Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
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. The supplied proof state st,
95 e.g. from conj_forward, should have the form
96 "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
97 and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
98 fun forward_res nf st =
99 let fun forward_tacf [prem] = rtac (nf prem) 1
100 | forward_tacf prems =
101 error ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:\n" ^
104 cat_lines (map string_of_thm prems))
106 case Seq.pull (ALLGOALS (METAHYPS forward_tacf) st)
108 | NONE => raise THM("forward_res", 0, [st])
111 (*Are any of the logical connectives in "bs" present in the term?*)
113 let fun has (Const(a,_)) = false
114 | has (Const("Trueprop",_) $ p) = has p
115 | has (Const("Not",_) $ p) = has p
116 | has (Const("op |",_) $ p $ q) = member (op =) bs "op |" orelse has p orelse has q
117 | has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q
118 | has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p
119 | has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p
124 (**** Clause handling ****)
126 fun literals (Const("Trueprop",_) $ P) = literals P
127 | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
128 | literals (Const("Not",_) $ P) = [(false,P)]
129 | literals P = [(true,P)];
131 (*number of literals in a term*)
132 val nliterals = length o literals;
135 (*** Tautology Checking ***)
137 fun signed_lits_aux (Const ("op |", _) $ P $ Q) (poslits, neglits) =
138 signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
139 | signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits)
140 | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
142 fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
144 (*Literals like X=X are tautologous*)
145 fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u
146 | taut_poslit (Const("True",_)) = true
147 | taut_poslit _ = false;
150 let val (poslits,neglits) = signed_lits th
151 in exists taut_poslit poslits
153 exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
155 handle TERM _ => false; (*probably dest_Trueprop on a weird theorem*)
158 (*** To remove trivial negated equality literals from clauses ***)
160 (*They are typically functional reflexivity axioms and are the converses of
161 injectivity equivalences*)
163 val not_refl_disj_D = thm"meson_not_refl_disj_D";
165 (*Is either term a Var that does not properly occur in the other term?*)
166 fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
167 | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
168 | eliminable _ = false;
170 fun refl_clause_aux 0 th = th
171 | refl_clause_aux n th =
172 case HOLogic.dest_Trueprop (concl_of th) of
173 (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) =>
174 refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*)
175 | (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) =>
177 then refl_clause_aux (n-1) (th RS not_refl_disj_D) (*Var inequation: delete*)
178 else refl_clause_aux (n-1) (th RS disj_comm) (*not between Vars: ignore*)
179 | (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
180 | _ => (*not a disjunction*) th;
182 fun notequal_lits_count (Const ("op |", _) $ P $ Q) =
183 notequal_lits_count P + notequal_lits_count Q
184 | notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1
185 | notequal_lits_count _ = 0;
187 (*Simplify a clause by applying reflexivity to its negated equality literals*)
189 let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
190 in zero_var_indexes (refl_clause_aux neqs th) end
191 handle TERM _ => th; (*probably dest_Trueprop on a weird theorem*)
194 (*** The basic CNF transformation ***)
196 val max_clauses = ref 20;
198 fun sum x y = if x < !max_clauses andalso y < !max_clauses then x+y else !max_clauses;
199 fun prod x y = if x < !max_clauses andalso y < !max_clauses then x*y else !max_clauses;
201 (*Estimate the number of clauses in order to detect infeasible theorems*)
202 fun signed_nclauses b (Const("Trueprop",_) $ t) = signed_nclauses b t
203 | signed_nclauses b (Const("Not",_) $ t) = signed_nclauses (not b) t
204 | signed_nclauses b (Const("op &",_) $ t $ u) =
205 if b then sum (signed_nclauses b t) (signed_nclauses b u)
206 else prod (signed_nclauses b t) (signed_nclauses b u)
207 | signed_nclauses b (Const("op |",_) $ t $ u) =
208 if b then prod (signed_nclauses b t) (signed_nclauses b u)
209 else sum (signed_nclauses b t) (signed_nclauses b u)
210 | signed_nclauses b (Const("op -->",_) $ t $ u) =
211 if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
212 else sum (signed_nclauses (not b) t) (signed_nclauses b u)
213 | signed_nclauses b (Const("op =", Type ("fun", [T, _])) $ t $ u) =
214 if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
215 if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
216 (prod (signed_nclauses (not b) u) (signed_nclauses b t))
217 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
218 (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
220 | signed_nclauses b (Const("Ex", _) $ Abs (_,_,t)) = signed_nclauses b t
221 | signed_nclauses b (Const("All",_) $ Abs (_,_,t)) = signed_nclauses b t
222 | signed_nclauses _ _ = 1; (* literal *)
224 val nclauses = signed_nclauses true;
226 fun too_many_clauses t = nclauses t >= !max_clauses;
228 (*Replaces universally quantified variables by FREE variables -- because
229 assumptions may not contain scheme variables. Later, call "generalize". *)
231 let val newname = gensym "mes_"
232 val spec' = read_instantiate [("x", newname)] spec
235 (*Used with METAHYPS below. There is one assumption, which gets bound to prem
236 and then normalized via function nf. The normal form is given to resolve_tac,
237 presumably to instantiate a Boolean variable.*)
238 fun resop nf [prem] = resolve_tac (nf prem) 1;
240 (*Any need to extend this list with
241 "HOL.type_class","Code_Generator.eq_class","ProtoPure.term"?*)
243 exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]);
245 fun apply_skolem_ths (th, rls) =
246 let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls)
247 | tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls)
250 (*Conjunctive normal form, adding clauses from th in front of ths (for foldr).
251 Strips universal quantifiers and breaks up conjunctions.
252 Eliminates existential quantifiers using skoths: Skolemization theorems.*)
253 fun cnf skoths (th,ths) =
254 let fun cnf_aux (th,ths) =
255 if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
256 else if not (has_conns ["All","Ex","op &"] (prop_of th))
257 then th::ths (*no work to do, terminate*)
258 else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
259 Const ("op &", _) => (*conjunction*)
260 cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
261 | Const ("All", _) => (*universal quantifier*)
262 cnf_aux (freeze_spec th, ths)
264 (*existential quantifier: Insert Skolem functions*)
265 cnf_aux (apply_skolem_ths (th,skoths), ths)
266 | Const ("op |", _) => (*disjunction*)
268 (METAHYPS (resop cnf_nil) 1) THEN
269 (fn st' => st' |> METAHYPS (resop cnf_nil) 1)
270 in Seq.list_of (tac (th RS disj_forward)) @ ths end
271 | _ => (*no work to do*) th::ths
272 and cnf_nil th = cnf_aux (th,[])
274 if too_many_clauses (concl_of th)
275 then (Output.debug ("cnf is ignoring: " ^ string_of_thm th); ths)
276 else cnf_aux (th,ths)
279 (*Convert all suitable free variables to schematic variables,
280 but don't discharge assumptions.*)
281 fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th));
283 fun make_cnf skoths th = cnf skoths (th, []);
285 (*Generalization, removal of redundant equalities, removal of tautologies.*)
286 fun finish_cnf ths = filter (not o is_taut) (map (refl_clause o generalize) ths);
289 (**** Removal of duplicate literals ****)
291 (*Forward proof, passing extra assumptions as theorems to the tactic*)
292 fun forward_res2 nf hyps st =
295 (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
298 | NONE => raise THM("forward_res2", 0, [st]);
300 (*Remove duplicates in P|Q by assuming ~P in Q
301 rls (initially []) accumulates assumptions of the form P==>False*)
302 fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
303 handle THM _ => tryres(th,rls)
304 handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
305 [disj_FalseD1, disj_FalseD2, asm_rl])
308 (*Remove duplicate literals, if there are any*)
310 if has_duplicates (op =) (literals (prop_of th))
311 then nodups_aux [] th
315 (**** Generation of contrapositives ****)
317 fun is_left (Const ("Trueprop", _) $
318 (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _)) = true
321 (*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
323 if is_left (prop_of th) then assoc_right (th RS disj_assoc)
326 (*Must check for negative literal first!*)
327 val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
329 (*For ordinary resolution. *)
330 val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
332 (*Create a goal or support clause, conclusing False*)
333 fun make_goal th = (*Must check for negative literal first!*)
334 make_goal (tryres(th, clause_rules))
335 handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
337 (*Sort clauses by number of literals*)
338 fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
340 fun sort_clauses ths = sort (make_ord fewerlits) ths;
342 (*True if the given type contains bool anywhere*)
343 fun has_bool (Type("bool",_)) = true
344 | has_bool (Type(_, Ts)) = exists has_bool Ts
345 | has_bool _ = false;
347 (*Is the string the name of a connective? Really only | and Not can remain,
348 since this code expects to be called on a clause form.*)
349 val is_conn = member (op =)
350 ["Trueprop", "op &", "op |", "op -->", "Not",
351 "All", "Ex", "Ball", "Bex"];
353 (*True if the term contains a function--not a logical connective--where the type
354 of any argument contains bool.*)
355 val has_bool_arg_const =
357 (fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T));
359 (*Raises an exception if any Vars in the theorem mention type bool.
360 Also rejects functions whose arguments are Booleans or other functions.*)
362 not (exists (has_bool o fastype_of) (term_vars t) orelse
363 not (Term.is_first_order ["all","All","Ex"] t) orelse
364 has_bool_arg_const t orelse
367 fun rigid t = not (is_Var (head_of t));
369 fun ok4horn (Const ("Trueprop",_) $ (Const ("op |", _) $ t $ _)) = rigid t
370 | ok4horn (Const ("Trueprop",_) $ t) = rigid t
373 (*Create a meta-level Horn clause*)
374 fun make_horn crules th =
375 if ok4horn (concl_of th)
376 then make_horn crules (tryres(th,crules)) handle THM _ => th
379 (*Generate Horn clauses for all contrapositives of a clause. The input, th,
380 is a HOL disjunction.*)
381 fun add_contras crules (th,hcs) =
382 let fun rots (0,th) = hcs
383 | rots (k,th) = zero_var_indexes (make_horn crules th) ::
384 rots(k-1, assoc_right (th RS disj_comm))
385 in case nliterals(prop_of th) of
387 | n => rots(n, assoc_right th)
390 (*Use "theorem naming" to label the clauses*)
391 fun name_thms label =
392 let fun name1 (th, (k,ths)) =
393 (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
395 in fn ths => #2 (foldr name1 (length ths, []) ths) end;
397 (*Is the given disjunction an all-negative support clause?*)
398 fun is_negative th = forall (not o #1) (literals (prop_of th));
400 val neg_clauses = List.filter is_negative;
403 (***** MESON PROOF PROCEDURE *****)
405 fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
406 As) = rhyps(phi, A::As)
407 | rhyps (_, As) = As;
409 (** Detecting repeated assumptions in a subgoal **)
411 (*The stringtree detects repeated assumptions.*)
412 fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net;
414 (*detects repetitions in a list of terms*)
415 fun has_reps [] = false
416 | has_reps [_] = false
417 | has_reps [t,u] = (t aconv u)
418 | has_reps ts = (Library.foldl ins_term (Net.empty, ts); false)
419 handle Net.INSERT => true;
421 (*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
422 fun TRYING_eq_assume_tac 0 st = Seq.single st
423 | TRYING_eq_assume_tac i st =
424 TRYING_eq_assume_tac (i-1) (eq_assumption i st)
425 handle THM _ => TRYING_eq_assume_tac (i-1) st;
427 fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
429 (*Loop checking: FAIL if trying to prove the same thing twice
430 -- if *ANY* subgoal has repeated literals*)
432 if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
433 then Seq.empty else Seq.single st;
436 (* net_resolve_tac actually made it slower... *)
437 fun prolog_step_tac horns i =
438 (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
439 TRYALL_eq_assume_tac;
441 (*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
442 fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
444 fun size_of_subgoals st = foldr addconcl 0 (prems_of st);
447 (*Negation Normal Form*)
448 val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
449 not_impD, not_iffD, not_allD, not_exD, not_notD];
451 fun ok4nnf (Const ("Trueprop",_) $ (Const ("Not", _) $ t)) = rigid t
452 | ok4nnf (Const ("Trueprop",_) $ t) = rigid t
456 if ok4nnf (concl_of th)
457 then make_nnf1 (tryres(th, nnf_rls))
459 forward_res make_nnf1
460 (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
464 (*The simplification removes defined quantifiers and occurrences of True and False.
465 nnf_ss also includes the one-point simprocs,
466 which are needed to avoid the various one-point theorems from generating junk clauses.*)
468 [simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True,
469 if_False, if_cancel, if_eq_cancel, cases_simp];
470 val nnf_extra_simps =
471 thms"split_ifs" @ ex_simps @ all_simps @ simp_thms;
474 HOL_basic_ss addsimps nnf_extra_simps
475 addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc];
477 fun make_nnf th = case prems_of th of
478 [] => th |> rewrite_rule (map safe_mk_meta_eq nnf_simps)
481 | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
483 (*Pull existential quantifiers to front. This accomplishes Skolemization for
484 clauses that arise from a subgoal.*)
486 if not (has_conns ["Ex"] (prop_of th)) then th
487 else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2,
488 disj_exD, disj_exD1, disj_exD2])))
490 skolemize (forward_res skolemize
491 (tryres (th, [conj_forward, disj_forward, all_forward])))
492 handle THM _ => forward_res skolemize (th RS ex_forward);
495 (*Make clauses from a list of theorems, previously Skolemized and put into nnf.
496 The resulting clauses are HOL disjunctions.*)
497 fun make_clauses ths =
498 (sort_clauses (map (generalize o nodups) (foldr (cnf[]) [] ths)));
500 (*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
503 (distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths));
505 (*Could simply use nprems_of, which would count remaining subgoals -- no
506 discrimination as to their size! With BEST_FIRST, fails for problem 41.*)
508 fun best_prolog_tac sizef horns =
509 BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
511 fun depth_prolog_tac horns =
512 DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
514 (*Return all negative clauses, as possible goal clauses*)
515 fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
517 fun skolemize_prems_tac prems =
518 cut_facts_tac (map (skolemize o make_nnf) prems) THEN'
521 (*Expand all definitions (presumably of Skolem functions) in a proof state.*)
522 fun expand_defs_tac st =
523 let val defs = filter (can dest_equals) (#hyps (crep_thm st))
524 in PRIMITIVE (LocalDefs.def_export false defs) st end;
526 (*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions*)
527 fun MESON cltac i st =
529 (EVERY [rtac ccontr 1,
531 EVERY1 [skolemize_prems_tac negs,
532 METAHYPS (cltac o make_clauses)]) 1,
533 expand_defs_tac]) i st
534 handle THM _ => no_tac st; (*probably from make_meta_clause, not first-order*)
536 (** Best-first search versions **)
538 (*ths is a list of additional clauses (HOL disjunctions) to use.*)
539 fun best_meson_tac sizef =
541 THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
542 (has_fewer_prems 1, sizef)
543 (prolog_step_tac (make_horns cls) 1));
545 (*First, breaks the goal into independent units*)
546 val safe_best_meson_tac =
547 SELECT_GOAL (TRY Safe_tac THEN
548 TRYALL (best_meson_tac size_of_subgoals));
550 (** Depth-first search version **)
552 val depth_meson_tac =
553 MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
554 depth_prolog_tac (make_horns cls)]);
557 (** Iterative deepening version **)
559 (*This version does only one inference per call;
560 having only one eq_assume_tac speeds it up!*)
561 fun prolog_step_tac' horns =
562 let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
563 take_prefix Thm.no_prems horns
564 val nrtac = net_resolve_tac horns
565 in fn i => eq_assume_tac i ORELSE
566 match_tac horn0s i ORELSE (*no backtracking if unit MATCHES*)
567 ((assume_tac i APPEND nrtac i) THEN check_tac)
570 fun iter_deepen_prolog_tac horns =
571 ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
573 fun iter_deepen_meson_tac ths = MESON
575 case (gocls (cls@ths)) of
576 [] => no_tac (*no goal clauses*)
578 let val horns = make_horns (cls@ths)
579 val _ = if !Output.show_debug_msgs
580 then Output.debug ("meson method called:\n" ^
581 space_implode "\n" (map string_of_thm (cls@ths)) ^
583 space_implode "\n" (map string_of_thm horns))
585 in THEN_ITER_DEEPEN (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
589 fun meson_claset_tac ths cs =
590 SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths));
592 val meson_tac = CLASET' (meson_claset_tac []);
595 (**** Code to support ordinary resolution, rather than Model Elimination ****)
597 (*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
598 with no contrapositives, for ordinary resolution.*)
600 (*Rules to convert the head literal into a negated assumption. If the head
601 literal is already negated, then using notEfalse instead of notEfalse'
602 prevents a double negation.*)
603 val notEfalse = read_instantiate [("R","False")] notE;
604 val notEfalse' = rotate_prems 1 notEfalse;
606 fun negated_asm_of_head th =
607 th RS notEfalse handle THM _ => th RS notEfalse';
609 (*Converting one clause*)
610 fun make_meta_clause th =
611 negated_asm_of_head (make_horn resolution_clause_rules th);
613 fun make_meta_clauses ths =
615 (distinct Drule.eq_thm_prop (map make_meta_clause ths));
617 (*Permute a rule's premises to move the i-th premise to the last position.*)
619 let val n = nprems_of th
620 in if 1 <= i andalso i <= n
621 then Thm.permute_prems (i-1) 1 th
622 else raise THM("select_literal", i, [th])
625 (*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
627 val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
629 (*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
630 fun select_literal i cl = negate_head (make_last i cl);
633 (*Top-level Skolemization. Allows part of the conversion to clauses to be
634 expressed as a tactic (or Isar method). Each assumption of the selected
635 goal is converted to NNF and then its existential quantifiers are pulled
636 to the front. Finally, all existential quantifiers are eliminated,
637 leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
638 might generate many subgoals.*)
640 fun skolemize_tac i st =
641 let val ts = Logic.strip_assums_hyp (List.nth (prems_of st, i-1))
644 (fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1
645 THEN REPEAT (etac exE 1))),
646 REPEAT_DETERM_N (length ts) o (etac thin_rl)] i st
648 handle Subscript => Seq.empty;
650 (*Top-level conversion to meta-level clauses. Each clause has
651 leading !!-bound universal variables, to express generality. To get
652 disjunctions instead of meta-clauses, remove "make_meta_clauses" below.*)
653 val make_clauses_tac =
656 let val ts = Logic.strip_assums_hyp prop
661 (map forall_intr_vars
662 (make_meta_clauses (make_clauses hyps))) 1)),
663 REPEAT_DETERM_N (length ts) o (etac thin_rl)]
667 (*** setup the special skoklemization methods ***)
669 (*No CHANGED_PROP here, since these always appear in the preamble*)
671 val skolemize_setup =
673 [("skolemize", Method.no_args (Method.SIMPLE_METHOD' skolemize_tac),
674 "Skolemization into existential quantifiers"),
675 ("make_clauses", Method.no_args (Method.SIMPLE_METHOD' make_clauses_tac),
676 "Conversion to !!-quantified meta-level clauses")];
680 structure BasicMeson: BASIC_MESON = Meson;