans (flat(map mk_rew_rules thms));
   442 	val anet' = foldr lhs_insert_thm (rwrls,anet)
   443     in  if !tracing andalso not(null new_rws)
   444 	then (writeln"Adding rewrites:";  prths new_rws;  ())
   445 	else ();
   446 	(ss,thm,anet',anet::ats,cs) 
   447     end;
   448 
   449 fun rew(seq,thm,ss,anet,ats,cs, more) = case Sequence.pull seq of
   450       Some(thm',seq') =>
   451 	    let val n = (nprems_of thm') - (nprems_of thm)
   452 	    in pr_rew(i,n,thm,thm',more);
   453 	       if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
   454 	       else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
   455 		     thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
   456 	    end
   457     | None => if more
   458 	    then rew(tapply(lhs_net_tac anet i THEN assume_tac i,thm),
   459 		     thm,ss,anet,ats,cs,false)
   460 	    else (ss,thm,anet,ats,cs);
   461 
   462 fun try_true(thm,ss,anet,ats,cs) =
   463     case Sequence.pull(tapply(auto_tac i,thm)) of
   464       Some(thm',_) => (ss,thm',anet,ats,cs)
   465     | None => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
   466 	      in if !tracing
   467 		 then (writeln"*** Failed to prove precondition. Normal form:";
   468 		       pr_goal_concl i thm;  writeln"")
   469 		 else ();
   470 		 rew(seq,thm0,ss0,anet0,ats0,cs0,more)
   471 	      end;
   472 
   473 fun if_exp(thm,ss,anet,ats,cs) =
   474 	case Sequence.pull(tapply(IF1_TAC (cong_tac i) i,thm)) of
   475 		Some(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
   476 	      | None => (ss,thm,anet,ats,cs);
   477 
   478 fun step(s::ss, thm, anet, ats, cs) = case s of
   479 	  MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
   480 	| ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
   481 	| SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
   482 	| REW => rew(tapply(net_tac net i,thm),thm,ss,anet,ats,cs,true)
   483 	| REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
   484 	| TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
   485 	| PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
   486 		    else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
   487 	| POP_ARTR => (ss,thm,hd ats,tl ats,cs)
   488 	| POP_CS => (ss,thm,anet,ats,tl cs)
   489 	| IF => if_exp(thm,ss,anet,ats,cs);
   490 
   491 fun exec(state as (s::ss, thm, _, _, _)) =
   492 	if s=STOP then thm else exec(step(state));
   493 
   494 in exec(ss, thm, Net.empty, [], []) end;
   495 
   496 
   497 fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
   498 let val cong_tac = net_tac cong_net
   499 in fn i => Tactic(fn thm =>
   500 	if i <= 0 orelse nprems_of thm < i then Sequence.null
   501 	else Sequence.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
   502 	   THEN TRY(auto_tac i)
   503 end;
   504 
   505 val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
   506 val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
   507 
   508 val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
   509 val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
   510 
   511 val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
   512 
   513 fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
   514 let val cong_tac = net_tac cong_net
   515 in fn thm => let val state = thm RSN (2,red1)
   516 	     in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
   517 end;
   518 
   519 val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
   520 
   521 
   522 (* Compute Congruence rules for individual constants using the substition
   523    rules *)
   524 
   525 val subst_thms = map standard subst_thms;
   526 
   527 
   528 fun exp_app(0,t) = t
   529   | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
   530 
   531 fun exp_abs(Type("fun",[T1,T2]),t,i) =
   532 	Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
   533   | exp_abs(T,t,i) = exp_app(i,t);
   534 
   535 fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
   536 
   537 
   538 fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
   539 let fun xn_list(x,n) =
   540 	let val ixs = map (fn i => (x^(radixstring(26,"a",i)),0)) (0 upto n);
   541 	in map eta_Var (ixs ~~ (take(n+1,Ts))) end
   542     val lhs = list_comb(f,xn_list("X",k-1))
   543     val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
   544 in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
   545 
   546 fun find_subst tsig T =
   547 let fun find (thm::thms) =
   548 	let val (Const(_,cT), va, vb) =	dest_red(hd(prems_of thm));
   549 	    val [P] = add_term_vars(concl_of thm,[]) \\ [va,vb]
   550 	    val eqT::_ = binder_types cT
   551         in if Type.typ_instance(tsig,T,eqT) then Some(thm,va,vb,P)
   552 	   else find thms
   553 	end
   554       | find [] = None
   555 in find subst_thms end;
   556 
   557 fun mk_cong sg (f,aTs,rT) (refl,eq) =
   558 let val tsig = #tsig(Sign.rep_sg sg);
   559     val k = length aTs;
   560     fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
   561 	let val ca = cterm_of sg va
   562 	    and cx = cterm_of sg (eta_Var(("X"^si,0),T))
   563 	    val cb = cterm_of sg vb
   564 	    and cy = cterm_of sg (eta_Var(("Y"^si,0),T))
   565 	    val cP = cterm_of sg P
   566 	    and cp = cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
   567 	in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
   568     fun mk(c,T::Ts,i,yik) =
   569 	let val si = radixstring(26,"a",i)
   570 	in case find_subst tsig T of
   571 	     None => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
   572 	   | Some s => let val c' = c RSN (2,ri(s,i,si,T,yik))
   573 		       in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
   574 	end
   575       | mk(c,[],_,_) = c;
   576 in mk(refl,rev aTs,k-1,[]) end;
   577 
   578 fun mk_cong_type sg (f,T) =
   579 let val (aTs,rT) = strip_type T;
   580     val tsig = #tsig(Sign.rep_sg sg);
   581     fun find_refl(r::rs) =
   582 	let val (Const(eq,eqT),_,_) = dest_red(concl_of r)
   583 	in if Type.typ_instance(tsig, rT, hd(binder_types eqT))
   584 	   then Some(r,(eq,body_type eqT)) else find_refl rs
   585 	end
   586       | find_refl([]) = None;
   587 in case find_refl refl_thms of
   588      None => []  |  Some(refl) => [mk_cong sg (f,aTs,rT) refl]
   589 end;
   590 
   591 fun mk_cong_thy thy f =
   592 let val sg = sign_of thy;
   593     val T = case Sign.Symtab.lookup(#const_tab(Sign.rep_sg sg),f) of
   594 		None => error(f^" not declared") | Some(T) => T;
   595     val T' = incr_tvar 9 T;
   596 in mk_cong_type sg (Const(f,T'),T') end;
   597 
   598 fun mk_congs thy = flat o map (mk_cong_thy thy);
   599 
   600 fun mk_typed_congs thy =
   601 let val sg = sign_of thy;
   602     val S0 = Type.defaultS(#tsig(Sign.rep_sg sg))
   603     fun readfT(f,s) =
   604 	let val T = incr_tvar 9 (Sign.read_typ(sg,K(Some(S0))) s);
   605 	    val t = case Sign.Symtab.lookup(#const_tab(Sign.rep_sg sg),f) of
   606 		      Some(_) => Const(f,T) | None => Free(f,T)
   607 	in (t,T) end
   608 in flat o map (mk_cong_type sg o readfT) end;
   609 
   610 end (* local *)
   611 end (* SIMP *);