1 (* Copyright (C) 2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
34 let check_equation env equation msg =
35 let w, proof, (eq_ty, left, right, order), metas, args = equation in
36 let metasenv, context, ugraph = env in
37 let metasenv' = metasenv @ metas in
39 CicTypeChecker.type_of_aux' metasenv' context left ugraph;
40 CicTypeChecker.type_of_aux' metasenv' context right ugraph;
43 CicUtil.Meta_not_found _ as exn ->
46 prerr_endline (CicPp.ppterm left);
47 prerr_endline (CicPp.ppterm right);
52 (* set to false to disable paramodulation inside auto_tac *)
53 let connect_to_auto = true;;
56 (* profiling statistics... *)
57 let infer_time = ref 0.;;
58 let forward_simpl_time = ref 0.;;
59 let forward_simpl_new_time = ref 0.;;
60 let backward_simpl_time = ref 0.;;
61 let passive_maintainance_time = ref 0.;;
63 (* limited-resource-strategy related globals *)
64 let processed_clauses = ref 0;; (* number of equalities selected so far... *)
65 let time_limit = ref 0.;; (* in seconds, settable by the user... *)
66 let start_time = ref 0.;; (* time at which the execution started *)
67 let elapsed_time = ref 0.;;
68 (* let maximal_weight = ref None;; *)
69 let maximal_retained_equality = ref None;;
71 (* equality-selection related globals *)
72 let use_fullred = ref true;;
73 let weight_age_ratio = ref 5 (* 5 *);; (* settable by the user *)
74 let weight_age_counter = ref !weight_age_ratio ;;
75 let symbols_ratio = ref 0 (* 3 *);;
76 let symbols_counter = ref 0;;
78 (* non-recursive Knuth-Bendix term ordering by default *)
79 (* Utils.compare_terms := Utils.rpo;; *)
80 (* Utils.compare_terms := Utils.nonrec_kbo;; *)
81 (* Utils.compare_terms := Utils.ao;; *)
84 let derived_clauses = ref 0;;
85 let kept_clauses = ref 0;;
87 (* index of the greatest Cic.Meta created - TODO: find a better way! *)
90 (* varbiables controlling the search-space *)
91 let maxdepth = ref 3;;
92 let maxwidth = ref 3;;
96 | ParamodulationFailure
97 | ParamodulationSuccess of Inference.proof option * environment
100 type goal = proof * Cic.metasenv * Cic.term;;
102 type theorem = Cic.term * Cic.term * Cic.metasenv;;
104 let symbols_of_equality (_, _, (_, left, right, _), _, _) =
105 let m1 = symbols_of_term left in
110 let c = TermMap.find k res in
111 TermMap.add k (c+v) res
114 (symbols_of_term right) m1
119 module OrderedEquality = struct
120 type t = Inference.equality
122 let compare eq1 eq2 =
123 match meta_convertibility_eq eq1 eq2 with
126 let w1, _, (ty, left, right, _), _, a = eq1
127 and w2, _, (ty', left', right', _), _, a' = eq2 in
128 match Pervasives.compare w1 w2 with
130 let res = (List.length a) - (List.length a') in
131 if res <> 0 then res else (
133 let res = Pervasives.compare (List.hd a) (List.hd a') in
134 if res <> 0 then res else Pervasives.compare eq1 eq2
135 with Failure "hd" -> Pervasives.compare eq1 eq2
140 module EqualitySet = Set.Make(OrderedEquality);;
142 exception Empty_list;;
144 let passive_is_empty = function
145 | ([], _), ([], _), _ -> true
150 let size_of_passive ((_, ns), (_, ps), _) =
151 (EqualitySet.cardinal ns) + (EqualitySet.cardinal ps)
155 let size_of_active (active_list, _) =
156 List.length active_list
159 let age_factor = 0.01;;
161 let min_elt weight l =
164 [] -> raise Empty_list
166 let wa = float_of_int (weight a) in
169 (fun (current,w) arg ->
171 let w1 = weight arg in
172 let wa = (float_of_int w1) +. !x *. age_factor in
173 if wa < w then (arg,wa) else (current,w))
178 let compare eq1 eq2 =
179 let w1, _, (ty, left, right, _), m1, _ = eq1 in
180 let w2, _, (ty', left', right', _), m2, _ = eq2 in
181 match Pervasives.compare w1 w2 with
182 | 0 -> (List.length m1) - (List.length m2)
188 selects one equality from passive. The selection strategy is a combination
189 of weight, age and goal-similarity
191 let rec select env goals passive (active, _) =
192 processed_clauses := !processed_clauses + 1;
194 match (List.rev goals) with (_, goal::_)::_ -> goal | _ -> assert false
196 let (neg_list, neg_set), (pos_list, pos_set), passive_table = passive in
198 List.filter (fun e -> e <> eq) l
200 if !weight_age_ratio > 0 then
201 weight_age_counter := !weight_age_counter - 1;
202 match !weight_age_counter with
204 weight_age_counter := !weight_age_ratio;
205 match neg_list, pos_list with
207 (* Negatives aren't indexed, no need to remove them... *)
209 ((tl, EqualitySet.remove hd neg_set), (pos, pos_set), passive_table)
210 | [], (hd:EqualitySet.elt)::tl ->
211 let w,_,_,_,_ = hd in
213 Indexing.remove_index passive_table hd
215 (([], neg_set), (tl, EqualitySet.remove hd pos_set), passive_table)
216 | _, _ -> assert false
218 | _ when (!symbols_counter > 0) && (EqualitySet.is_empty neg_set) ->
219 (symbols_counter := !symbols_counter - 1;
220 let cardinality map =
221 TermMap.fold (fun k v res -> res + v) map 0
224 let _, _, term = goal in
227 let card = cardinality symbols in
228 let foldfun k v (r1, r2) =
229 if TermMap.mem k symbols then
230 let c = TermMap.find k symbols in
231 let c1 = abs (c - v) in
237 let f equality (i, e) =
239 TermMap.fold foldfun (symbols_of_equality equality) (0, 0)
241 let c = others + (abs (common - card)) in
242 if c < i then (c, equality)
245 let e1 = EqualitySet.min_elt pos_set in
248 TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
250 (others + (abs (common - card))), e1
252 let _, current = EqualitySet.fold f pos_set initial in
254 Indexing.remove_index passive_table current
258 (remove current pos_list, EqualitySet.remove current pos_set),
262 symbols_counter := !symbols_ratio;
263 let set_selection set = EqualitySet.min_elt set in
264 (* let set_selection l = min_elt (fun (w,_,_,_,_) -> w) l in *)
265 if EqualitySet.is_empty neg_set then
266 let current = set_selection pos_set in
269 (remove current pos_list, EqualitySet.remove current pos_set),
270 Indexing.remove_index passive_table current
272 (Positive, current), passive
274 let current = set_selection neg_set in
276 (remove current neg_list, EqualitySet.remove current neg_set),
280 (Negative, current), passive
284 (* initializes the passive set of equalities *)
285 let make_passive neg pos =
286 let set_of equalities =
287 List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities
290 List.fold_left (fun tbl e -> Indexing.index tbl e) Indexing.empty pos
303 (* adds to passive a list of equalities: new_neg is a list of negative
304 equalities, new_pos a list of positive equalities *)
305 let add_to_passive passive (new_neg, new_pos) =
306 let (neg_list, neg_set), (pos_list, pos_set), table = passive in
307 let ok set equality = not (EqualitySet.mem equality set) in
308 let neg = List.filter (ok neg_set) new_neg
309 and pos = List.filter (ok pos_set) new_pos in
311 List.fold_left (fun tbl e -> Indexing.index tbl e) table pos
313 let add set equalities =
314 List.fold_left (fun s e -> EqualitySet.add e s) set equalities
316 (neg @ neg_list, add neg_set neg),
317 (pos_list @ pos, add pos_set pos),
322 (* removes from passive equalities that are estimated impossible to activate
323 within the current time limit *)
324 let prune_passive howmany (active, _) passive =
325 let (nl, ns), (pl, ps), tbl = passive in
326 let howmany = float_of_int howmany
327 and ratio = float_of_int !weight_age_ratio in
330 int_of_float (if t -. v < 0.5 then t else v)
332 let in_weight = round (howmany *. ratio /. (ratio +. 1.))
333 and in_age = round (howmany /. (ratio +. 1.)) in
335 (lazy (Printf.sprintf "in_weight: %d, in_age: %d\n" in_weight in_age));
338 | (Negative, e)::_ ->
339 let symbols = symbols_of_equality e in
340 let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
344 let counter = ref !symbols_ratio in
345 let rec pickw w ns ps =
347 if not (EqualitySet.is_empty ns) then
348 let e = EqualitySet.min_elt ns in
349 let ns', ps = pickw (w-1) (EqualitySet.remove e ns) ps in
350 EqualitySet.add e ns', ps
351 else if !counter > 0 then
353 counter := !counter - 1;
354 if !counter = 0 then counter := !symbols_ratio
358 let e = EqualitySet.min_elt ps in
359 let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
360 ns, EqualitySet.add e ps'
362 let foldfun k v (r1, r2) =
363 if TermMap.mem k symbols then
364 let c = TermMap.find k symbols in
365 let c1 = abs (c - v) in
371 let f equality (i, e) =
373 TermMap.fold foldfun (symbols_of_equality equality) (0, 0)
375 let c = others + (abs (common - card)) in
376 if c < i then (c, equality)
379 let e1 = EqualitySet.min_elt ps in
382 TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
384 (others + (abs (common - card))), e1
386 let _, e = EqualitySet.fold f ps initial in
387 let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
388 ns, EqualitySet.add e ps'
390 let e = EqualitySet.min_elt ps in
391 let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
392 ns, EqualitySet.add e ps'
394 EqualitySet.empty, EqualitySet.empty
396 let ns, ps = pickw in_weight ns ps in
397 let rec picka w s l =
401 | hd::tl when not (EqualitySet.mem hd s) ->
402 let w, s, l = picka (w-1) s tl in
403 w, EqualitySet.add hd s, hd::l
405 let w, s, l = picka w s tl in
410 let in_age, ns, nl = picka in_age ns nl in
411 let _, ps, pl = picka in_age ps pl in
412 if not (EqualitySet.is_empty ps) then
413 maximal_retained_equality := Some (EqualitySet.max_elt ps);
416 (fun e tbl -> Indexing.index tbl e) ps Indexing.empty
418 (nl, ns), (pl, ps), tbl
422 (** inference of new equalities between current and some in active *)
423 let infer env sign current (active_list, active_table) =
425 if Utils.debug_metas then
426 (ignore(Indexing.check_target c current "infer1");
427 ignore(List.map (function (_,current) -> Indexing.check_target c current "infer2") active_list));
428 let new_neg, new_pos =
432 Indexing.superposition_left !maxmeta env active_table current in
433 if Utils.debug_metas then
436 Indexing.check_target c current "sup-1") res);
441 Indexing.superposition_right !maxmeta env active_table current in
442 if Utils.debug_metas then
445 Indexing.check_target c current "sup0") res);
447 let rec infer_positive table = function
449 | (Negative, equality)::tl ->
451 Indexing.superposition_left !maxmeta env table equality in
453 if Utils.debug_metas then
456 Indexing.check_target c current "supl") res);
457 let neg, pos = infer_positive table tl in
459 | (Positive, equality)::tl ->
461 Indexing.superposition_right !maxmeta env table equality in
463 if Utils.debug_metas then
467 Indexing.check_target c current "sup2") res);
468 let neg, pos = infer_positive table tl in
471 let curr_table = Indexing.index Indexing.empty current in
472 let neg, pos = infer_positive curr_table active_list in
473 if Utils.debug_metas then
476 Indexing.check_target c current "sup3") pos);
479 derived_clauses := !derived_clauses + (List.length new_neg) +
480 (List.length new_pos);
481 match !maximal_retained_equality with
483 if Utils.debug_metas then
486 Indexing.check_target c current "sup4") new_pos);
489 Indexing.check_target c current "sup5") new_neg));
492 ignore(assert false);
493 (* if we have a maximal_retained_equality, we can discard all equalities
494 "greater" than it, as they will never be reached... An equality is
495 greater than maximal_retained_equality if it is bigger
496 wrt. OrderedEquality.compare and it is less similar than
497 maximal_retained_equality to the current goal *)
499 match active_list with
500 | (Negative, e)::_ ->
501 let symbols = symbols_of_equality e in
502 let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
509 List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos
512 if OrderedEquality.compare e eq <= 0 then
515 let foldfun k v (r1, r2) =
516 if TermMap.mem k symbols then
517 let c = TermMap.find k symbols in
518 let c1 = abs (c - v) in
526 TermMap.fold foldfun (symbols_of_equality eq) (0, 0) in
527 others + (abs (common - card))
530 TermMap.fold foldfun (symbols_of_equality e) (0, 0) in
531 let c = others + (abs (common - card)) in
532 if c < initial then true else false
534 List.filter filterfun new_pos
540 let contains_empty env (negative, positive) =
541 let metasenv, context, ugraph = env in
545 (fun (w, proof, (ty, left, right, ordering), m, a) ->
546 fst (CicReduction.are_convertible context left right ugraph))
555 (** simplifies current using active and passive *)
556 let forward_simplify env (sign, current) ?passive (active_list, active_table) =
557 let _, context, _ = env in
558 let pl, passive_table =
561 | Some ((pn, _), (pp, _), pt) ->
562 let pn = List.map (fun e -> (Negative, e)) pn
563 and pp = List.map (fun e -> (Positive, e)) pp in
566 let all = if pl = [] then active_list else active_list @ pl in
568 let demodulate table current =
569 let newmeta, newcurrent =
570 Indexing.demodulation_equality !maxmeta env table sign current in
572 if is_identity env newcurrent then
573 if sign = Negative then Some (sign, newcurrent)
577 (* (Printf.sprintf "\ncurrent was: %s\nnewcurrent is: %s\n" *)
578 (* (string_of_equality current) *)
579 (* (string_of_equality newcurrent))); *)
582 (* (Printf.sprintf "active is: %s" *)
583 (* (String.concat "\n" *)
584 (* (List.map (fun (_, e) -> (string_of_equality e)) active_list)))); *)
588 Some (sign, newcurrent)
591 if Utils.debug_metas then
592 ignore (Indexing.check_target context current "demod0");
593 let res = demodulate active_table current in
594 if Utils.debug_metas then
595 ignore ((function None -> () | Some (_,x) ->
596 Indexing.check_target context x "demod1";()) res);
599 | Some (sign, newcurrent) ->
600 match passive_table with
602 | Some passive_table -> demodulate passive_table newcurrent
606 | Some (Negative, c) ->
609 (fun (s, eq) -> s = Negative && meta_convertibility_eq eq c)
612 if ok then res else None
613 | Some (Positive, c) ->
614 if Indexing.in_index active_table c then
617 match passive_table with
619 if fst (Indexing.subsumption env active_table c) then
623 | Some passive_table ->
624 if Indexing.in_index passive_table c then None
626 let r1, _ = Indexing.subsumption env active_table c in
628 let r2, _ = Indexing.subsumption env passive_table c in
629 if r2 then None else res
632 type fs_time_info_t = {
633 mutable build_all: float;
634 mutable demodulate: float;
635 mutable subsumption: float;
638 let fs_time_info = { build_all = 0.; demodulate = 0.; subsumption = 0. };;
641 (** simplifies new using active and passive *)
642 let forward_simplify_new env (new_neg, new_pos) ?passive active =
643 if Utils.debug_metas then
648 Indexing.check_target c current "forward new neg") new_neg);
650 (fun current -> Indexing.check_target c current "forward new pos")
653 let t1 = Unix.gettimeofday () in
655 let active_list, active_table = active in
656 let pl, passive_table =
659 | Some ((pn, _), (pp, _), pt) ->
660 let pn = List.map (fun e -> (Negative, e)) pn
661 and pp = List.map (fun e -> (Positive, e)) pp in
665 let t2 = Unix.gettimeofday () in
666 fs_time_info.build_all <- fs_time_info.build_all +. (t2 -. t1);
668 let demodulate sign table target =
669 let newmeta, newtarget =
670 Indexing.demodulation_equality !maxmeta env table sign target in
674 let t1 = Unix.gettimeofday () in
676 let new_neg, new_pos =
677 let new_neg = List.map (demodulate Negative active_table) new_neg
678 and new_pos = List.map (demodulate Positive active_table) new_pos in
681 match passive_table with
682 | None -> new_neg, new_pos
683 | Some passive_table ->
684 List.map (demodulate Negative passive_table) new_neg,
685 List.map (demodulate Positive passive_table) new_pos *)
688 let t2 = Unix.gettimeofday () in
689 fs_time_info.demodulate <- fs_time_info.demodulate +. (t2 -. t1);
694 if not (Inference.is_identity env e) then
695 if EqualitySet.mem e s then s
696 else EqualitySet.add e s
698 EqualitySet.empty new_pos
700 let new_pos = EqualitySet.elements new_pos_set in
703 match passive_table with
705 (fun e -> not (fst (Indexing.subsumption env active_table e)))
706 | Some passive_table ->
707 (fun e -> not ((fst (Indexing.subsumption env active_table e)) ||
708 (fst (Indexing.subsumption env passive_table e))))
710 (* let t1 = Unix.gettimeofday () in *)
711 (* let t2 = Unix.gettimeofday () in *)
712 (* fs_time_info.subsumption <- fs_time_info.subsumption +. (t2 -. t1); *)
714 match passive_table with
716 (fun e -> not (Indexing.in_index active_table e))
717 | Some passive_table ->
719 not ((Indexing.in_index active_table e) ||
720 (Indexing.in_index passive_table e)))
722 new_neg, List.filter subs (List.filter is_duplicate new_pos)
726 (** simplifies active usign new *)
727 let backward_simplify_active env new_pos new_table min_weight active =
728 let active_list, active_table = active in
729 let active_list, newa =
731 (fun (s, equality) (res, newn) ->
732 let ew, _, _, _, _ = equality in
733 if ew < min_weight then
734 (s, equality)::res, newn
736 match forward_simplify env (s, equality) (new_pos, new_table) with
746 List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
750 (fun (s, eq) (res, tbl) ->
751 if List.mem (s, eq) res then
753 else if (is_identity env eq) || (find eq res) then (
757 (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
758 active_list ([], Indexing.empty),
760 (fun (s, eq) (n, p) ->
761 if (s <> Negative) && (is_identity env eq) then (
764 if s = Negative then eq::n, p
769 | [], [] -> active, None
770 | _ -> active, Some newa
774 (** simplifies passive using new *)
775 let backward_simplify_passive env new_pos new_table min_weight passive =
776 let (nl, ns), (pl, ps), passive_table = passive in
777 let f sign equality (resl, ress, newn) =
778 let ew, _, _, _, _ = equality in
779 if ew < min_weight then
780 equality::resl, ress, newn
782 match forward_simplify env (sign, equality) (new_pos, new_table) with
783 | None -> resl, EqualitySet.remove equality ress, newn
786 equality::resl, ress, newn
788 let ress = EqualitySet.remove equality ress in
791 let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
792 and pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in
795 (fun tbl e -> Indexing.index tbl e) Indexing.empty pl
797 match newn, newp with
798 | [], [] -> ((nl, ns), (pl, ps), passive_table), None
799 | _, _ -> ((nl, ns), (pl, ps), passive_table), Some (newn, newp)
803 let backward_simplify env new' ?passive active =
804 let new_pos, new_table, min_weight =
807 let ew, _, _, _, _ = e in
808 (Positive, e)::l, Indexing.index t e, min ew w)
809 ([], Indexing.empty, 1000000) (snd new')
812 backward_simplify_active env new_pos new_table min_weight active in
815 active, (make_passive [] []), newa, None
817 active, passive, newa, None
820 backward_simplify_passive env new_pos new_table min_weight passive in
821 active, passive, newa, newp *)
825 let close env new' given =
826 let new_pos, new_table, min_weight =
829 let ew, _, _, _, _ = e in
830 (Positive, e)::l, Indexing.index t e, min ew w)
831 ([], Indexing.empty, 1000000) (snd new')
835 let neg,pos = infer env s c (new_pos,new_table) in
840 let is_commutative_law eq =
841 let w, proof, (eq_ty, left, right, order), metas, args = snd eq in
842 match left,right with
843 Cic.Appl[f1;Cic.Meta _ as a1;Cic.Meta _ as b1],
844 Cic.Appl[f2;Cic.Meta _ as a2;Cic.Meta _ as b2] ->
845 f1 = f2 && a1 = b2 && a2 = b1
849 let prova env new' active =
850 let given = List.filter is_commutative_law (fst active) in
854 (Printf.sprintf "symmetric:\n%s\n"
857 (fun (s, e) -> (string_of_sign s) ^ " " ^
858 (string_of_equality ~env e))
863 (* returns an estimation of how many equalities in passive can be activated
864 within the current time limit *)
865 let get_selection_estimate () =
866 elapsed_time := (Unix.gettimeofday ()) -. !start_time;
867 (* !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *)
869 ceil ((float_of_int !processed_clauses) *.
870 ((!time_limit (* *. 2. *)) /. !elapsed_time -. 1.)))
874 (** initializes the set of goals *)
875 let make_goals goal =
877 and passive = [0, [goal]] in
882 (** initializes the set of theorems *)
883 let make_theorems theorems =
888 let activate_goal (active, passive) =
890 | goal_conj::tl -> true, (goal_conj::active, tl)
891 | [] -> false, (active, passive)
895 let activate_theorem (active, passive) =
897 | theorem::tl -> true, (theorem::active, tl)
898 | [] -> false, (active, passive)
902 (** simplifies a goal with equalities in active and passive *)
903 let simplify_goal env goal ?passive (active_list, active_table) =
904 let pl, passive_table =
907 | Some ((pn, _), (pp, _), pt) ->
908 let pn = List.map (fun e -> (Negative, e)) pn
909 and pp = List.map (fun e -> (Positive, e)) pp in
913 let demodulate table goal =
914 let newmeta, newgoal =
915 Indexing.demodulation_goal !maxmeta env table goal in
917 goal != newgoal, newgoal
920 match passive_table with
921 | None -> demodulate active_table goal
922 | Some passive_table ->
923 let changed, goal = demodulate active_table goal in
924 let changed', goal = demodulate passive_table goal in
925 (changed || changed'), goal
931 let simplify_goals env goals ?passive active =
932 let a_goals, p_goals = goals in
937 List.map (fun g -> snd (simplify_goal env g ?passive active)) gl in
943 (fun (a, p) (d, gl) ->
944 let changed = ref false in
948 let c, g = simplify_goal env g ?passive active in
949 changed := !changed || c; g) gl in
950 if !changed then (a, (d, gl)::p) else ((d, gl)::a, p))
951 ([], p_goals) a_goals
957 let simplify_theorems env theorems ?passive (active_list, active_table) =
958 let pl, passive_table =
961 | Some ((pn, _), (pp, _), pt) ->
962 let pn = List.map (fun e -> (Negative, e)) pn
963 and pp = List.map (fun e -> (Positive, e)) pp in
966 let a_theorems, p_theorems = theorems in
967 let demodulate table theorem =
968 let newmeta, newthm =
969 Indexing.demodulation_theorem !maxmeta env table theorem in
971 theorem != newthm, newthm
973 let foldfun table (a, p) theorem =
974 let changed, theorem = demodulate table theorem in
975 if changed then (a, theorem::p) else (theorem::a, p)
977 let mapfun table theorem = snd (demodulate table theorem) in
978 match passive_table with
980 let p_theorems = List.map (mapfun active_table) p_theorems in
981 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems
982 | Some passive_table ->
983 let p_theorems = List.map (mapfun active_table) p_theorems in
984 let p_theorems, a_theorems =
985 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems in
986 let p_theorems = List.map (mapfun passive_table) p_theorems in
987 List.fold_left (foldfun passive_table) ([], p_theorems) a_theorems
991 let rec simpl env e others others_simpl =
992 let active = others @ others_simpl in
995 (fun t (_, e) -> Indexing.index t e)
996 Indexing.empty active
998 let res = forward_simplify env e (active, tbl) in
1002 | None -> simpl env hd tl others_simpl
1003 | Some e -> simpl env hd tl (e::others_simpl)
1007 | None -> others_simpl
1008 | Some e -> e::others_simpl
1012 let simplify_equalities env equalities =
1015 (Printf.sprintf "equalities:\n%s\n"
1017 (List.map string_of_equality equalities))));
1018 debug_print (lazy "SIMPLYFYING EQUALITIES...");
1019 match equalities with
1022 let others = List.map (fun e -> (Positive, e)) tl in
1024 List.rev (List.map snd (simpl env (Positive, hd) others []))
1028 (Printf.sprintf "equalities AFTER:\n%s\n"
1030 (List.map string_of_equality res))));
1034 (* applies equality to goal to see if the goal can be closed *)
1035 let apply_equality_to_goal env equality goal =
1036 let module C = Cic in
1037 let module HL = HelmLibraryObjects in
1038 let module I = Inference in
1039 let metasenv, context, ugraph = env in
1040 let _, proof, (ty, left, right, _), metas, args = equality in
1042 C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right] in
1043 let gproof, gmetas, gterm = goal in
1046 (* (Printf.sprintf "APPLY EQUALITY TO GOAL: %s, %s" *)
1047 (* (string_of_equality equality) (CicPp.ppterm gterm))); *)
1049 let subst, metasenv', _ =
1050 let menv = metasenv @ metas @ gmetas in
1051 Inference.unification metas gmetas context eqterm gterm ugraph
1055 | I.BasicProof t -> I.BasicProof (CicMetaSubst.apply_subst subst t)
1056 | I.ProofBlock (s, uri, nt, t, pe, p) ->
1057 I.ProofBlock (subst @ s, uri, nt, t, pe, p)
1061 let rec repl = function
1062 | I.ProofGoalBlock (_, gp) -> I.ProofGoalBlock (newproof, gp)
1063 | I.NoProof -> newproof
1064 | I.BasicProof p -> newproof
1065 | I.SubProof (t, i, p) -> I.SubProof (t, i, repl p)
1070 true, subst, newgproof
1071 with CicUnification.UnificationFailure _ ->
1072 false, [], I.NoProof
1077 let new_meta metasenv =
1078 let m = CicMkImplicit.new_meta metasenv [] in
1080 while !maxmeta <= m do incr maxmeta done;
1085 (* applies a theorem or an equality to goal, returning a list of subgoals or
1086 an indication of failure *)
1087 let apply_to_goal env theorems ?passive active goal =
1088 let metasenv, context, ugraph = env in
1089 let proof, metas, term = goal in
1092 (* (Printf.sprintf "apply_to_goal with goal: %s" *)
1093 (* (\* (string_of_proof proof) *\)(CicPp.ppterm term))); *)
1096 CicMkImplicit.identity_relocation_list_for_metavariable context in
1097 let proof', newmeta =
1098 let rec get_meta = function
1099 | SubProof (t, i, p) ->
1100 let t', i' = get_meta p in
1101 if i' = -1 then t, i else t', i'
1102 | ProofGoalBlock (_, p) -> get_meta p
1103 | _ -> Cic.Implicit None, -1
1105 let p, m = get_meta proof in
1107 let n = new_meta (metasenv @ metas) in
1108 Cic.Meta (n, irl), n
1112 let metasenv = (newmeta, context, term)::metasenv @ metas in
1113 let bit = new_meta metasenv, context, term in
1114 let metasenv' = bit::metasenv in
1115 ((None, metasenv', Cic.Meta (newmeta, irl), term), newmeta)
1117 let rec aux = function
1119 | (theorem, thmty, _)::tl ->
1121 let subst, (newproof, newgoals) =
1122 PrimitiveTactics.apply_tac_verbose_with_subst ~term:theorem status
1124 if newgoals = [] then
1125 let _, _, p, _ = newproof in
1127 let rec repl = function
1128 | Inference.ProofGoalBlock (_, gp) ->
1129 Inference.ProofGoalBlock (Inference.BasicProof p, gp)
1130 | Inference.NoProof -> Inference.BasicProof p
1131 | Inference.BasicProof _ -> Inference.BasicProof p
1132 | Inference.SubProof (t, i, p2) ->
1133 Inference.SubProof (t, i, repl p2)
1138 let _, m = status in
1139 let subst = List.filter (fun (i, _) -> i = m) subst in
1140 `Ok (subst, [newp, metas, term])
1142 let _, menv, p, _ = newproof in
1144 CicMkImplicit.identity_relocation_list_for_metavariable context
1149 let _, _, ty = CicUtil.lookup_meta i menv in
1151 let rec gp = function
1152 | SubProof (t, i, p) ->
1153 SubProof (t, i, gp p)
1154 | ProofGoalBlock (sp1, sp2) ->
1155 ProofGoalBlock (sp1, gp sp2)
1158 SubProof (p, i, BasicProof (Cic.Meta (i, irl)))
1159 | ProofSymBlock (s, sp) ->
1160 ProofSymBlock (s, gp sp)
1161 | ProofBlock (s, u, nt, t, pe, sp) ->
1162 ProofBlock (s, u, nt, t, pe, gp sp)
1170 let w, m = weight_of_term t in
1171 w + 2 * (List.length m)
1174 (fun (_, _, t1) (_, _, t2) ->
1175 Pervasives.compare (weight t1) (weight t2))
1178 let best = aux tl in
1180 | `Ok (_, _) -> best
1181 | `No -> `GoOn ([subst, goals])
1182 | `GoOn sl -> `GoOn ((subst, goals)::sl)
1183 with ProofEngineTypes.Fail msg ->
1187 if Inference.term_is_equality term then
1188 let rec appleq_a = function
1189 | [] -> false, [], []
1190 | (Positive, equality)::tl ->
1191 let ok, s, newproof = apply_equality_to_goal env equality goal in
1192 if ok then true, s, [newproof, metas, term] else appleq_a tl
1193 | _::tl -> appleq_a tl
1195 let rec appleq_p = function
1196 | [] -> false, [], []
1198 let ok, s, newproof = apply_equality_to_goal env equality goal in
1199 if ok then true, s, [newproof, metas, term] else appleq_p tl
1201 let al, _ = active in
1203 | None -> appleq_a al
1204 | Some (_, (pl, _), _) ->
1205 let r, s, l = appleq_a al in if r then r, s, l else appleq_p pl
1209 if r = true then `Ok (s, l) else aux theorems
1213 (* sorts a conjunction of goals in order to detect earlier if it is
1214 unsatisfiable. Non-predicate goals are placed at the end of the list *)
1215 let sort_goal_conj (metasenv, context, ugraph) (depth, gl) =
1218 (fun (_, e1, g1) (_, e2, g2) ->
1220 CicTypeChecker.type_of_aux' (e1 @ metasenv) context g1 ugraph
1222 CicTypeChecker.type_of_aux' (e2 @ metasenv) context g2 ugraph
1226 CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty1 ugraph
1231 CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty2 ugraph
1235 if prop1 = 0 && prop2 = 0 then
1236 let e1 = if Inference.term_is_equality g1 then 0 else 1
1237 and e2 = if Inference.term_is_equality g2 then 0 else 1 in
1247 let is_meta_closed goals =
1248 List.for_all (fun (_, _, g) -> CicUtil.is_meta_closed g) goals
1252 (* applies a series of theorems/equalities to a conjunction of goals *)
1253 let rec apply_to_goal_conj env theorems ?passive active (depth, goals) =
1254 let aux (goal, r) tl =
1255 let propagate_subst subst (proof, metas, term) =
1256 let rec repl = function
1257 | NoProof -> NoProof
1259 BasicProof (CicMetaSubst.apply_subst subst t)
1260 | ProofGoalBlock (p, pb) ->
1261 let pb' = repl pb in
1262 ProofGoalBlock (p, pb')
1263 | SubProof (t, i, p) ->
1264 let t' = CicMetaSubst.apply_subst subst t in
1267 | ProofSymBlock (ens, p) -> ProofSymBlock (ens, repl p)
1268 | ProofBlock (s, u, nty, t, pe, p) ->
1269 ProofBlock (subst @ s, u, nty, t, pe, p)
1270 in (repl proof, metas, term)
1272 (* let r = apply_to_goal env theorems ?passive active goal in *) (
1274 | `No -> `No (depth, goals)
1279 let tl = List.map (propagate_subst s) tl in
1280 sort_goal_conj env (depth+1, gl @ tl)) sl
1283 | `Ok (subst, gl) ->
1287 let p, _, _ = List.hd gl in
1289 let rec repl = function
1290 | SubProof (_, _, p) -> repl p
1291 | ProofGoalBlock (p1, p2) ->
1292 ProofGoalBlock (repl p1, repl p2)
1295 build_proof_term (repl p)
1298 let rec get_meta = function
1299 | SubProof (_, i, p) ->
1300 let i' = get_meta p in
1301 if i' = -1 then i else i'
1302 (* max i (get_meta p) *)
1303 | ProofGoalBlock (_, p) -> get_meta p
1309 let _, (context, _, _) = List.hd subst in
1310 [i, (context, subproof, Cic.Implicit None)]
1312 let tl = List.map (propagate_subst subst) tl in
1313 let conj = sort_goal_conj env (depth(* +1 *), tl) in
1317 if depth > !maxdepth || (List.length goals) > !maxwidth then
1320 let rec search_best res = function
1323 let r = apply_to_goal env theorems ?passive active goal in
1325 | `Ok _ -> (goal, r)
1326 | `No -> search_best res tl
1330 | _, `Ok _ -> assert false
1333 if (List.length l) < (List.length l2) then goal, r else res
1335 search_best newres tl
1337 let hd = List.hd goals in
1338 let res = hd, (apply_to_goal env theorems ?passive active hd) in
1342 | _, _ -> search_best res (List.tl goals)
1344 let res = aux best (List.filter (fun g -> g != (fst best)) goals) in
1346 | `GoOn ([conj]) when is_meta_closed (snd conj) &&
1347 (List.length (snd conj)) < (List.length goals)->
1348 apply_to_goal_conj env theorems ?passive active conj
1354 module OrderedGoals = struct
1355 type t = int * (Inference.proof * Cic.metasenv * Cic.term) list
1362 else let r = (List.length l1) - (List.length l2) in
1368 (fun (_, _, t1) (_, _, t2) ->
1369 let r = Pervasives.compare t1 t2 in
1378 module GoalsSet = Set.Make(OrderedGoals);;
1381 exception SearchSpaceOver;;
1386 let apply_to_goals env is_passive_empty theorems active goals =
1387 debug_print (lazy "\n\n\tapply_to_goals\n\n");
1388 let add_to set goals =
1389 List.fold_left (fun s g -> GoalsSet.add g s) set goals
1391 let rec aux set = function
1393 debug_print (lazy "HERE!!!");
1394 if is_passive_empty then raise SearchSpaceOver else false, set
1396 let res = apply_to_goal_conj env theorems active goals in
1402 | (d, (p, _, t)::_) -> d, p, t
1407 (Printf.sprintf "\nOK!!!!\ndepth: %d\nProof: %s\ngoal: %s\n"
1408 d (string_of_proof p) (CicPp.ppterm t)))
1410 true, GoalsSet.singleton newgoals
1412 let set' = add_to set (goals::tl) in
1413 let set' = add_to set' newgoals in
1418 let n = List.length goals in
1419 let res, goals = aux (add_to GoalsSet.empty goals) goals in
1420 let goals = GoalsSet.elements goals in
1421 debug_print (lazy "\n\tapply_to_goals end\n");
1422 let m = List.length goals in
1423 if m = n && is_passive_empty then
1424 raise SearchSpaceOver
1431 (* sorts the list of passive goals to minimize the search for a proof (doesn't
1432 work that well yet...) *)
1433 let sort_passive_goals goals =
1435 (fun (d1, l1) (d2, l2) ->
1437 and r2 = (List.length l1) - (List.length l2) in
1438 let foldfun ht (_, _, t) =
1439 let _ = List.map (fun i -> Hashtbl.replace ht i 1) (metas_of_term t)
1442 let m1 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l1)
1443 and m2 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l2)
1444 in let r3 = m1 - m2 in
1446 else if r2 <> 0 then r2
1448 (* let _, _, g1 = List.hd l1 *)
1449 (* and _, _, g2 = List.hd l2 in *)
1450 (* let e1 = if Inference.term_is_equality g1 then 0 else 1 *)
1451 (* and e2 = if Inference.term_is_equality g2 then 0 else 1 *)
1452 (* in let r4 = e1 - e2 in *)
1453 (* if r4 <> 0 then r3 else r1) *)
1458 let print_goals goals =
1465 (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl
1467 Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
1471 (* tries to prove the first conjunction in goals with applications of
1472 theorems/equalities, returning new sub-goals or an indication of success *)
1473 let apply_goal_to_theorems dbd env theorems ?passive active goals =
1474 let theorems, _ = theorems in
1475 let a_goals, p_goals = goals in
1476 let goal = List.hd a_goals in
1477 let not_in_active gl =
1481 if (List.length gl) = (List.length gl') then
1482 List.for_all2 (fun (_, _, g1) (_, _, g2) -> g1 = g2) gl gl'
1488 let res = apply_to_goal_conj env theorems ?passive active goal in
1491 true, ([newgoals], [])
1493 false, (a_goals, p_goals)
1498 (d <= !maxdepth) && (List.length gl) <= !maxwidth &&
1501 let p_goals = newgoals @ p_goals in
1502 let p_goals = sort_passive_goals p_goals in
1503 false, (a_goals, p_goals)
1509 let apply_theorem_to_goals env theorems active goals =
1510 let a_goals, p_goals = goals in
1511 let theorem = List.hd (fst theorems) in
1512 let theorems = [theorem] in
1513 let rec aux p = function
1514 | [] -> false, ([], p)
1516 let res = apply_to_goal_conj env theorems active goal in
1518 | `Ok newgoals -> true, ([newgoals], [])
1520 | `GoOn newgoals -> aux (newgoals @ p) tl
1522 let ok, (a, p) = aux p_goals a_goals in
1528 (fun (d1, l1) (d2, l2) ->
1531 else let r = (List.length l1) - (List.length l2) in
1537 (fun (_, _, t1) (_, _, t2) ->
1538 let r = Pervasives.compare t1 t2 in
1539 if r <> 0 then (res := r; true) else false) l1 l2
1543 ok, (a_goals, p_goals)
1547 (* given-clause algorithm with lazy reduction strategy *)
1548 let rec given_clause dbd env goals theorems passive active =
1549 let _,context,_ = env in
1550 let goals = simplify_goals env goals active in
1551 let ok, goals = activate_goal goals in
1552 (* let theorems = simplify_theorems env theorems active in *)
1554 let ok, goals = apply_goal_to_theorems dbd env theorems active goals in
1557 match (fst goals) with
1558 | (_, [proof, _, _])::_ -> Some proof
1561 ParamodulationSuccess (proof, env)
1563 given_clause_aux dbd env goals theorems passive active
1565 (* let ok', theorems = activate_theorem theorems in *)
1566 let ok', theorems = false, theorems in
1568 let ok, goals = apply_theorem_to_goals env theorems active goals in
1571 match (fst goals) with
1572 | (_, [proof, _, _])::_ -> Some proof
1575 ParamodulationSuccess (proof, env)
1577 given_clause_aux dbd env goals theorems passive active
1579 if (passive_is_empty passive) then ParamodulationFailure
1580 else given_clause_aux dbd env goals theorems passive active
1582 and given_clause_aux dbd env goals theorems passive active =
1583 let _,context,_ = env in
1584 let time1 = Unix.gettimeofday () in
1586 let selection_estimate = get_selection_estimate () in
1587 let kept = size_of_passive passive in
1589 if !time_limit = 0. || !processed_clauses = 0 then
1591 else if !elapsed_time > !time_limit then (
1592 debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
1593 !time_limit !elapsed_time));
1595 ) else if kept > selection_estimate then (
1597 (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
1598 "(kept: %d, selection_estimate: %d)\n")
1599 kept selection_estimate));
1600 prune_passive selection_estimate active passive
1605 let time2 = Unix.gettimeofday () in
1606 passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
1608 kept_clauses := (size_of_passive passive) + (size_of_active active);
1609 match passive_is_empty passive with
1610 | true -> (* ParamodulationFailure *)
1611 given_clause dbd env goals theorems passive active
1613 let (sign, current), passive = select env (fst goals) passive active in
1614 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1615 prerr_endline ("Selected = " ^
1616 (CicPp.pp (Inference.term_of_equality current) names));
1617 let time1 = Unix.gettimeofday () in
1618 let res = forward_simplify env (sign, current) ~passive active in
1619 let time2 = Unix.gettimeofday () in
1620 forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
1623 given_clause dbd env goals theorems passive active
1624 | Some (sign, current) ->
1625 if (sign = Negative) && (is_identity env current) then (
1627 (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
1628 (string_of_equality ~env current)));
1629 let _, proof, _, _, _ = current in
1630 ParamodulationSuccess (Some proof, env)
1633 (lazy "\n================================================");
1634 debug_print (lazy (Printf.sprintf "selected: %s %s"
1635 (string_of_sign sign)
1636 (string_of_equality ~env current)));
1638 let t1 = Unix.gettimeofday () in
1639 let new' = infer env sign current active in
1640 let t2 = Unix.gettimeofday () in
1641 infer_time := !infer_time +. (t2 -. t1);
1643 let res, goal' = contains_empty env new' in
1647 | Some goal -> let _, proof, _, _, _ = goal in Some proof
1650 ParamodulationSuccess (proof, env)
1652 let t1 = Unix.gettimeofday () in
1653 let new' = forward_simplify_new env new' active in
1654 let t2 = Unix.gettimeofday () in
1656 forward_simpl_new_time :=
1657 !forward_simpl_new_time +. (t2 -. t1)
1661 | Negative -> active
1663 let t1 = Unix.gettimeofday () in
1664 let active, _, newa, _ =
1665 backward_simplify env ([], [current]) active
1667 let t2 = Unix.gettimeofday () in
1668 backward_simpl_time :=
1669 !backward_simpl_time +. (t2 -. t1);
1673 let al, tbl = active in
1674 let nn = List.map (fun e -> Negative, e) n in
1679 Indexing.index tbl e)
1684 match contains_empty env new' with
1687 let al, tbl = active in
1689 | Negative -> (sign, current)::al, tbl
1691 al @ [(sign, current)], Indexing.index tbl current
1693 let passive = add_to_passive passive new' in
1694 given_clause dbd env goals theorems passive active
1699 let _, proof, _, _, _ = goal in Some proof
1702 ParamodulationSuccess (proof, env)
1707 (** given-clause algorithm with full reduction strategy *)
1708 let rec given_clause_fullred dbd env goals theorems passive active =
1709 let goals = simplify_goals env goals ~passive active in
1710 let _,context,_ = env in
1711 let ok, goals = activate_goal goals in
1712 (* let theorems = simplify_theorems env theorems ~passive active in *)
1714 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1715 let _, _, t = List.hd (snd (List.hd (fst goals))) in
1716 let _ = prerr_endline ("goal activated = " ^ (CicPp.pp t names)) in
1720 (* (Printf.sprintf "\ngoals = \nactive\n%s\npassive\n%s\n" *)
1721 (* (print_goals (fst goals)) (print_goals (snd goals)))); *)
1722 (* let current = List.hd (fst goals) in *)
1723 (* let p, _, t = List.hd (snd current) in *)
1726 (* (Printf.sprintf "goal activated:\n%s\n%s\n" *)
1727 (* (CicPp.ppterm t) (string_of_proof p))); *)
1730 apply_goal_to_theorems dbd env theorems ~passive active goals
1734 match (fst goals) with
1735 | (_, [proof, _, _])::_ -> Some proof
1738 ( prerr_endline "esco qui";
1739 let s = Printf.sprintf "actives:\n%s\n"
1742 (fun (s, e) -> (string_of_sign s) ^ " " ^
1743 (string_of_equality ~env e))
1745 let sp = Printf.sprintf "passives:\n%s\n"
1748 (string_of_equality ~env)
1749 (let x,y,_ = passive in (fst x)@(fst y)))) in
1752 ParamodulationSuccess (proof, env))
1754 given_clause_fullred_aux dbd env goals theorems passive active
1756 (* let ok', theorems = activate_theorem theorems in *)
1758 (* let ok, goals = apply_theorem_to_goals env theorems active goals in *)
1761 (* match (fst goals) with *)
1762 (* | (_, [proof, _, _])::_ -> Some proof *)
1763 (* | _ -> assert false *)
1765 (* ParamodulationSuccess (proof, env) *)
1767 (* given_clause_fullred_aux env goals theorems passive active *)
1769 if (passive_is_empty passive) then ParamodulationFailure
1770 else given_clause_fullred_aux dbd env goals theorems passive active
1772 and given_clause_fullred_aux dbd env goals theorems passive active =
1773 prerr_endline ("MAXMETA: " ^ string_of_int !maxmeta ^
1774 " LOCALMAX: " ^ string_of_int !Indexing.local_max ^
1775 " #ACTIVES: " ^ string_of_int (size_of_active active) ^
1776 " #PASSIVES: " ^ string_of_int (size_of_passive passive));
1777 if (size_of_active active) mod 54 = 0 then
1778 (let s = Printf.sprintf "actives:\n%s\n"
1781 (fun (s, e) -> (string_of_sign s) ^ " " ^
1782 (string_of_equality ~env e))
1784 let sp = Printf.sprintf "passives:\n%s\n"
1787 (string_of_equality ~env)
1788 (let x,y,_ = passive in (fst x)@(fst y)))) in
1791 let time1 = Unix.gettimeofday () in
1792 let (_,context,_) = env in
1793 let selection_estimate = get_selection_estimate () in
1794 let kept = size_of_passive passive in
1796 if !time_limit = 0. || !processed_clauses = 0 then
1798 else if !elapsed_time > !time_limit then (
1799 debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
1800 !time_limit !elapsed_time));
1802 ) else if kept > selection_estimate then (
1804 (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
1805 "(kept: %d, selection_estimate: %d)\n")
1806 kept selection_estimate));
1807 prune_passive selection_estimate active passive
1812 let time2 = Unix.gettimeofday () in
1813 passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
1815 kept_clauses := (size_of_passive passive) + (size_of_active active);
1816 match passive_is_empty passive with
1817 | true -> (* ParamodulationFailure *)
1818 given_clause_fullred dbd env goals theorems passive active
1820 let (sign, current), passive = select env (fst goals) passive active in
1821 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1822 prerr_endline ("Selected = " ^ (string_of_sign sign) ^ " " ^
1823 string_of_equality ~env current);
1824 (* (CicPp.pp (Inference.term_of_equality current) names));*)
1825 let time1 = Unix.gettimeofday () in
1826 let res = forward_simplify env (sign, current) ~passive active in
1827 let time2 = Unix.gettimeofday () in
1828 forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
1831 given_clause_fullred dbd env goals theorems passive active
1832 | Some (sign, current) ->
1833 if (sign = Negative) && (is_identity env current) then (
1835 (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
1836 (string_of_equality ~env current)));
1837 let _, proof, _, _, _ = current in
1838 ParamodulationSuccess (Some proof, env)
1841 (lazy "\n================================================");
1842 debug_print (lazy (Printf.sprintf "selected: %s %s"
1843 (string_of_sign sign)
1844 (string_of_equality ~env current)));
1846 let t1 = Unix.gettimeofday () in
1847 let new' = infer env sign current active in
1853 (Printf.sprintf "new' (senza semplificare):\n%s\n"
1856 (fun e -> "Negative " ^
1857 (string_of_equality ~env e)) neg) @
1859 (fun e -> "Positive " ^
1860 (string_of_equality ~env e)) pos)))))
1862 let t2 = Unix.gettimeofday () in
1863 infer_time := !infer_time +. (t2 -. t1);
1865 if is_identity env current then active
1867 let al, tbl = active in
1869 | Negative -> (sign, current)::al, tbl
1871 al @ [(sign, current)], Indexing.index tbl current
1873 let rec simplify new' active passive =
1874 let t1 = Unix.gettimeofday () in
1875 let new' = forward_simplify_new env new' ~passive active in
1876 let t2 = Unix.gettimeofday () in
1877 forward_simpl_new_time :=
1878 !forward_simpl_new_time +. (t2 -. t1);
1879 let t1 = Unix.gettimeofday () in
1880 let active, passive, newa, retained =
1881 backward_simplify env new' ~passive active in
1882 let t2 = Unix.gettimeofday () in
1883 backward_simpl_time := !backward_simpl_time +. (t2 -. t1);
1884 match newa, retained with
1885 | None, None -> active, passive, new'
1887 | None, Some (n, p) ->
1888 let nn, np = new' in
1889 if Utils.debug_metas then
1891 List.map (fun x -> Indexing.check_target context x "simplify1")n;
1892 List.map (fun x -> Indexing.check_target context x "simplify2")p);
1893 simplify (nn @ n, np @ p) active passive
1894 | Some (n, p), Some (rn, rp) ->
1895 let nn, np = new' in
1896 simplify (nn @ n @ rn, np @ p @ rp) active passive
1898 let active, passive, new' = simplify new' active passive in
1900 let new1 = prova env new' active in
1901 let new' = (fst new') @ (fst new1), (snd new') @ (snd new1) in
1907 (Printf.sprintf "new1:\n%s\n"
1910 (fun e -> "Negative " ^
1911 (string_of_equality ~env e)) neg) @
1913 (fun e -> "Positive " ^
1914 (string_of_equality ~env e)) pos)))))
1917 let k = size_of_passive passive in
1918 if k < (kept - 1) then
1919 processed_clauses := !processed_clauses + (kept - 1 - k);
1924 (Printf.sprintf "active:\n%s\n"
1927 (fun (s, e) -> (string_of_sign s) ^ " " ^
1928 (string_of_equality ~env e))
1936 (Printf.sprintf "new':\n%s\n"
1939 (fun e -> "Negative " ^
1940 (string_of_equality ~env e)) neg) @
1942 (fun e -> "Positive " ^
1943 (string_of_equality ~env e)) pos)))))
1945 match contains_empty env new' with
1947 let passive = add_to_passive passive new' in
1948 given_clause_fullred dbd env goals theorems passive active
1952 | Some goal -> let _, proof, _, _, _ = goal in Some proof
1955 ParamodulationSuccess (proof, env)
1960 let rec saturate_equations env goal accept_fun passive active =
1961 elapsed_time := Unix.gettimeofday () -. !start_time;
1962 if !elapsed_time > !time_limit then
1965 let (sign, current), passive = select env [1, [goal]] passive active in
1966 let res = forward_simplify env (sign, current) ~passive active in
1969 saturate_equations env goal accept_fun passive active
1970 | Some (sign, current) ->
1971 assert (sign = Positive);
1973 (lazy "\n================================================");
1974 debug_print (lazy (Printf.sprintf "selected: %s %s"
1975 (string_of_sign sign)
1976 (string_of_equality ~env current)));
1977 let new' = infer env sign current active in
1979 if is_identity env current then active
1981 let al, tbl = active in
1982 al @ [(sign, current)], Indexing.index tbl current
1984 let rec simplify new' active passive =
1985 let new' = forward_simplify_new env new' ~passive active in
1986 let active, passive, newa, retained =
1987 backward_simplify env new' ~passive active in
1988 match newa, retained with
1989 | None, None -> active, passive, new'
1991 | None, Some (n, p) ->
1992 let nn, np = new' in
1993 simplify (nn @ n, np @ p) active passive
1994 | Some (n, p), Some (rn, rp) ->
1995 let nn, np = new' in
1996 simplify (nn @ n @ rn, np @ p @ rp) active passive
1998 let active, passive, new' = simplify new' active passive in
2002 (Printf.sprintf "active:\n%s\n"
2005 (fun (s, e) -> (string_of_sign s) ^ " " ^
2006 (string_of_equality ~env e))
2014 (Printf.sprintf "new':\n%s\n"
2017 (fun e -> "Negative " ^
2018 (string_of_equality ~env e)) neg) @
2020 (fun e -> "Positive " ^
2021 (string_of_equality ~env e)) pos)))))
2023 let new' = match new' with _, pos -> [], List.filter accept_fun pos in
2024 let passive = add_to_passive passive new' in
2025 saturate_equations env goal accept_fun passive active
2031 let main dbd full term metasenv ugraph =
2032 let module C = Cic in
2033 let module T = CicTypeChecker in
2034 let module PET = ProofEngineTypes in
2035 let module PP = CicPp in
2036 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2037 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2038 let proof, goals = status in
2039 let goal' = List.nth goals 0 in
2040 let _, metasenv, meta_proof, _ = proof in
2041 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2042 let eq_indexes, equalities, maxm = find_equalities context proof in
2043 let lib_eq_uris, library_equalities, maxm =
2045 find_library_equalities dbd context (proof, goal') (maxm+2)
2047 let library_equalities = List.map snd library_equalities in
2048 maxmeta := maxm+2; (* TODO ugly!! *)
2049 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2050 let new_meta_goal, metasenv, type_of_goal =
2051 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2054 (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n\n" (CicPp.ppterm ty)));
2055 Cic.Meta (maxm+1, irl),
2056 (maxm+1, context, ty)::metasenv,
2059 let env = (metasenv, context, ugraph) in
2060 let t1 = Unix.gettimeofday () in
2063 let theorems = find_library_theorems dbd env (proof, goal') lib_eq_uris in
2064 let context_hyp = find_context_hypotheses env eq_indexes in
2065 context_hyp @ theorems, []
2068 let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
2069 UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
2071 let t = CicUtil.term_of_uri refl_equal in
2072 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
2075 let t2 = Unix.gettimeofday () in
2078 (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
2083 "Theorems:\n-------------------------------------\n%s\n"
2088 "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty))
2092 let goal = Inference.BasicProof new_meta_goal, [], goal in
2093 let equalities = simplify_equalities env
2094 (equalities@library_equalities) in
2095 let active = make_active () in
2096 let passive = make_passive [] equalities in
2097 Printf.printf "\ncurrent goal: %s\n"
2098 (let _, _, g = goal in CicPp.ppterm g);
2099 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
2100 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
2101 Printf.printf "\nequalities:\n%s\n"
2104 (string_of_equality ~env) equalities));
2105 (* (equalities @ library_equalities))); *)
2106 print_endline "--------------------------------------------------";
2107 let start = Unix.gettimeofday () in
2108 print_endline "GO!";
2109 start_time := Unix.gettimeofday ();
2111 let goals = make_goals goal in
2112 (if !use_fullred then given_clause_fullred else given_clause)
2113 dbd env goals theorems passive active
2115 let finish = Unix.gettimeofday () in
2118 | ParamodulationFailure ->
2119 Printf.printf "NO proof found! :-(\n\n"
2120 | ParamodulationSuccess (Some proof, env) ->
2121 let proof = Inference.build_proof_term proof in
2122 Printf.printf "OK, found a proof!\n";
2123 (* REMEMBER: we have to instantiate meta_proof, we should use
2124 apply the "apply" tactic to proof and status
2126 let names = names_of_context context in
2127 print_endline (PP.pp proof names);
2130 (fun m (_, _, _, menv, _) -> m @ menv) metasenv equalities
2135 CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
2137 print_endline (string_of_float (finish -. start));
2139 "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n\n"
2140 (CicPp.pp type_of_goal names) (CicPp.pp ty names)
2142 (fst (CicReduction.are_convertible
2143 context type_of_goal ty ug)));
2145 Printf.printf "\nEXCEPTION!!! %s\n" (Printexc.to_string e);
2146 Printf.printf "MAXMETA USED: %d\n" !maxmeta;
2147 print_endline (string_of_float (finish -. start));*)
2151 | ParamodulationSuccess (None, env) ->
2152 Printf.printf "Success, but no proof?!?\n\n"
2157 ((Printf.sprintf ("infer_time: %.9f\nforward_simpl_time: %.9f\n" ^^
2158 "forward_simpl_new_time: %.9f\n" ^^
2159 "backward_simpl_time: %.9f\n")
2160 !infer_time !forward_simpl_time !forward_simpl_new_time
2161 !backward_simpl_time) ^
2162 (Printf.sprintf "beta_expand_time: %.9f\n"
2163 !Indexing.beta_expand_time) ^
2164 (Printf.sprintf "passive_maintainance_time: %.9f\n"
2165 !passive_maintainance_time) ^
2166 (Printf.sprintf " successful unification/matching time: %.9f\n"
2167 !Indexing.match_unif_time_ok) ^
2168 (Printf.sprintf " failed unification/matching time: %.9f\n"
2169 !Indexing.match_unif_time_no) ^
2170 (Printf.sprintf " indexing retrieval time: %.9f\n"
2171 !Indexing.indexing_retrieval_time) ^
2172 (Printf.sprintf " demodulate_term.build_newtarget_time: %.9f\n"
2173 !Indexing.build_newtarget_time) ^
2174 (Printf.sprintf "derived %d clauses, kept %d clauses.\n"
2175 !derived_clauses !kept_clauses))
2179 print_endline ("EXCEPTION: " ^ (Printexc.to_string exc));
2185 let default_depth = !maxdepth
2186 and default_width = !maxwidth;;
2190 Indexing.local_max := 100;
2191 symbols_counter := 0;
2192 weight_age_counter := !weight_age_ratio;
2193 processed_clauses := 0;
2196 maximal_retained_equality := None;
2198 forward_simpl_time := 0.;
2199 forward_simpl_new_time := 0.;
2200 backward_simpl_time := 0.;
2201 passive_maintainance_time := 0.;
2202 derived_clauses := 0;
2204 Indexing.beta_expand_time := 0.;
2205 Inference.metas_of_proof_time := 0.;
2209 dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status =
2210 let module C = Cic in
2212 Indexing.init_index ();
2215 let proof, goal = status in
2217 let uri, metasenv, meta_proof, term_to_prove = proof in
2218 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2219 let eq_indexes, equalities, maxm = find_equalities context proof in
2220 let new_meta_goal, metasenv, type_of_goal =
2222 CicMkImplicit.identity_relocation_list_for_metavariable context in
2223 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2225 (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty)));
2226 Cic.Meta (maxm+1, irl),
2227 (maxm+1, context, ty)::metasenv,
2230 let ugraph = CicUniv.empty_ugraph in
2231 let env = (metasenv, context, ugraph) in
2232 let goal = Inference.BasicProof new_meta_goal, [], goal in
2234 let t1 = Unix.gettimeofday () in
2235 let lib_eq_uris, library_equalities, maxm =
2236 find_library_equalities dbd context (proof, goal') (maxm+2)
2238 let library_equalities = List.map snd library_equalities in
2239 let t2 = Unix.gettimeofday () in
2241 let equalities = simplify_equalities env (equalities@library_equalities) in
2244 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)));
2245 let t1 = Unix.gettimeofday () in
2248 let thms = find_library_theorems dbd env (proof, goal') lib_eq_uris in
2249 let context_hyp = find_context_hypotheses env eq_indexes in
2250 context_hyp @ thms, []
2253 let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
2254 UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
2256 let t = CicUtil.term_of_uri refl_equal in
2257 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
2260 let t2 = Unix.gettimeofday () in
2265 "Theorems:\n-------------------------------------\n%s\n"
2270 "Term: %s, type: %s"
2271 (CicPp.ppterm t) (CicPp.ppterm ty))
2275 (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
2277 let active = make_active () in
2278 let passive = make_passive [] equalities in
2279 let start = Unix.gettimeofday () in
2281 let goals = make_goals goal in
2282 given_clause_fullred dbd env goals theorems passive active
2284 let finish = Unix.gettimeofday () in
2285 (res, finish -. start)
2288 | ParamodulationSuccess (Some proof, env) ->
2289 debug_print (lazy "OK, found a proof!");
2290 let proof = Inference.build_proof_term proof in
2291 let names = names_of_context context in
2294 match new_meta_goal with
2295 | C.Meta (i, _) -> i | _ -> assert false
2297 List.filter (fun (i, _, _) -> i <> i1 && i <> goal') metasenv
2302 CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
2304 debug_print (lazy (CicPp.pp proof [](* names *)));
2308 "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n"
2309 (CicPp.pp type_of_goal names) (CicPp.pp ty names)
2311 (fst (CicReduction.are_convertible
2312 context type_of_goal ty ug)))));
2313 let equality_for_replace i t1 =
2315 | C.Meta (n, _) -> n = i
2319 ProofEngineReduction.replace
2320 ~equality:equality_for_replace
2321 ~what:[goal'] ~with_what:[proof]
2326 (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n"
2327 (match uri with Some uri -> UriManager.string_of_uri uri
2329 (print_metasenv newmetasenv)
2330 (CicPp.pp real_proof [](* names *))
2331 (CicPp.pp term_to_prove names)));
2332 ((uri, newmetasenv, real_proof, term_to_prove), [])
2333 with CicTypeChecker.TypeCheckerFailure _ ->
2334 debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
2335 debug_print (lazy (CicPp.pp proof names));
2336 raise (ProofEngineTypes.Fail
2337 (lazy "Found a proof, but it doesn't typecheck"))
2339 let tall = fs_time_info.build_all in
2340 let tdemodulate = fs_time_info.demodulate in
2341 let tsubsumption = fs_time_info.subsumption in
2345 (Printf.sprintf "\nTIME NEEDED: %.9f" time) ^
2346 (Printf.sprintf "\ntall: %.9f" tall) ^
2347 (Printf.sprintf "\ntdemod: %.9f" tdemodulate) ^
2348 (Printf.sprintf "\ntsubsumption: %.9f" tsubsumption) ^
2349 (Printf.sprintf "\ninfer_time: %.9f" !infer_time) ^
2350 (Printf.sprintf "\nbeta_expand_time: %.9f\n"
2351 !Indexing.beta_expand_time) ^
2352 (Printf.sprintf "\nmetas_of_proof: %.9f\n"
2353 !Inference.metas_of_proof_time) ^
2354 (Printf.sprintf "\nforward_simpl_times: %.9f" !forward_simpl_time) ^
2355 (Printf.sprintf "\nforward_simpl_new_times: %.9f"
2356 !forward_simpl_new_time) ^
2357 (Printf.sprintf "\nbackward_simpl_times: %.9f" !backward_simpl_time) ^
2358 (Printf.sprintf "\npassive_maintainance_time: %.9f"
2359 !passive_maintainance_time))
2363 raise (ProofEngineTypes.Fail (lazy "NO proof found"))
2366 (* dummy function called within matita to trigger linkage *)
2370 let retrieve_and_print dbd term metasenv ugraph =
2371 let module C = Cic in
2372 let module T = CicTypeChecker in
2373 let module PET = ProofEngineTypes in
2374 let module PP = CicPp in
2375 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2376 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2377 let proof, goals = status in
2378 let goal' = List.nth goals 0 in
2379 let uri, metasenv, meta_proof, term_to_prove = proof in
2380 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2381 let eq_indexes, equalities, maxm = find_equalities context proof in
2382 let new_meta_goal, metasenv, type_of_goal =
2384 CicMkImplicit.identity_relocation_list_for_metavariable context in
2385 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2387 (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty)));
2388 Cic.Meta (maxm+1, irl),
2389 (maxm+1, context, ty)::metasenv,
2392 let ugraph = CicUniv.empty_ugraph in
2393 let env = (metasenv, context, ugraph) in
2394 let t1 = Unix.gettimeofday () in
2395 let lib_eq_uris, library_equalities, maxm =
2396 find_library_equalities dbd context (proof, goal') (maxm+2) in
2397 let t2 = Unix.gettimeofday () in
2399 let equalities = (* equalities @ *) library_equalities in
2402 (Printf.sprintf "\n\nequalities:\n%s\n"
2406 (* Printf.sprintf "%s: %s" *)
2407 (UriManager.string_of_uri u)
2408 (* (string_of_equality e) *)
2411 debug_print (lazy "RETR: SIMPLYFYING EQUALITIES...");
2412 let rec simpl e others others_simpl =
2414 let active = List.map (fun (u, e) -> (Positive, e))
2415 (others @ others_simpl) in
2418 (fun t (_, e) -> Indexing.index t e)
2419 Indexing.empty active
2421 let res = forward_simplify env (Positive, e) (active, tbl) in
2425 | None -> simpl hd tl others_simpl
2426 | Some e -> simpl hd tl ((u, (snd e))::others_simpl)
2430 | None -> others_simpl
2431 | Some e -> (u, (snd e))::others_simpl
2435 match equalities with
2438 let others = tl in (* List.map (fun e -> (Positive, e)) tl in *)
2440 List.rev (simpl (*(Positive,*) hd others [])
2444 (Printf.sprintf "\nequalities AFTER:\n%s\n"
2448 Printf.sprintf "%s: %s"
2449 (UriManager.string_of_uri u)
2450 (string_of_equality e)
2456 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)))
2460 let main_demod_equalities dbd term metasenv ugraph =
2461 let module C = Cic in
2462 let module T = CicTypeChecker in
2463 let module PET = ProofEngineTypes in
2464 let module PP = CicPp in
2465 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2466 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2467 let proof, goals = status in
2468 let goal' = List.nth goals 0 in
2469 let _, metasenv, meta_proof, _ = proof in
2470 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2471 let eq_indexes, equalities, maxm = find_equalities context proof in
2472 let lib_eq_uris, library_equalities, maxm =
2473 find_library_equalities dbd context (proof, goal') (maxm+2)
2475 let library_equalities = List.map snd library_equalities in
2476 maxmeta := maxm+2; (* TODO ugly!! *)
2477 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2478 let new_meta_goal, metasenv, type_of_goal =
2479 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2482 (Printf.sprintf "\n\nTRYING TO INFER EQUALITIES MATCHING: %s\n\n"
2483 (CicPp.ppterm ty)));
2484 Cic.Meta (maxm+1, irl),
2485 (maxm+1, context, ty)::metasenv,
2488 let env = (metasenv, context, ugraph) in
2490 let goal = Inference.BasicProof new_meta_goal, [], goal in
2491 let equalities = simplify_equalities env (equalities@library_equalities) in
2492 let active = make_active () in
2493 let passive = make_passive [] equalities in
2494 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
2495 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
2496 Printf.printf "\nequalities:\n%s\n"
2499 (string_of_equality ~env) equalities));
2500 print_endline "--------------------------------------------------";
2501 print_endline "GO!";
2502 start_time := Unix.gettimeofday ();
2503 if !time_limit < 1. then time_limit := 60.;
2505 saturate_equations env goal (fun e -> true) passive active
2509 List.fold_left (fun s e -> EqualitySet.add e s)
2510 EqualitySet.empty equalities
2513 if not (EqualitySet.mem e initial) then EqualitySet.add e s else s
2518 | (n, _), (p, _), _ ->
2519 EqualitySet.elements (List.fold_left addfun EqualitySet.empty p)
2522 let l = List.map snd (fst ra) in
2523 EqualitySet.elements (List.fold_left addfun EqualitySet.empty l)
2525 Printf.printf "\n\nRESULTS:\nActive:\n%s\n\nPassive:\n%s\n"
2526 (String.concat "\n" (List.map (string_of_equality ~env) active))
2527 (* (String.concat "\n"
2528 (List.map (fun e -> CicPp.ppterm (term_of_equality e)) active)) *)
2529 (* (String.concat "\n" (List.map (string_of_equality ~env) passive)); *)
2531 (List.map (fun e -> CicPp.ppterm (term_of_equality e)) passive));
2535 debug_print (lazy ("EXCEPTION: " ^ (Printexc.to_string e)))
2539 let demodulate_tac ~dbd ~pattern ((proof,goal) as initialstatus) =
2540 let module I = Inference in
2541 let curi,metasenv,pbo,pty = proof in
2542 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
2543 let eq_indexes, equalities, maxm = I.find_equalities context proof in
2544 let lib_eq_uris, library_equalities, maxm =
2545 I.find_library_equalities dbd context (proof, goal) (maxm+2) in
2546 if library_equalities = [] then prerr_endline "VUOTA!!!";
2547 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2548 let library_equalities = List.map snd library_equalities in
2549 let goalterm = Cic.Meta (metano,irl) in
2550 let initgoal = Inference.BasicProof goalterm, [], ty in
2551 let env = (metasenv, context, CicUniv.empty_ugraph) in
2552 let equalities = simplify_equalities env (equalities@library_equalities) in
2555 (fun tbl eq -> Indexing.index tbl eq)
2556 Indexing.empty equalities
2558 let newmeta,(newproof,newmetasenv, newty) = Indexing.demodulation_goal
2559 maxm (metasenv,context,CicUniv.empty_ugraph) table initgoal
2561 if newmeta != maxm then
2563 let opengoal = Cic.Meta(maxm,irl) in
2565 Inference.build_proof_term ~noproof:opengoal newproof in
2566 let extended_metasenv = (maxm,context,newty)::metasenv in
2567 let extended_status =
2568 (curi,extended_metasenv,pbo,pty),goal in
2569 let (status,newgoals) =
2570 ProofEngineTypes.apply_tactic
2571 (PrimitiveTactics.apply_tac ~term:proofterm)
2573 (status,maxm::newgoals)
2575 else if newty = ty then
2576 raise (ProofEngineTypes.Fail (lazy "no progress"))
2577 else ProofEngineTypes.apply_tactic
2578 (ReductionTactics.simpl_tac ~pattern)
2582 let demodulate_tac ~dbd ~pattern =
2583 ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~pattern)