better skolemization, using first-order resolution rather than hoping for the right result
1 (* Title: HOL/Tools/meson.ML
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Copyright 1992 University of Cambridge
6 The MESON resolution proof procedure for HOL.
8 When making clauses, avoids using the rewriter -- instead uses RS recursively
10 NEED TO SORT LITERALS BY # OF VARS, USING ==>I/E. ELIMINATES NEED FOR
11 FUNCTION nodups -- if done to goal clauses too!
14 signature BASIC_MESON =
16 val size_of_subgoals : thm -> int
17 val make_cnf : thm list -> thm -> thm list
18 val finish_cnf : thm list -> thm list
19 val make_nnf : thm -> thm
20 val make_nnf1 : thm -> thm
21 val skolemize : thm -> thm
22 val make_clauses : thm list -> thm list
23 val make_horns : thm list -> thm list
24 val best_prolog_tac : (thm -> int) -> thm list -> tactic
25 val depth_prolog_tac : thm list -> tactic
26 val gocls : thm list -> thm list
27 val skolemize_prems_tac : thm list -> int -> tactic
28 val MESON : (thm list -> tactic) -> int -> tactic
29 val best_meson_tac : (thm -> int) -> int -> tactic
30 val safe_best_meson_tac : int -> tactic
31 val depth_meson_tac : int -> tactic
32 val prolog_step_tac' : thm list -> int -> tactic
33 val iter_deepen_prolog_tac : thm list -> tactic
34 val iter_deepen_meson_tac : thm list -> int -> tactic
35 val meson_tac : int -> tactic
36 val negate_head : thm -> thm
37 val select_literal : int -> thm -> thm
38 val skolemize_tac : int -> tactic
39 val make_clauses_tac : int -> tactic
46 val not_conjD = thm "meson_not_conjD";
47 val not_disjD = thm "meson_not_disjD";
48 val not_notD = thm "meson_not_notD";
49 val not_allD = thm "meson_not_allD";
50 val not_exD = thm "meson_not_exD";
51 val imp_to_disjD = thm "meson_imp_to_disjD";
52 val not_impD = thm "meson_not_impD";
53 val iff_to_disjD = thm "meson_iff_to_disjD";
54 val not_iffD = thm "meson_not_iffD";
55 val conj_exD1 = thm "meson_conj_exD1";
56 val conj_exD2 = thm "meson_conj_exD2";
57 val disj_exD = thm "meson_disj_exD";
58 val disj_exD1 = thm "meson_disj_exD1";
59 val disj_exD2 = thm "meson_disj_exD2";
60 val disj_assoc = thm "meson_disj_assoc";
61 val disj_comm = thm "meson_disj_comm";
62 val disj_FalseD1 = thm "meson_disj_FalseD1";
63 val disj_FalseD2 = thm "meson_disj_FalseD2";
65 val depth_limit = ref 2000;
67 (**** Operators for forward proof ****)
70 (** First-order Resolution **)
72 fun typ_pair_of (ix, (sort,ty)) = (TVar (ix,sort), ty);
73 fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
75 val Envir.Envir {asol = tenv0, iTs = tyenv0, ...} = Envir.empty 0
77 (*FIXME: currently does not "rename variables apart"*)
78 fun first_order_resolve thA thB =
79 let val thy = theory_of_thm thA
80 val tmA = concl_of thA
81 fun match pat = Pattern.first_order_match thy (pat,tmA) (tyenv0,tenv0)
82 val Const("==>",_) $ tmB $ _ = prop_of thB
83 val (tyenv,tenv) = match tmB
84 val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
85 in thA RS (cterm_instantiate ct_pairs thB) end
86 handle _ => raise THM ("first_order_resolve", 0, [thA,thB]);
88 (*raises exception if no rules apply -- unlike RL*)
89 fun tryres (th, rls) =
90 let fun tryall [] = raise THM("tryres", 0, th::rls)
91 | tryall (rl::rls) = (th RS rl handle THM _ => tryall rls)
94 (*Permits forward proof from rules that discharge assumptions*)
95 fun forward_res nf st =
96 case Seq.pull (ALLGOALS (METAHYPS (fn [prem] => rtac (nf prem) 1)) st)
98 | NONE => raise THM("forward_res", 0, [st]);
101 (*Are any of the logical connectives in "bs" present in the term?*)
103 let fun has (Const(a,_)) = false
104 | has (Const("Trueprop",_) $ p) = has p
105 | has (Const("Not",_) $ p) = has p
106 | has (Const("op |",_) $ p $ q) = member (op =) bs "op |" orelse has p orelse has q
107 | has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q
108 | has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p
109 | has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p
114 (**** Clause handling ****)
116 fun literals (Const("Trueprop",_) $ P) = literals P
117 | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
118 | literals (Const("Not",_) $ P) = [(false,P)]
119 | literals P = [(true,P)];
121 (*number of literals in a term*)
122 val nliterals = length o literals;
125 (*** Tautology Checking ***)
127 fun signed_lits_aux (Const ("op |", _) $ P $ Q) (poslits, neglits) =
128 signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
129 | signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits)
130 | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
132 fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
134 (*Literals like X=X are tautologous*)
135 fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u
136 | taut_poslit (Const("True",_)) = true
137 | taut_poslit _ = false;
140 let val (poslits,neglits) = signed_lits th
141 in exists taut_poslit poslits
143 exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
145 handle TERM _ => false; (*probably dest_Trueprop on a weird theorem*)
148 (*** To remove trivial negated equality literals from clauses ***)
150 (*They are typically functional reflexivity axioms and are the converses of
151 injectivity equivalences*)
153 val not_refl_disj_D = thm"meson_not_refl_disj_D";
155 (*Is either term a Var that does not properly occur in the other term?*)
156 fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
157 | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
158 | eliminable _ = false;
160 fun refl_clause_aux 0 th = th
161 | refl_clause_aux n th =
162 case HOLogic.dest_Trueprop (concl_of th) of
163 (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) =>
164 refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*)
165 | (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) =>
167 then refl_clause_aux (n-1) (th RS not_refl_disj_D) (*Var inequation: delete*)
168 else refl_clause_aux (n-1) (th RS disj_comm) (*not between Vars: ignore*)
169 | (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
170 | _ => (*not a disjunction*) th;
172 fun notequal_lits_count (Const ("op |", _) $ P $ Q) =
173 notequal_lits_count P + notequal_lits_count Q
174 | notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1
175 | notequal_lits_count _ = 0;
177 (*Simplify a clause by applying reflexivity to its negated equality literals*)
179 let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
180 in zero_var_indexes (refl_clause_aux neqs th) end
181 handle TERM _ => th; (*probably dest_Trueprop on a weird theorem*)
184 (*** The basic CNF transformation ***)
186 (*Estimate the number of clauses in order to detect infeasible theorems*)
187 fun nclauses (Const("Trueprop",_) $ t) = nclauses t
188 | nclauses (Const("op &",_) $ t $ u) = nclauses t + nclauses u
189 | nclauses (Const("Ex", _) $ Abs (_,_,t)) = nclauses t
190 | nclauses (Const("All",_) $ Abs (_,_,t)) = nclauses t
191 | nclauses (Const("op |",_) $ t $ u) = nclauses t * nclauses u
192 | nclauses _ = 1; (* literal *)
194 (*Replaces universally quantified variables by FREE variables -- because
195 assumptions may not contain scheme variables. Later, call "generalize". *)
197 let val newname = gensym "mes_"
198 val spec' = read_instantiate [("x", newname)] spec
201 (*Used with METAHYPS below. There is one assumption, which gets bound to prem
202 and then normalized via function nf. The normal form is given to resolve_tac,
203 presumably to instantiate a Boolean variable.*)
204 fun resop nf [prem] = resolve_tac (nf prem) 1;
207 exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]);
209 fun apply_skolem_ths (th, rls) =
210 let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls)
211 | tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls)
214 (*Conjunctive normal form, adding clauses from th in front of ths (for foldr).
215 Strips universal quantifiers and breaks up conjunctions.
216 Eliminates existential quantifiers using skoths: Skolemization theorems.*)
217 fun cnf skoths (th,ths) =
218 let fun cnf_aux (th,ths) =
219 if has_meta_conn (prop_of th) then ths (*meta-level: ignore*)
220 else if not (has_conns ["All","Ex","op &"] (prop_of th))
221 then th::ths (*no work to do, terminate*)
222 else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
223 Const ("op &", _) => (*conjunction*)
224 cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
225 | Const ("All", _) => (*universal quantifier*)
226 cnf_aux (freeze_spec th, ths)
228 (*existential quantifier: Insert Skolem functions*)
229 cnf_aux (apply_skolem_ths (th,skoths), ths)
230 | Const ("op |", _) => (*disjunction*)
232 (METAHYPS (resop cnf_nil) 1) THEN
233 (fn st' => st' |> METAHYPS (resop cnf_nil) 1)
234 in Seq.list_of (tac (th RS disj_forward)) @ ths end
235 | _ => (*no work to do*) th::ths
236 and cnf_nil th = cnf_aux (th,[])
238 if nclauses (concl_of th) > 20
239 then (Output.debug ("cnf is ignoring: " ^ string_of_thm th); ths)
240 else cnf_aux (th,ths)
243 (*Convert all suitable free variables to schematic variables,
244 but don't discharge assumptions.*)
245 fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th));
247 fun make_cnf skoths th = cnf skoths (th, []);
249 (*Generalization, removal of redundant equalities, removal of tautologies.*)
250 fun finish_cnf ths = filter (not o is_taut) (map (refl_clause o generalize) ths);
253 (**** Removal of duplicate literals ****)
255 (*Forward proof, passing extra assumptions as theorems to the tactic*)
256 fun forward_res2 nf hyps st =
259 (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
262 | NONE => raise THM("forward_res2", 0, [st]);
264 (*Remove duplicates in P|Q by assuming ~P in Q
265 rls (initially []) accumulates assumptions of the form P==>False*)
266 fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
267 handle THM _ => tryres(th,rls)
268 handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
269 [disj_FalseD1, disj_FalseD2, asm_rl])
272 (*Remove duplicate literals, if there are any*)
274 if null(findrep(literals(prop_of th))) then th
275 else nodups_aux [] th;
278 (**** Generation of contrapositives ****)
280 (*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
281 fun assoc_right th = assoc_right (th RS disj_assoc)
284 (*Must check for negative literal first!*)
285 val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
287 (*For ordinary resolution. *)
288 val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
290 (*Create a goal or support clause, conclusing False*)
291 fun make_goal th = (*Must check for negative literal first!*)
292 make_goal (tryres(th, clause_rules))
293 handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
295 (*Sort clauses by number of literals*)
296 fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
298 fun sort_clauses ths = sort (make_ord fewerlits) ths;
300 (*True if the given type contains bool anywhere*)
301 fun has_bool (Type("bool",_)) = true
302 | has_bool (Type(_, Ts)) = exists has_bool Ts
303 | has_bool _ = false;
305 (*Is the string the name of a connective? It doesn't matter if this list is
306 incomplete, since when actually called, the only connectives likely to
307 remain are & | Not.*)
308 val is_conn = member (op =)
309 ["Trueprop", "op &", "op |", "op -->", "op =", "Not",
310 "All", "Ex", "Ball", "Bex"];
312 (*True if the term contains a function where the type of any argument contains
314 val has_bool_arg_const =
316 (fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T));
318 (*Raises an exception if any Vars in the theorem mention type bool; they
319 could cause make_horn to loop! Also rejects functions whose arguments are
320 Booleans or other functions.*)
322 not (exists (has_bool o fastype_of) (term_vars t) orelse
323 not (Term.is_first_order ["all","All","Ex"] t) orelse
324 has_bool_arg_const t orelse
327 (*Create a meta-level Horn clause*)
328 fun make_horn crules th = make_horn crules (tryres(th,crules))
331 (*Generate Horn clauses for all contrapositives of a clause. The input, th,
332 is a HOL disjunction.*)
333 fun add_contras crules (th,hcs) =
334 let fun rots (0,th) = hcs
335 | rots (k,th) = zero_var_indexes (make_horn crules th) ::
336 rots(k-1, assoc_right (th RS disj_comm))
337 in case nliterals(prop_of th) of
339 | n => rots(n, assoc_right th)
342 (*Use "theorem naming" to label the clauses*)
343 fun name_thms label =
344 let fun name1 (th, (k,ths)) =
345 (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
347 in fn ths => #2 (foldr name1 (length ths, []) ths) end;
349 (*Is the given disjunction an all-negative support clause?*)
350 fun is_negative th = forall (not o #1) (literals (prop_of th));
352 val neg_clauses = List.filter is_negative;
355 (***** MESON PROOF PROCEDURE *****)
357 fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
358 As) = rhyps(phi, A::As)
359 | rhyps (_, As) = As;
361 (** Detecting repeated assumptions in a subgoal **)
363 (*The stringtree detects repeated assumptions.*)
364 fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net;
366 (*detects repetitions in a list of terms*)
367 fun has_reps [] = false
368 | has_reps [_] = false
369 | has_reps [t,u] = (t aconv u)
370 | has_reps ts = (Library.foldl ins_term (Net.empty, ts); false)
371 handle Net.INSERT => true;
373 (*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
374 fun TRYING_eq_assume_tac 0 st = Seq.single st
375 | TRYING_eq_assume_tac i st =
376 TRYING_eq_assume_tac (i-1) (eq_assumption i st)
377 handle THM _ => TRYING_eq_assume_tac (i-1) st;
379 fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
381 (*Loop checking: FAIL if trying to prove the same thing twice
382 -- if *ANY* subgoal has repeated literals*)
384 if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
385 then Seq.empty else Seq.single st;
388 (* net_resolve_tac actually made it slower... *)
389 fun prolog_step_tac horns i =
390 (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
391 TRYALL_eq_assume_tac;
393 (*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
394 fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
396 fun size_of_subgoals st = foldr addconcl 0 (prems_of st);
399 (*Negation Normal Form*)
400 val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
401 not_impD, not_iffD, not_allD, not_exD, not_notD];
403 fun make_nnf1 th = make_nnf1 (tryres(th, nnf_rls))
405 forward_res make_nnf1
406 (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
409 (*The simplification removes defined quantifiers and occurrences of True and False.
410 nnf_ss also includes the one-point simprocs,
411 which are needed to avoid the various one-point theorems from generating junk clauses.*)
413 [simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True,
414 if_False, if_cancel, if_eq_cancel, cases_simp];
415 val nnf_extra_simps =
416 thms"split_ifs" @ ex_simps @ all_simps @ simp_thms;
419 HOL_basic_ss addsimps nnf_extra_simps
420 addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc];
422 fun make_nnf th = th |> rewrite_rule (map safe_mk_meta_eq nnf_simps)
423 |> simplify nnf_ss (*But this doesn't simplify premises...*)
426 (*Pull existential quantifiers to front. This accomplishes Skolemization for
427 clauses that arise from a subgoal.*)
429 if not (has_conns ["Ex"] (prop_of th)) then th
430 else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2,
431 disj_exD, disj_exD1, disj_exD2])))
433 skolemize (forward_res skolemize
434 (tryres (th, [conj_forward, disj_forward, all_forward])))
435 handle THM _ => forward_res skolemize (th RS ex_forward);
438 (*Make clauses from a list of theorems, previously Skolemized and put into nnf.
439 The resulting clauses are HOL disjunctions.*)
440 fun make_clauses ths =
441 (sort_clauses (map (generalize o nodups) (foldr (cnf[]) [] ths)));
443 (*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
446 (distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths));
448 (*Could simply use nprems_of, which would count remaining subgoals -- no
449 discrimination as to their size! With BEST_FIRST, fails for problem 41.*)
451 fun best_prolog_tac sizef horns =
452 BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
454 fun depth_prolog_tac horns =
455 DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
457 (*Return all negative clauses, as possible goal clauses*)
458 fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
460 fun skolemize_prems_tac prems =
461 cut_facts_tac (map (skolemize o make_nnf) prems) THEN'
464 (*Expand all definitions (presumably of Skolem functions) in a proof state.*)
465 fun expand_defs_tac st =
466 let val defs = filter (can dest_equals) (#hyps (crep_thm st))
467 in PRIMITIVE (LocalDefs.def_export false defs) st end;
469 (*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions*)
470 fun MESON cltac i st =
472 (EVERY [rtac ccontr 1,
474 EVERY1 [skolemize_prems_tac negs,
475 METAHYPS (cltac o make_clauses)]) 1,
476 expand_defs_tac]) i st
477 handle THM _ => no_tac st; (*probably from make_meta_clause, not first-order*)
479 (** Best-first search versions **)
481 (*ths is a list of additional clauses (HOL disjunctions) to use.*)
482 fun best_meson_tac sizef =
484 THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
485 (has_fewer_prems 1, sizef)
486 (prolog_step_tac (make_horns cls) 1));
488 (*First, breaks the goal into independent units*)
489 val safe_best_meson_tac =
490 SELECT_GOAL (TRY Safe_tac THEN
491 TRYALL (best_meson_tac size_of_subgoals));
493 (** Depth-first search version **)
495 val depth_meson_tac =
496 MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
497 depth_prolog_tac (make_horns cls)]);
500 (** Iterative deepening version **)
502 (*This version does only one inference per call;
503 having only one eq_assume_tac speeds it up!*)
504 fun prolog_step_tac' horns =
505 let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
506 take_prefix Thm.no_prems horns
507 val nrtac = net_resolve_tac horns
508 in fn i => eq_assume_tac i ORELSE
509 match_tac horn0s i ORELSE (*no backtracking if unit MATCHES*)
510 ((assume_tac i APPEND nrtac i) THEN check_tac)
513 fun iter_deepen_prolog_tac horns =
514 ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
516 fun iter_deepen_meson_tac ths =
518 case (gocls (cls@ths)) of
519 [] => no_tac (*no goal clauses*)
521 (THEN_ITER_DEEPEN (resolve_tac goes 1)
523 (prolog_step_tac' (make_horns (cls@ths)))));
525 fun meson_claset_tac ths cs =
526 SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths));
528 val meson_tac = CLASET' (meson_claset_tac []);
531 (**** Code to support ordinary resolution, rather than Model Elimination ****)
533 (*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
534 with no contrapositives, for ordinary resolution.*)
536 (*Rules to convert the head literal into a negated assumption. If the head
537 literal is already negated, then using notEfalse instead of notEfalse'
538 prevents a double negation.*)
539 val notEfalse = read_instantiate [("R","False")] notE;
540 val notEfalse' = rotate_prems 1 notEfalse;
542 fun negated_asm_of_head th =
543 th RS notEfalse handle THM _ => th RS notEfalse';
545 (*Converting one clause*)
546 fun make_meta_clause th =
547 if is_fol_term (prop_of th)
548 then negated_asm_of_head (make_horn resolution_clause_rules th)
549 else raise THM("make_meta_clause", 0, [th]);
551 fun make_meta_clauses ths =
553 (distinct Drule.eq_thm_prop (map make_meta_clause ths));
555 (*Permute a rule's premises to move the i-th premise to the last position.*)
557 let val n = nprems_of th
558 in if 1 <= i andalso i <= n
559 then Thm.permute_prems (i-1) 1 th
560 else raise THM("select_literal", i, [th])
563 (*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
565 val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
567 (*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
568 fun select_literal i cl = negate_head (make_last i cl);
571 (*Top-level Skolemization. Allows part of the conversion to clauses to be
572 expressed as a tactic (or Isar method). Each assumption of the selected
573 goal is converted to NNF and then its existential quantifiers are pulled
574 to the front. Finally, all existential quantifiers are eliminated,
575 leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
576 might generate many subgoals.*)
578 fun skolemize_tac i st =
579 let val ts = Logic.strip_assums_hyp (List.nth (prems_of st, i-1))
582 (fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1
583 THEN REPEAT (etac exE 1))),
584 REPEAT_DETERM_N (length ts) o (etac thin_rl)] i st
586 handle Subscript => Seq.empty;
588 (*Top-level conversion to meta-level clauses. Each clause has
589 leading !!-bound universal variables, to express generality. To get
590 disjunctions instead of meta-clauses, remove "make_meta_clauses" below.*)
591 val make_clauses_tac =
594 let val ts = Logic.strip_assums_hyp prop
599 (map forall_intr_vars
600 (make_meta_clauses (make_clauses hyps))) 1)),
601 REPEAT_DETERM_N (length ts) o (etac thin_rl)]
605 (*** setup the special skoklemization methods ***)
607 (*No CHANGED_PROP here, since these always appear in the preamble*)
609 val skolemize_meth = Method.SIMPLE_METHOD' HEADGOAL skolemize_tac;
611 val make_clauses_meth = Method.SIMPLE_METHOD' HEADGOAL make_clauses_tac;
613 val skolemize_setup =
615 [("skolemize", Method.no_args skolemize_meth,
616 "Skolemization into existential quantifiers"),
617 ("make_clauses", Method.no_args make_clauses_meth,
618 "Conversion to !!-quantified meta-level clauses")];
622 structure BasicMeson: BASIC_MESON = Meson;