3 Copyright 1993 University of Cambridge
7 Generic simplifier, suitable for most logics. (from Provers)
9 This version allows instantiation of Vars in the subgoal, since the proof
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
27 infix 4 addrews addcongs delrews delcongs setauto;
32 val empty_ss : simpset
33 val addcongs : simpset * thm list -> simpset
34 val addrews : simpset * thm list -> 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
52 val tracing : bool ref
55 functor SimpFun (Simp_data: SIMP_DATA) : SIMP =
58 local open Simp_data in
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;
64 (*** Indexing and filtering of theorems ***)
66 fun eq_brl ((b1 : bool, th1), (b2, th2)) = b1 = b2 andalso Thm.eq_thm_prop (th1, th2);
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 (concl_of th), (false,th)) net
71 handle Net.INSERT => net;
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.*)
77 SUBGOAL(fn (prem,i) =>
78 resolve_tac (Net.unify_term net (Logic.strip_assums_concl prem)) i);
80 (*match subgoal i against possible theorems indexed by lhs in the net*)
82 SUBGOAL(fn (prem,i) =>
83 biresolve_tac (Net.unify_term net
84 (lhs_of (Logic.strip_assums_concl prem))) i);
86 fun nth_subgoal i thm = List.nth(prems_of thm,i-1);
88 fun goal_concl i thm = Logic.strip_assums_concl (nth_subgoal i thm);
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);
94 let fun var(Var _) = true
95 | var(Abs(_,_,t)) = var t
98 in var(lhs_of_eq i thm) end;
100 fun contains_op opns =
101 let fun contains(Const(s,_)) = s mem opns |
102 contains(s$t) = contains s orelse contains t |
103 contains(Abs(_,_,t)) = contains t |
107 fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i;
109 val (normI_thms,normE_thms) = split_list norm_thms;
111 (*Get the norm constants from norm_thms*)
114 case lhs_of(concl_of thm) of
116 | _ => error "No constant in lhs of a norm_thm"
117 in map norm normE_thms end;
119 fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
120 Const(s,_)$_ => s mem norms | _ => false;
122 val refl_tac = resolve_tac refl_thms;
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
129 val mk_trans = find_res trans_thms;
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;
136 (*Applies tactic and returns the first resulting state, FAILS if none!*)
137 fun one_result(tac,thm) = case Seq.pull(tac thm) of
139 | NONE => raise THM("Simplifier: could not continue", 0, [thm]);
141 fun res1(thm,thms,i) = one_result(resolve_tac thms i,thm);
144 (**** Adding "NORM" tags ****)
146 (*get name of the constant from conclusion of a congruence rule*)
147 fun cong_const cong =
148 case head_of (lhs_of (concl_of cong)) of
150 | _ => "" (*a placeholder distinct from const names*);
152 (*true if the term is an atomic proposition (no ==> signs) *)
153 val atomic = null o Logic.strip_assums_hyp;
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) => OldTerm.add_term_vars(body,hvars)
159 | _$_ => let val (f,args) = strip_comb tm
162 if member (op =) ccs c
163 then fold_rev add_hvars args hvars
164 else OldTerm.add_term_vars (tm, hvars)
165 | _ => OldTerm.add_term_vars (tm, hvars)
170 fun add_new_asm_vars new_asms =
171 let fun itf (tm, at) vars =
172 if at then vars else OldTerm.add_term_vars(tm,vars)
173 fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
174 in if length(tml)=length(al)
175 then fold_rev itf (tml ~~ al) vars
178 fun add_vars (tm,vars) = case tm of
179 Abs (_,_,body) => add_vars(body,vars)
180 | r$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)))
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 = 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(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 OldTerm.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 ixn mem hvs then refl1_tac
207 else resolve_tac normI_thms 1 ORELSE refl1_tac
208 | Const _ => resolve_tac normI_thms 1 ORELSE
209 resolve_tac congs 1 ORELSE refl1_tac
210 | Free _ => resolve_tac congs 1 ORELSE 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')
216 fun add_norm_tags congs =
217 let val ccs = map cong_const congs
218 val new_asms = List.filter (exists not o #2)
219 (ccs ~~ (map (map atomic o prems_of) congs));
220 in add_norms(congs,ccs,new_asms) end;
222 fun normed_rews congs =
223 let val add_norms = add_norm_tags congs in
224 fn thm => Variable.tradeT
225 (K (map (add_norms o mk_trans) o maps mk_rew_rules)) (Variable.thm_context thm) [thm]
228 fun NORM norm_lhs_tac = EVERY'[rtac red2 , norm_lhs_tac, refl_tac];
230 val trans_norms = map mk_trans normE_thms;
236 SS of {auto_tac: int -> tactic,
238 cong_net: thm Net.net,
239 mk_simps: thm -> thm list,
240 simps: (thm * thm list) list,
241 simp_net: thm Net.net}
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};
246 (** Insertion of congruences and rewrites **)
248 (*insert a thm in a thm net*)
249 fun insert_thm_warn th net =
250 Net.insert_term Thm.eq_thm_prop (concl_of th, th) net
252 (writeln ("Duplicate rewrite or congruence rule:\n" ^
253 Display.string_of_thm_without_context th); net);
255 val insert_thms = fold_rev insert_thm_warn;
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}
263 val op addrews = Library.foldl addrew;
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}
272 (** Deletion of congruences and rewrites **)
274 (*delete a thm from a thm net*)
275 fun delete_thm_warn th net =
276 Net.delete_term Thm.eq_thm_prop (concl_of th, th) net
278 (writeln ("No such rewrite or congruence rule:\n" ^
279 Display.string_of_thm_without_context th); net);
281 val delete_thms = fold_rev delete_thm_warn;
283 fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
284 let val congs' = fold (remove Thm.eq_thm_prop) thms congs
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}
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 Thm.eq_thm_prop(thm,th) then (ths,ps@ps') else find(ps',p::ps)
294 (writeln ("No such rewrite or congruence rule:\n" ^
295 Display.string_of_thm_without_context thm); ([], 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 }
301 val op delrews = Library.foldl delrew;
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};
309 (** Inspection of a simpset **)
311 fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
313 fun print_ss(SS{congs,simps,...}) =
315 (["Congruences:"] @ map Display.string_of_thm_without_context congs @
316 ["Rewrite Rules:"] @ map (Display.string_of_thm_without_context o #1) simps));
319 (* Rewriting with conditionals *)
321 val (case_thms,case_consts) = split_list case_splits;
322 val case_rews = map mk_trans case_thms;
324 fun if_rewritable ifc i thm =
325 let val tm = goal_concl i thm
326 fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
327 | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
328 | nobound(Bound n,j,k) = n < k orelse k+j <= n
330 fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
331 fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
332 | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
333 case f of Const(c,_) => if c=ifc then check_args(al,j)
334 else find_if(s,j) orelse find_if(t,j)
335 | _ => find_if(s,j) orelse find_if(t,j) end
336 | find_if(_) = false;
337 in find_if(tm,0) end;
339 fun IF1_TAC cong_tac i =
340 let fun seq_try (ifth::ifths,ifc::ifcs) thm =
341 (COND (if_rewritable ifc i) (DETERM(rtac ifth i))
342 (seq_try(ifths,ifcs))) thm
343 | seq_try([],_) thm = no_tac thm
344 and try_rew thm = (seq_try(case_rews,case_consts) ORELSE one_subt) thm
346 let val test = has_fewer_prems (nprems_of thm + 1)
349 ((try_rew THEN DEPTH_FIRST test (refl_tac i))
350 ORELSE (refl_tac i THEN loop)) thm
351 in (cong_tac THEN loop) thm end
352 in COND (may_match(case_consts,i)) try_rew no_tac end;
354 fun CASE_TAC (SS{cong_net,...}) i =
355 let val cong_tac = net_tac cong_net i
356 in NORM (IF1_TAC cong_tac) i end;
358 (* Rewriting Automaton *)
360 datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
361 | PROVE | POP_CS | POP_ARTR | IF;
363 fun simp_refl([],_,ss) = ss
364 | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
365 else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
369 val tracing = ref false;
371 (*Replace parameters by Free variables in P*)
372 fun variants_abs ([],P) = P
373 | variants_abs ((a,T)::aTs, P) =
374 variants_abs (aTs, #2 (Syntax.variant_abs(a,T,P)));
376 (*Select subgoal i from proof state; substitute parameters, for printing*)
377 fun prepare_goal i st =
378 let val subgi = nth_subgoal i st
379 val params = rev (Logic.strip_params subgi)
380 in variants_abs (params, Logic.strip_assums_concl subgi) end;
382 (*print lhs of conclusion of subgoal i*)
383 fun pr_goal_lhs i st =
384 writeln (Syntax.string_of_term_global (Thm.theory_of_thm st)
385 (lhs_of (prepare_goal i st)));
387 (*print conclusion of subgoal i*)
388 fun pr_goal_concl i st =
389 writeln (Syntax.string_of_term_global (Thm.theory_of_thm st) (prepare_goal i st))
391 (*print subgoals i to j (inclusive)*)
392 fun pr_goals (i,j) st =
394 else (pr_goal_concl i st; pr_goals (i+1,j) st);
396 (*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
397 thm=old state, thm'=new state *)
398 fun pr_rew (i,n,thm,thm',not_asms) =
400 then (if not_asms then () else writeln"Assumption used in";
401 pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
402 if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
407 (* Skip the first n hyps of a goal, and return the rest in generalized form *)
408 fun strip_varify(Const("==>", _) $ H $ B, n, vs) =
409 if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
410 else strip_varify(B,n-1,vs)
411 | strip_varify(Const("all",_)$Abs(_,T,t), n, vs) =
412 strip_varify(t,n,Var(("?",length vs),T)::vs)
413 | strip_varify _ = [];
415 fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
417 fun simp_lhs(thm,ss,anet,ats,cs) =
418 if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
419 if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
420 else case Seq.pull(cong_tac i thm) of
422 let val ps = prems_of thm and ps' = prems_of thm';
423 val n = length(ps')-length(ps);
424 val a = length(Logic.strip_assums_hyp(List.nth(ps,i-1)))
425 val l = map (fn p => length(Logic.strip_assums_hyp(p)))
426 (Library.take(n,Library.drop(i-1,ps')));
427 in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
428 | NONE => (REW::ss,thm,anet,ats,cs);
430 (*NB: the "Adding rewrites:" trace will look strange because assumptions
431 are represented by rules, generalized over their parameters*)
432 fun add_asms(ss,thm,a,anet,ats,cs) =
433 let val As = strip_varify(nth_subgoal i thm, a, []);
434 val thms = map (trivial o cterm_of(Thm.theory_of_thm thm)) As;
435 val new_rws = List.concat(map mk_rew_rules thms);
436 val rwrls = map mk_trans (List.concat(map mk_rew_rules thms));
437 val anet' = List.foldr lhs_insert_thm anet rwrls
438 in if !tracing andalso not(null new_rws)
439 then writeln (cat_lines
440 ("Adding rewrites:" :: map Display.string_of_thm_without_context new_rws))
442 (ss,thm,anet',anet::ats,cs)
445 fun rew(seq,thm,ss,anet,ats,cs, more) = case Seq.pull seq of
447 let val n = (nprems_of thm') - (nprems_of thm)
448 in pr_rew(i,n,thm,thm',more);
449 if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
450 else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
451 thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
454 then rew((lhs_net_tac anet i THEN assume_tac i) thm,
455 thm,ss,anet,ats,cs,false)
456 else (ss,thm,anet,ats,cs);
458 fun try_true(thm,ss,anet,ats,cs) =
459 case Seq.pull(auto_tac i thm) of
460 SOME(thm',_) => (ss,thm',anet,ats,cs)
461 | NONE => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
463 then (writeln"*** Failed to prove precondition. Normal form:";
464 pr_goal_concl i thm; writeln"")
466 rew(seq,thm0,ss0,anet0,ats0,cs0,more)
469 fun if_exp(thm,ss,anet,ats,cs) =
470 case Seq.pull (IF1_TAC (cong_tac i) i thm) of
471 SOME(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
472 | NONE => (ss,thm,anet,ats,cs);
474 fun step(s::ss, thm, anet, ats, cs) = case s of
475 MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
476 | ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
477 | SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
478 | REW => rew(net_tac net i thm,thm,ss,anet,ats,cs,true)
479 | REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
480 | TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
481 | PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
482 else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
483 | POP_ARTR => (ss,thm,hd ats,tl ats,cs)
484 | POP_CS => (ss,thm,anet,ats,tl cs)
485 | IF => if_exp(thm,ss,anet,ats,cs);
487 fun exec(state as (s::ss, thm, _, _, _)) =
488 if s=STOP then thm else exec(step(state));
490 in exec(ss, thm, Net.empty, [], []) end;
493 fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
494 let val cong_tac = net_tac cong_net
497 if i <= 0 orelse nprems_of thm < i then Seq.empty
498 else Seq.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
502 val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
503 val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
505 val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
506 val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
508 val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
510 fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
511 let val cong_tac = net_tac cong_net
512 in fn thm => let val state = thm RSN (2,red1)
513 in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
516 val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
519 (* Compute Congruence rules for individual constants using the substition
522 val subst_thms = map standard subst_thms;
526 | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
528 fun exp_abs(Type("fun",[T1,T2]),t,i) =
529 Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
530 | exp_abs(T,t,i) = exp_app(i,t);
532 fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
535 fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
536 let fun xn_list(x,n) =
537 let val ixs = map (fn i => (x^(radixstring(26,"a",i)),0)) (0 upto n);
538 in ListPair.map eta_Var (ixs, Library.take(n+1,Ts)) end
539 val lhs = list_comb(f,xn_list("X",k-1))
540 val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
541 in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
543 fun find_subst sg T =
544 let fun find (thm::thms) =
545 let val (Const(_,cT), va, vb) = dest_red(hd(prems_of thm));
546 val [P] = OldTerm.add_term_vars(concl_of thm,[]) \\ [va,vb]
547 val eqT::_ = binder_types cT
548 in if Sign.typ_instance sg (T,eqT) then SOME(thm,va,vb,P)
552 in find subst_thms end;
554 fun mk_cong sg (f,aTs,rT) (refl,eq) =
555 let val k = length aTs;
556 fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
557 let val ca = cterm_of sg va
558 and cx = cterm_of sg (eta_Var(("X"^si,0),T))
559 val cb = cterm_of sg vb
560 and cy = cterm_of sg (eta_Var(("Y"^si,0),T))
561 val cP = cterm_of sg P
562 and cp = cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
563 in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
564 fun mk(c,T::Ts,i,yik) =
565 let val si = radixstring(26,"a",i)
566 in case find_subst sg T of
567 NONE => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
568 | SOME s => let val c' = c RSN (2,ri(s,i,si,T,yik))
569 in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
572 in mk(refl,rev aTs,k-1,[]) end;
574 fun mk_cong_type sg (f,T) =
575 let val (aTs,rT) = strip_type T;
576 fun find_refl(r::rs) =
577 let val (Const(eq,eqT),_,_) = dest_red(concl_of r)
578 in if Sign.typ_instance sg (rT, hd(binder_types eqT))
579 then SOME(r,(eq,body_type eqT)) else find_refl rs
581 | find_refl([]) = NONE;
582 in case find_refl refl_thms of
583 NONE => [] | SOME(refl) => [mk_cong sg (f,aTs,rT) refl]
586 fun mk_cong_thy thy f =
587 let val T = case Sign.const_type thy f of
588 NONE => error(f^" not declared") | SOME(T) => T;
589 val T' = Logic.incr_tvar 9 T;
590 in mk_cong_type thy (Const(f,T'),T') end;
592 fun mk_congs thy = List.concat o map (mk_cong_thy thy);
594 fun mk_typed_congs thy =
598 val T = Logic.incr_tvar 9 (Syntax.read_typ_global thy s);
599 val t = case Sign.const_type thy f of
600 SOME(_) => Const(f,T) | NONE => Free(f,T)
602 in List.concat o map (mk_cong_type thy o readfT) end;