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 4 (* 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 maxm, copy_of_current = Inference.fix_metas !maxmeta current in
473 let curr_table = Indexing.index Indexing.empty current in
475 infer_positive curr_table ((sign,copy_of_current)::active_list)
477 if Utils.debug_metas then
480 Indexing.check_target c current "sup3") pos);
483 derived_clauses := !derived_clauses + (List.length new_neg) +
484 (List.length new_pos);
485 match !maximal_retained_equality with
487 if Utils.debug_metas then
490 Indexing.check_target c current "sup4") new_pos);
493 Indexing.check_target c current "sup5") new_neg));
496 ignore(assert false);
497 (* if we have a maximal_retained_equality, we can discard all equalities
498 "greater" than it, as they will never be reached... An equality is
499 greater than maximal_retained_equality if it is bigger
500 wrt. OrderedEquality.compare and it is less similar than
501 maximal_retained_equality to the current goal *)
503 match active_list with
504 | (Negative, e)::_ ->
505 let symbols = symbols_of_equality e in
506 let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
513 List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos
516 if OrderedEquality.compare e eq <= 0 then
519 let foldfun k v (r1, r2) =
520 if TermMap.mem k symbols then
521 let c = TermMap.find k symbols in
522 let c1 = abs (c - v) in
530 TermMap.fold foldfun (symbols_of_equality eq) (0, 0) in
531 others + (abs (common - card))
534 TermMap.fold foldfun (symbols_of_equality e) (0, 0) in
535 let c = others + (abs (common - card)) in
536 if c < initial then true else false
538 List.filter filterfun new_pos
544 let contains_empty env (negative, positive) =
545 let metasenv, context, ugraph = env in
549 (fun (w, proof, (ty, left, right, ordering), m, a) ->
550 fst (CicReduction.are_convertible context left right ugraph))
559 (** simplifies current using active and passive *)
560 let forward_simplify env (sign, current) ?passive (active_list, active_table) =
561 let _, context, _ = env in
562 let pl, passive_table =
565 | Some ((pn, _), (pp, _), pt) ->
566 let pn = List.map (fun e -> (Negative, e)) pn
567 and pp = List.map (fun e -> (Positive, e)) pp in
570 let all = if pl = [] then active_list else active_list @ pl in
572 let demodulate table current =
573 let newmeta, newcurrent =
574 Indexing.demodulation_equality !maxmeta env table sign current in
576 if is_identity env newcurrent then
577 if sign = Negative then Some (sign, newcurrent)
581 (* (Printf.sprintf "\ncurrent was: %s\nnewcurrent is: %s\n" *)
582 (* (string_of_equality current) *)
583 (* (string_of_equality newcurrent))); *)
586 (* (Printf.sprintf "active is: %s" *)
587 (* (String.concat "\n" *)
588 (* (List.map (fun (_, e) -> (string_of_equality e)) active_list)))); *)
592 Some (sign, newcurrent)
595 if Utils.debug_metas then
596 ignore (Indexing.check_target context current "demod0");
597 let res = demodulate active_table current in
598 if Utils.debug_metas then
599 ignore ((function None -> () | Some (_,x) ->
600 Indexing.check_target context x "demod1";()) res);
603 | Some (sign, newcurrent) ->
604 match passive_table with
606 | Some passive_table -> demodulate passive_table newcurrent
610 | Some (Negative, c) ->
613 (fun (s, eq) -> s = Negative && meta_convertibility_eq eq c)
616 if ok then res else None
617 | Some (Positive, c) ->
618 if Indexing.in_index active_table c then
621 match passive_table with
623 if fst (Indexing.subsumption env active_table c) then
627 | Some passive_table ->
628 if Indexing.in_index passive_table c then None
630 let r1, _ = Indexing.subsumption env active_table c in
632 let r2, _ = Indexing.subsumption env passive_table c in
633 if r2 then None else res
636 type fs_time_info_t = {
637 mutable build_all: float;
638 mutable demodulate: float;
639 mutable subsumption: float;
642 let fs_time_info = { build_all = 0.; demodulate = 0.; subsumption = 0. };;
645 (** simplifies new using active and passive *)
646 let forward_simplify_new env (new_neg, new_pos) ?passive active =
647 if Utils.debug_metas then
652 Indexing.check_target c current "forward new neg") new_neg);
654 (fun current -> Indexing.check_target c current "forward new pos")
657 let t1 = Unix.gettimeofday () in
659 let active_list, active_table = active in
660 let pl, passive_table =
663 | Some ((pn, _), (pp, _), pt) ->
664 let pn = List.map (fun e -> (Negative, e)) pn
665 and pp = List.map (fun e -> (Positive, e)) pp in
669 let t2 = Unix.gettimeofday () in
670 fs_time_info.build_all <- fs_time_info.build_all +. (t2 -. t1);
672 let demodulate sign table target =
673 let newmeta, newtarget =
674 Indexing.demodulation_equality !maxmeta env table sign target in
678 let t1 = Unix.gettimeofday () in
680 let new_neg, new_pos =
681 let new_neg = List.map (demodulate Negative active_table) new_neg
682 and new_pos = List.map (demodulate Positive active_table) new_pos in
685 match passive_table with
686 | None -> new_neg, new_pos
687 | Some passive_table ->
688 List.map (demodulate Negative passive_table) new_neg,
689 List.map (demodulate Positive passive_table) new_pos *)
692 let t2 = Unix.gettimeofday () in
693 fs_time_info.demodulate <- fs_time_info.demodulate +. (t2 -. t1);
698 if not (Inference.is_identity env e) then
699 if EqualitySet.mem e s then s
700 else EqualitySet.add e s
702 EqualitySet.empty new_pos
704 let new_pos = EqualitySet.elements new_pos_set in
707 match passive_table with
709 (fun e -> not (fst (Indexing.subsumption env active_table e)))
710 | Some passive_table ->
711 (fun e -> not ((fst (Indexing.subsumption env active_table e)) ||
712 (fst (Indexing.subsumption env passive_table e))))
714 (* let t1 = Unix.gettimeofday () in *)
715 (* let t2 = Unix.gettimeofday () in *)
716 (* fs_time_info.subsumption <- fs_time_info.subsumption +. (t2 -. t1); *)
718 match passive_table with
720 (fun e -> not (Indexing.in_index active_table e))
721 | Some passive_table ->
723 not ((Indexing.in_index active_table e) ||
724 (Indexing.in_index passive_table e)))
726 new_neg, List.filter subs (List.filter is_duplicate new_pos)
730 (** simplifies active usign new *)
731 let backward_simplify_active env new_pos new_table min_weight active =
732 let active_list, active_table = active in
733 let active_list, newa =
735 (fun (s, equality) (res, newn) ->
736 let ew, _, _, _, _ = equality in
737 if ew < min_weight then
738 (s, equality)::res, newn
740 match forward_simplify env (s, equality) (new_pos, new_table) with
750 List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
754 (fun (s, eq) (res, tbl) ->
755 if List.mem (s, eq) res then
757 else if (is_identity env eq) || (find eq res) then (
761 (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
762 active_list ([], Indexing.empty),
764 (fun (s, eq) (n, p) ->
765 if (s <> Negative) && (is_identity env eq) then (
768 if s = Negative then eq::n, p
773 | [], [] -> active, None
774 | _ -> active, Some newa
778 (** simplifies passive using new *)
779 let backward_simplify_passive env new_pos new_table min_weight passive =
780 let (nl, ns), (pl, ps), passive_table = passive in
781 let f sign equality (resl, ress, newn) =
782 let ew, _, _, _, _ = equality in
783 if ew < min_weight then
784 equality::resl, ress, newn
786 match forward_simplify env (sign, equality) (new_pos, new_table) with
787 | None -> resl, EqualitySet.remove equality ress, newn
790 equality::resl, ress, newn
792 let ress = EqualitySet.remove equality ress in
795 let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
796 and pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in
799 (fun tbl e -> Indexing.index tbl e) Indexing.empty pl
801 match newn, newp with
802 | [], [] -> ((nl, ns), (pl, ps), passive_table), None
803 | _, _ -> ((nl, ns), (pl, ps), passive_table), Some (newn, newp)
807 let backward_simplify env new' ?passive active =
808 let new_pos, new_table, min_weight =
811 let ew, _, _, _, _ = e in
812 (Positive, e)::l, Indexing.index t e, min ew w)
813 ([], Indexing.empty, 1000000) (snd new')
816 backward_simplify_active env new_pos new_table min_weight active in
819 active, (make_passive [] []), newa, None
821 active, passive, newa, None
824 backward_simplify_passive env new_pos new_table min_weight passive in
825 active, passive, newa, newp *)
829 let close env new' given =
830 let new_pos, new_table, min_weight =
833 let ew, _, _, _, _ = e in
834 (Positive, e)::l, Indexing.index t e, min ew w)
835 ([], Indexing.empty, 1000000) (snd new')
839 let neg,pos = infer env s c (new_pos,new_table) in
844 let is_commutative_law eq =
845 let w, proof, (eq_ty, left, right, order), metas, args = snd eq in
846 match left,right with
847 Cic.Appl[f1;Cic.Meta _ as a1;Cic.Meta _ as b1],
848 Cic.Appl[f2;Cic.Meta _ as a2;Cic.Meta _ as b2] ->
849 f1 = f2 && a1 = b2 && a2 = b1
853 let prova env new' active =
854 let given = List.filter is_commutative_law (fst active) in
858 (Printf.sprintf "symmetric:\n%s\n"
861 (fun (s, e) -> (string_of_sign s) ^ " " ^
862 (string_of_equality ~env e))
867 (* returns an estimation of how many equalities in passive can be activated
868 within the current time limit *)
869 let get_selection_estimate () =
870 elapsed_time := (Unix.gettimeofday ()) -. !start_time;
871 (* !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *)
873 ceil ((float_of_int !processed_clauses) *.
874 ((!time_limit (* *. 2. *)) /. !elapsed_time -. 1.)))
878 (** initializes the set of goals *)
879 let make_goals goal =
881 and passive = [0, [goal]] in
886 (** initializes the set of theorems *)
887 let make_theorems theorems =
892 let activate_goal (active, passive) =
894 | goal_conj::tl -> true, (goal_conj::active, tl)
895 | [] -> false, (active, passive)
899 let activate_theorem (active, passive) =
901 | theorem::tl -> true, (theorem::active, tl)
902 | [] -> false, (active, passive)
906 (** simplifies a goal with equalities in active and passive *)
907 let simplify_goal env goal ?passive (active_list, active_table) =
908 let pl, passive_table =
911 | Some ((pn, _), (pp, _), pt) ->
912 let pn = List.map (fun e -> (Negative, e)) pn
913 and pp = List.map (fun e -> (Positive, e)) pp in
917 let demodulate table goal =
918 let newmeta, newgoal =
919 Indexing.demodulation_goal !maxmeta env table goal in
921 goal != newgoal, newgoal
924 match passive_table with
925 | None -> demodulate active_table goal
926 | Some passive_table ->
927 let changed, goal = demodulate active_table goal in
928 let changed', goal = demodulate passive_table goal in
929 (changed || changed'), goal
935 let simplify_goals env goals ?passive active =
936 let a_goals, p_goals = goals in
941 List.map (fun g -> snd (simplify_goal env g ?passive active)) gl in
947 (fun (a, p) (d, gl) ->
948 let changed = ref false in
952 let c, g = simplify_goal env g ?passive active in
953 changed := !changed || c; g) gl in
954 if !changed then (a, (d, gl)::p) else ((d, gl)::a, p))
955 ([], p_goals) a_goals
961 let simplify_theorems env theorems ?passive (active_list, active_table) =
962 let pl, passive_table =
965 | Some ((pn, _), (pp, _), pt) ->
966 let pn = List.map (fun e -> (Negative, e)) pn
967 and pp = List.map (fun e -> (Positive, e)) pp in
970 let a_theorems, p_theorems = theorems in
971 let demodulate table theorem =
972 let newmeta, newthm =
973 Indexing.demodulation_theorem !maxmeta env table theorem in
975 theorem != newthm, newthm
977 let foldfun table (a, p) theorem =
978 let changed, theorem = demodulate table theorem in
979 if changed then (a, theorem::p) else (theorem::a, p)
981 let mapfun table theorem = snd (demodulate table theorem) in
982 match passive_table with
984 let p_theorems = List.map (mapfun active_table) p_theorems in
985 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems
986 | Some passive_table ->
987 let p_theorems = List.map (mapfun active_table) p_theorems in
988 let p_theorems, a_theorems =
989 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems in
990 let p_theorems = List.map (mapfun passive_table) p_theorems in
991 List.fold_left (foldfun passive_table) ([], p_theorems) a_theorems
995 let rec simpl env e others others_simpl =
996 let active = others @ others_simpl in
999 (fun t (_, e) -> Indexing.index t e)
1000 Indexing.empty active
1002 let res = forward_simplify env e (active, tbl) in
1006 | None -> simpl env hd tl others_simpl
1007 | Some e -> simpl env hd tl (e::others_simpl)
1011 | None -> others_simpl
1012 | Some e -> e::others_simpl
1016 let simplify_equalities env equalities =
1019 (Printf.sprintf "equalities:\n%s\n"
1021 (List.map string_of_equality equalities))));
1022 debug_print (lazy "SIMPLYFYING EQUALITIES...");
1023 match equalities with
1026 let others = List.map (fun e -> (Positive, e)) tl in
1028 List.rev (List.map snd (simpl env (Positive, hd) others []))
1032 (Printf.sprintf "equalities AFTER:\n%s\n"
1034 (List.map string_of_equality res))));
1038 (* applies equality to goal to see if the goal can be closed *)
1039 let apply_equality_to_goal env equality goal =
1040 let module C = Cic in
1041 let module HL = HelmLibraryObjects in
1042 let module I = Inference in
1043 let metasenv, context, ugraph = env in
1044 let _, proof, (ty, left, right, _), metas, args = equality in
1046 C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right] in
1047 let gproof, gmetas, gterm = goal in
1050 (* (Printf.sprintf "APPLY EQUALITY TO GOAL: %s, %s" *)
1051 (* (string_of_equality equality) (CicPp.ppterm gterm))); *)
1053 let subst, metasenv', _ =
1054 let menv = metasenv @ metas @ gmetas in
1055 Inference.unification metas gmetas context eqterm gterm ugraph
1059 | I.BasicProof t -> I.BasicProof (CicMetaSubst.apply_subst subst t)
1060 | I.ProofBlock (s, uri, nt, t, pe, p) ->
1061 I.ProofBlock (subst @ s, uri, nt, t, pe, p)
1065 let rec repl = function
1066 | I.ProofGoalBlock (_, gp) -> I.ProofGoalBlock (newproof, gp)
1067 | I.NoProof -> newproof
1068 | I.BasicProof p -> newproof
1069 | I.SubProof (t, i, p) -> I.SubProof (t, i, repl p)
1074 true, subst, newgproof
1075 with CicUnification.UnificationFailure _ ->
1076 false, [], I.NoProof
1081 let new_meta metasenv =
1082 let m = CicMkImplicit.new_meta metasenv [] in
1084 while !maxmeta <= m do incr maxmeta done;
1089 (* applies a theorem or an equality to goal, returning a list of subgoals or
1090 an indication of failure *)
1091 let apply_to_goal env theorems ?passive active goal =
1092 let metasenv, context, ugraph = env in
1093 let proof, metas, term = goal in
1096 (* (Printf.sprintf "apply_to_goal with goal: %s" *)
1097 (* (\* (string_of_proof proof) *\)(CicPp.ppterm term))); *)
1100 CicMkImplicit.identity_relocation_list_for_metavariable context in
1101 let proof', newmeta =
1102 let rec get_meta = function
1103 | SubProof (t, i, p) ->
1104 let t', i' = get_meta p in
1105 if i' = -1 then t, i else t', i'
1106 | ProofGoalBlock (_, p) -> get_meta p
1107 | _ -> Cic.Implicit None, -1
1109 let p, m = get_meta proof in
1111 let n = new_meta (metasenv @ metas) in
1112 Cic.Meta (n, irl), n
1116 let metasenv = (newmeta, context, term)::metasenv @ metas in
1117 let bit = new_meta metasenv, context, term in
1118 let metasenv' = bit::metasenv in
1119 ((None, metasenv', Cic.Meta (newmeta, irl), term), newmeta)
1121 let rec aux = function
1123 | (theorem, thmty, _)::tl ->
1125 let subst, (newproof, newgoals) =
1126 PrimitiveTactics.apply_tac_verbose_with_subst ~term:theorem status
1128 if newgoals = [] then
1129 let _, _, p, _ = newproof in
1131 let rec repl = function
1132 | Inference.ProofGoalBlock (_, gp) ->
1133 Inference.ProofGoalBlock (Inference.BasicProof p, gp)
1134 | Inference.NoProof -> Inference.BasicProof p
1135 | Inference.BasicProof _ -> Inference.BasicProof p
1136 | Inference.SubProof (t, i, p2) ->
1137 Inference.SubProof (t, i, repl p2)
1142 let _, m = status in
1143 let subst = List.filter (fun (i, _) -> i = m) subst in
1144 `Ok (subst, [newp, metas, term])
1146 let _, menv, p, _ = newproof in
1148 CicMkImplicit.identity_relocation_list_for_metavariable context
1153 let _, _, ty = CicUtil.lookup_meta i menv in
1155 let rec gp = function
1156 | SubProof (t, i, p) ->
1157 SubProof (t, i, gp p)
1158 | ProofGoalBlock (sp1, sp2) ->
1159 ProofGoalBlock (sp1, gp sp2)
1162 SubProof (p, i, BasicProof (Cic.Meta (i, irl)))
1163 | ProofSymBlock (s, sp) ->
1164 ProofSymBlock (s, gp sp)
1165 | ProofBlock (s, u, nt, t, pe, sp) ->
1166 ProofBlock (s, u, nt, t, pe, gp sp)
1174 let w, m = weight_of_term t in
1175 w + 2 * (List.length m)
1178 (fun (_, _, t1) (_, _, t2) ->
1179 Pervasives.compare (weight t1) (weight t2))
1182 let best = aux tl in
1184 | `Ok (_, _) -> best
1185 | `No -> `GoOn ([subst, goals])
1186 | `GoOn sl -> `GoOn ((subst, goals)::sl)
1187 with ProofEngineTypes.Fail msg ->
1191 if Inference.term_is_equality term then
1192 let rec appleq_a = function
1193 | [] -> false, [], []
1194 | (Positive, equality)::tl ->
1195 let ok, s, newproof = apply_equality_to_goal env equality goal in
1196 if ok then true, s, [newproof, metas, term] else appleq_a tl
1197 | _::tl -> appleq_a tl
1199 let rec appleq_p = function
1200 | [] -> false, [], []
1202 let ok, s, newproof = apply_equality_to_goal env equality goal in
1203 if ok then true, s, [newproof, metas, term] else appleq_p tl
1205 let al, _ = active in
1207 | None -> appleq_a al
1208 | Some (_, (pl, _), _) ->
1209 let r, s, l = appleq_a al in if r then r, s, l else appleq_p pl
1213 if r = true then `Ok (s, l) else aux theorems
1217 (* sorts a conjunction of goals in order to detect earlier if it is
1218 unsatisfiable. Non-predicate goals are placed at the end of the list *)
1219 let sort_goal_conj (metasenv, context, ugraph) (depth, gl) =
1222 (fun (_, e1, g1) (_, e2, g2) ->
1224 CicTypeChecker.type_of_aux' (e1 @ metasenv) context g1 ugraph
1226 CicTypeChecker.type_of_aux' (e2 @ metasenv) context g2 ugraph
1230 CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty1 ugraph
1235 CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty2 ugraph
1239 if prop1 = 0 && prop2 = 0 then
1240 let e1 = if Inference.term_is_equality g1 then 0 else 1
1241 and e2 = if Inference.term_is_equality g2 then 0 else 1 in
1251 let is_meta_closed goals =
1252 List.for_all (fun (_, _, g) -> CicUtil.is_meta_closed g) goals
1256 (* applies a series of theorems/equalities to a conjunction of goals *)
1257 let rec apply_to_goal_conj env theorems ?passive active (depth, goals) =
1258 let aux (goal, r) tl =
1259 let propagate_subst subst (proof, metas, term) =
1260 let rec repl = function
1261 | NoProof -> NoProof
1263 BasicProof (CicMetaSubst.apply_subst subst t)
1264 | ProofGoalBlock (p, pb) ->
1265 let pb' = repl pb in
1266 ProofGoalBlock (p, pb')
1267 | SubProof (t, i, p) ->
1268 let t' = CicMetaSubst.apply_subst subst t in
1271 | ProofSymBlock (ens, p) -> ProofSymBlock (ens, repl p)
1272 | ProofBlock (s, u, nty, t, pe, p) ->
1273 ProofBlock (subst @ s, u, nty, t, pe, p)
1274 in (repl proof, metas, term)
1276 (* let r = apply_to_goal env theorems ?passive active goal in *) (
1278 | `No -> `No (depth, goals)
1283 let tl = List.map (propagate_subst s) tl in
1284 sort_goal_conj env (depth+1, gl @ tl)) sl
1287 | `Ok (subst, gl) ->
1291 let p, _, _ = List.hd gl in
1293 let rec repl = function
1294 | SubProof (_, _, p) -> repl p
1295 | ProofGoalBlock (p1, p2) ->
1296 ProofGoalBlock (repl p1, repl p2)
1299 build_proof_term (repl p)
1302 let rec get_meta = function
1303 | SubProof (_, i, p) ->
1304 let i' = get_meta p in
1305 if i' = -1 then i else i'
1306 (* max i (get_meta p) *)
1307 | ProofGoalBlock (_, p) -> get_meta p
1313 let _, (context, _, _) = List.hd subst in
1314 [i, (context, subproof, Cic.Implicit None)]
1316 let tl = List.map (propagate_subst subst) tl in
1317 let conj = sort_goal_conj env (depth(* +1 *), tl) in
1321 if depth > !maxdepth || (List.length goals) > !maxwidth then
1324 let rec search_best res = function
1327 let r = apply_to_goal env theorems ?passive active goal in
1329 | `Ok _ -> (goal, r)
1330 | `No -> search_best res tl
1334 | _, `Ok _ -> assert false
1337 if (List.length l) < (List.length l2) then goal, r else res
1339 search_best newres tl
1341 let hd = List.hd goals in
1342 let res = hd, (apply_to_goal env theorems ?passive active hd) in
1346 | _, _ -> search_best res (List.tl goals)
1348 let res = aux best (List.filter (fun g -> g != (fst best)) goals) in
1350 | `GoOn ([conj]) when is_meta_closed (snd conj) &&
1351 (List.length (snd conj)) < (List.length goals)->
1352 apply_to_goal_conj env theorems ?passive active conj
1358 module OrderedGoals = struct
1359 type t = int * (Inference.proof * Cic.metasenv * Cic.term) list
1366 else let r = (List.length l1) - (List.length l2) in
1372 (fun (_, _, t1) (_, _, t2) ->
1373 let r = Pervasives.compare t1 t2 in
1382 module GoalsSet = Set.Make(OrderedGoals);;
1385 exception SearchSpaceOver;;
1390 let apply_to_goals env is_passive_empty theorems active goals =
1391 debug_print (lazy "\n\n\tapply_to_goals\n\n");
1392 let add_to set goals =
1393 List.fold_left (fun s g -> GoalsSet.add g s) set goals
1395 let rec aux set = function
1397 debug_print (lazy "HERE!!!");
1398 if is_passive_empty then raise SearchSpaceOver else false, set
1400 let res = apply_to_goal_conj env theorems active goals in
1406 | (d, (p, _, t)::_) -> d, p, t
1411 (Printf.sprintf "\nOK!!!!\ndepth: %d\nProof: %s\ngoal: %s\n"
1412 d (string_of_proof p) (CicPp.ppterm t)))
1414 true, GoalsSet.singleton newgoals
1416 let set' = add_to set (goals::tl) in
1417 let set' = add_to set' newgoals in
1422 let n = List.length goals in
1423 let res, goals = aux (add_to GoalsSet.empty goals) goals in
1424 let goals = GoalsSet.elements goals in
1425 debug_print (lazy "\n\tapply_to_goals end\n");
1426 let m = List.length goals in
1427 if m = n && is_passive_empty then
1428 raise SearchSpaceOver
1435 (* sorts the list of passive goals to minimize the search for a proof (doesn't
1436 work that well yet...) *)
1437 let sort_passive_goals goals =
1439 (fun (d1, l1) (d2, l2) ->
1441 and r2 = (List.length l1) - (List.length l2) in
1442 let foldfun ht (_, _, t) =
1443 let _ = List.map (fun i -> Hashtbl.replace ht i 1) (metas_of_term t)
1446 let m1 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l1)
1447 and m2 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l2)
1448 in let r3 = m1 - m2 in
1450 else if r2 <> 0 then r2
1452 (* let _, _, g1 = List.hd l1 *)
1453 (* and _, _, g2 = List.hd l2 in *)
1454 (* let e1 = if Inference.term_is_equality g1 then 0 else 1 *)
1455 (* and e2 = if Inference.term_is_equality g2 then 0 else 1 *)
1456 (* in let r4 = e1 - e2 in *)
1457 (* if r4 <> 0 then r3 else r1) *)
1462 let print_goals goals =
1469 (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl
1471 Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
1475 (* tries to prove the first conjunction in goals with applications of
1476 theorems/equalities, returning new sub-goals or an indication of success *)
1477 let apply_goal_to_theorems dbd env theorems ?passive active goals =
1478 let theorems, _ = theorems in
1479 let a_goals, p_goals = goals in
1480 let goal = List.hd a_goals in
1481 let not_in_active gl =
1485 if (List.length gl) = (List.length gl') then
1486 List.for_all2 (fun (_, _, g1) (_, _, g2) -> g1 = g2) gl gl'
1492 let res = apply_to_goal_conj env theorems ?passive active goal in
1495 true, ([newgoals], [])
1497 false, (a_goals, p_goals)
1502 (d <= !maxdepth) && (List.length gl) <= !maxwidth &&
1505 let p_goals = newgoals @ p_goals in
1506 let p_goals = sort_passive_goals p_goals in
1507 false, (a_goals, p_goals)
1513 let apply_theorem_to_goals env theorems active goals =
1514 let a_goals, p_goals = goals in
1515 let theorem = List.hd (fst theorems) in
1516 let theorems = [theorem] in
1517 let rec aux p = function
1518 | [] -> false, ([], p)
1520 let res = apply_to_goal_conj env theorems active goal in
1522 | `Ok newgoals -> true, ([newgoals], [])
1524 | `GoOn newgoals -> aux (newgoals @ p) tl
1526 let ok, (a, p) = aux p_goals a_goals in
1532 (fun (d1, l1) (d2, l2) ->
1535 else let r = (List.length l1) - (List.length l2) in
1541 (fun (_, _, t1) (_, _, t2) ->
1542 let r = Pervasives.compare t1 t2 in
1543 if r <> 0 then (res := r; true) else false) l1 l2
1547 ok, (a_goals, p_goals)
1551 (* given-clause algorithm with lazy reduction strategy *)
1552 let rec given_clause dbd env goals theorems passive active =
1553 let _,context,_ = env in
1554 let goals = simplify_goals env goals active in
1555 let ok, goals = activate_goal goals in
1556 (* let theorems = simplify_theorems env theorems active in *)
1558 let ok, goals = apply_goal_to_theorems dbd env theorems active goals in
1561 match (fst goals) with
1562 | (_, [proof, _, _])::_ -> Some proof
1565 ParamodulationSuccess (proof, env)
1567 given_clause_aux dbd env goals theorems passive active
1569 (* let ok', theorems = activate_theorem theorems in *)
1570 let ok', theorems = false, theorems in
1572 let ok, goals = apply_theorem_to_goals env theorems active goals in
1575 match (fst goals) with
1576 | (_, [proof, _, _])::_ -> Some proof
1579 ParamodulationSuccess (proof, env)
1581 given_clause_aux dbd env goals theorems passive active
1583 if (passive_is_empty passive) then ParamodulationFailure
1584 else given_clause_aux dbd env goals theorems passive active
1586 and given_clause_aux dbd env goals theorems passive active =
1587 let _,context,_ = env in
1588 let time1 = Unix.gettimeofday () in
1590 let selection_estimate = get_selection_estimate () in
1591 let kept = size_of_passive passive in
1593 if !time_limit = 0. || !processed_clauses = 0 then
1595 else if !elapsed_time > !time_limit then (
1596 debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
1597 !time_limit !elapsed_time));
1599 ) else if kept > selection_estimate then (
1601 (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
1602 "(kept: %d, selection_estimate: %d)\n")
1603 kept selection_estimate));
1604 prune_passive selection_estimate active passive
1609 let time2 = Unix.gettimeofday () in
1610 passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
1612 kept_clauses := (size_of_passive passive) + (size_of_active active);
1613 match passive_is_empty passive with
1614 | true -> (* ParamodulationFailure *)
1615 given_clause dbd env goals theorems passive active
1617 let (sign, current), passive = select env (fst goals) passive active in
1618 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1619 prerr_endline ("Selected = " ^
1620 (CicPp.pp (Inference.term_of_equality current) names));
1621 let time1 = Unix.gettimeofday () in
1622 let res = forward_simplify env (sign, current) ~passive active in
1623 let time2 = Unix.gettimeofday () in
1624 forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
1627 given_clause dbd env goals theorems passive active
1628 | Some (sign, current) ->
1629 if (sign = Negative) && (is_identity env current) then (
1631 (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
1632 (string_of_equality ~env current)));
1633 let _, proof, _, _, _ = current in
1634 ParamodulationSuccess (Some proof, env)
1637 (lazy "\n================================================");
1638 debug_print (lazy (Printf.sprintf "selected: %s %s"
1639 (string_of_sign sign)
1640 (string_of_equality ~env current)));
1642 let t1 = Unix.gettimeofday () in
1643 let new' = infer env sign current active in
1644 let t2 = Unix.gettimeofday () in
1645 infer_time := !infer_time +. (t2 -. t1);
1647 let res, goal' = contains_empty env new' in
1651 | Some goal -> let _, proof, _, _, _ = goal in Some proof
1654 ParamodulationSuccess (proof, env)
1656 let t1 = Unix.gettimeofday () in
1657 let new' = forward_simplify_new env new' active in
1658 let t2 = Unix.gettimeofday () in
1660 forward_simpl_new_time :=
1661 !forward_simpl_new_time +. (t2 -. t1)
1665 | Negative -> active
1667 let t1 = Unix.gettimeofday () in
1668 let active, _, newa, _ =
1669 backward_simplify env ([], [current]) active
1671 let t2 = Unix.gettimeofday () in
1672 backward_simpl_time :=
1673 !backward_simpl_time +. (t2 -. t1);
1677 let al, tbl = active in
1678 let nn = List.map (fun e -> Negative, e) n in
1683 Indexing.index tbl e)
1688 match contains_empty env new' with
1691 let al, tbl = active in
1693 | Negative -> (sign, current)::al, tbl
1695 al @ [(sign, current)], Indexing.index tbl current
1697 let passive = add_to_passive passive new' in
1698 given_clause dbd env goals theorems passive active
1703 let _, proof, _, _, _ = goal in Some proof
1706 ParamodulationSuccess (proof, env)
1711 (** given-clause algorithm with full reduction strategy *)
1712 let rec given_clause_fullred dbd env goals theorems passive active =
1713 let goals = simplify_goals env goals ~passive active in
1714 let _,context,_ = env in
1715 let ok, goals = activate_goal goals in
1716 (* let theorems = simplify_theorems env theorems ~passive active in *)
1718 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1719 let _, _, t = List.hd (snd (List.hd (fst goals))) in
1720 let _ = prerr_endline ("goal activated = " ^ (CicPp.pp t names)) in
1724 (* (Printf.sprintf "\ngoals = \nactive\n%s\npassive\n%s\n" *)
1725 (* (print_goals (fst goals)) (print_goals (snd goals)))); *)
1726 (* let current = List.hd (fst goals) in *)
1727 (* let p, _, t = List.hd (snd current) in *)
1730 (* (Printf.sprintf "goal activated:\n%s\n%s\n" *)
1731 (* (CicPp.ppterm t) (string_of_proof p))); *)
1734 apply_goal_to_theorems dbd env theorems ~passive active goals
1738 match (fst goals) with
1739 | (_, [proof, _, _])::_ -> Some proof
1742 ( prerr_endline "esco qui";
1743 let s = Printf.sprintf "actives:\n%s\n"
1746 (fun (s, e) -> (string_of_sign s) ^ " " ^
1747 (string_of_equality ~env e))
1749 let sp = Printf.sprintf "passives:\n%s\n"
1752 (string_of_equality ~env)
1753 (let x,y,_ = passive in (fst x)@(fst y)))) in
1756 ParamodulationSuccess (proof, env))
1758 given_clause_fullred_aux dbd env goals theorems passive active
1760 (* let ok', theorems = activate_theorem theorems in *)
1762 (* let ok, goals = apply_theorem_to_goals env theorems active goals in *)
1765 (* match (fst goals) with *)
1766 (* | (_, [proof, _, _])::_ -> Some proof *)
1767 (* | _ -> assert false *)
1769 (* ParamodulationSuccess (proof, env) *)
1771 (* given_clause_fullred_aux env goals theorems passive active *)
1773 if (passive_is_empty passive) then ParamodulationFailure
1774 else given_clause_fullred_aux dbd env goals theorems passive active
1776 and given_clause_fullred_aux dbd env goals theorems passive active =
1777 prerr_endline ("MAXMETA: " ^ string_of_int !maxmeta ^
1778 " LOCALMAX: " ^ string_of_int !Indexing.local_max ^
1779 " #ACTIVES: " ^ string_of_int (size_of_active active) ^
1780 " #PASSIVES: " ^ string_of_int (size_of_passive passive));
1781 if (size_of_active active) mod 50 = 0 then
1782 (let s = Printf.sprintf "actives:\n%s\n"
1785 (fun (s, e) -> (string_of_sign s) ^ " " ^
1786 (string_of_equality ~env e))
1788 let sp = Printf.sprintf "passives:\n%s\n"
1791 (string_of_equality ~env)
1792 (let x,y,_ = passive in (fst x)@(fst y)))) in
1795 let time1 = Unix.gettimeofday () in
1796 let (_,context,_) = env in
1797 let selection_estimate = get_selection_estimate () in
1798 let kept = size_of_passive passive in
1800 if !time_limit = 0. || !processed_clauses = 0 then
1802 else if !elapsed_time > !time_limit then (
1803 debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
1804 !time_limit !elapsed_time));
1806 ) else if kept > selection_estimate then (
1808 (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^
1809 "(kept: %d, selection_estimate: %d)\n")
1810 kept selection_estimate));
1811 prune_passive selection_estimate active passive
1816 let time2 = Unix.gettimeofday () in
1817 passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1);
1819 kept_clauses := (size_of_passive passive) + (size_of_active active);
1820 match passive_is_empty passive with
1821 | true -> (* ParamodulationFailure *)
1822 given_clause_fullred dbd env goals theorems passive active
1824 let (sign, current), passive = select env (fst goals) passive active in
1825 let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in
1826 prerr_endline ("Selected = " ^ (string_of_sign sign) ^ " " ^
1827 string_of_equality ~env current);
1828 (* (CicPp.pp (Inference.term_of_equality current) names));*)
1829 let time1 = Unix.gettimeofday () in
1830 let res = forward_simplify env (sign, current) ~passive active in
1831 let time2 = Unix.gettimeofday () in
1832 forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
1835 (* weight_age_counter := !weight_age_counter + 1; *)
1836 given_clause_fullred dbd env goals theorems passive active
1837 | Some (sign, current) ->
1838 if (sign = Negative) && (is_identity env current) then (
1840 (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
1841 (string_of_equality ~env current)));
1842 let _, proof, _, _, _ = current in
1843 ParamodulationSuccess (Some proof, env)
1846 (lazy "\n================================================");
1847 debug_print (lazy (Printf.sprintf "selected: %s %s"
1848 (string_of_sign sign)
1849 (string_of_equality ~env current)));
1851 let t1 = Unix.gettimeofday () in
1852 let new' = infer env sign current active in
1858 (Printf.sprintf "new' (senza semplificare):\n%s\n"
1861 (fun e -> "Negative " ^
1862 (string_of_equality ~env e)) neg) @
1864 (fun e -> "Positive " ^
1865 (string_of_equality ~env e)) pos)))))
1867 let t2 = Unix.gettimeofday () in
1868 infer_time := !infer_time +. (t2 -. t1);
1870 if is_identity env current then active
1872 let al, tbl = active in
1874 | Negative -> (sign, current)::al, tbl
1876 al @ [(sign, current)], Indexing.index tbl current
1878 let rec simplify new' active passive =
1879 let t1 = Unix.gettimeofday () in
1880 let new' = forward_simplify_new env new' ~passive active in
1881 let t2 = Unix.gettimeofday () in
1882 forward_simpl_new_time :=
1883 !forward_simpl_new_time +. (t2 -. t1);
1884 let t1 = Unix.gettimeofday () in
1885 let active, passive, newa, retained =
1886 backward_simplify env new' ~passive active in
1887 let t2 = Unix.gettimeofday () in
1888 backward_simpl_time := !backward_simpl_time +. (t2 -. t1);
1889 match newa, retained with
1890 | None, None -> active, passive, new'
1892 | None, Some (n, p) ->
1893 let nn, np = new' in
1894 if Utils.debug_metas then
1896 List.map (fun x -> Indexing.check_target context x "simplify1")n;
1897 List.map (fun x -> Indexing.check_target context x "simplify2")p);
1898 simplify (nn @ n, np @ p) active passive
1899 | Some (n, p), Some (rn, rp) ->
1900 let nn, np = new' in
1901 simplify (nn @ n @ rn, np @ p @ rp) active passive
1903 let active, passive, new' = simplify new' active passive in
1905 let new1 = prova env new' active in
1906 let new' = (fst new') @ (fst new1), (snd new') @ (snd new1) in
1912 (Printf.sprintf "new1:\n%s\n"
1915 (fun e -> "Negative " ^
1916 (string_of_equality ~env e)) neg) @
1918 (fun e -> "Positive " ^
1919 (string_of_equality ~env e)) pos)))))
1922 let k = size_of_passive passive in
1923 if k < (kept - 1) then
1924 processed_clauses := !processed_clauses + (kept - 1 - k);
1929 (Printf.sprintf "active:\n%s\n"
1932 (fun (s, e) -> (string_of_sign s) ^ " " ^
1933 (string_of_equality ~env e))
1941 (Printf.sprintf "new':\n%s\n"
1944 (fun e -> "Negative " ^
1945 (string_of_equality ~env e)) neg) @
1947 (fun e -> "Positive " ^
1948 (string_of_equality ~env e)) pos)))))
1950 match contains_empty env new' with
1952 let passive = add_to_passive passive new' in
1953 given_clause_fullred dbd env goals theorems passive active
1957 | Some goal -> let _, proof, _, _, _ = goal in Some proof
1960 ParamodulationSuccess (proof, env)
1965 let rec saturate_equations env goal accept_fun passive active =
1966 elapsed_time := Unix.gettimeofday () -. !start_time;
1967 if !elapsed_time > !time_limit then
1970 let (sign, current), passive = select env [1, [goal]] passive active in
1971 let res = forward_simplify env (sign, current) ~passive active in
1974 saturate_equations env goal accept_fun passive active
1975 | Some (sign, current) ->
1976 assert (sign = Positive);
1978 (lazy "\n================================================");
1979 debug_print (lazy (Printf.sprintf "selected: %s %s"
1980 (string_of_sign sign)
1981 (string_of_equality ~env current)));
1982 let new' = infer env sign current active in
1984 if is_identity env current then active
1986 let al, tbl = active in
1987 al @ [(sign, current)], Indexing.index tbl current
1989 let rec simplify new' active passive =
1990 let new' = forward_simplify_new env new' ~passive active in
1991 let active, passive, newa, retained =
1992 backward_simplify env new' ~passive active in
1993 match newa, retained with
1994 | None, None -> active, passive, new'
1996 | None, Some (n, p) ->
1997 let nn, np = new' in
1998 simplify (nn @ n, np @ p) active passive
1999 | Some (n, p), Some (rn, rp) ->
2000 let nn, np = new' in
2001 simplify (nn @ n @ rn, np @ p @ rp) active passive
2003 let active, passive, new' = simplify new' active passive in
2007 (Printf.sprintf "active:\n%s\n"
2010 (fun (s, e) -> (string_of_sign s) ^ " " ^
2011 (string_of_equality ~env e))
2019 (Printf.sprintf "new':\n%s\n"
2022 (fun e -> "Negative " ^
2023 (string_of_equality ~env e)) neg) @
2025 (fun e -> "Positive " ^
2026 (string_of_equality ~env e)) pos)))))
2028 let new' = match new' with _, pos -> [], List.filter accept_fun pos in
2029 let passive = add_to_passive passive new' in
2030 saturate_equations env goal accept_fun passive active
2036 let main dbd full term metasenv ugraph =
2037 let module C = Cic in
2038 let module T = CicTypeChecker in
2039 let module PET = ProofEngineTypes in
2040 let module PP = CicPp in
2041 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2042 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2043 let proof, goals = status in
2044 let goal' = List.nth goals 0 in
2045 let _, metasenv, meta_proof, _ = proof in
2046 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2047 let eq_indexes, equalities, maxm = find_equalities context proof in
2048 let lib_eq_uris, library_equalities, maxm =
2050 find_library_equalities dbd context (proof, goal') (maxm+2)
2052 let library_equalities = List.map snd library_equalities in
2053 maxmeta := maxm+2; (* TODO ugly!! *)
2054 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2055 let new_meta_goal, metasenv, type_of_goal =
2056 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2059 (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n\n" (CicPp.ppterm ty)));
2060 Cic.Meta (maxm+1, irl),
2061 (maxm+1, context, ty)::metasenv,
2064 let env = (metasenv, context, ugraph) in
2065 let t1 = Unix.gettimeofday () in
2068 let theorems = find_library_theorems dbd env (proof, goal') lib_eq_uris in
2069 let context_hyp = find_context_hypotheses env eq_indexes in
2070 context_hyp @ theorems, []
2073 let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
2074 UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
2076 let t = CicUtil.term_of_uri refl_equal in
2077 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
2080 let t2 = Unix.gettimeofday () in
2083 (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
2088 "Theorems:\n-------------------------------------\n%s\n"
2093 "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty))
2097 let goal = Inference.BasicProof new_meta_goal, [], goal in
2098 let equalities = simplify_equalities env
2099 (equalities@library_equalities) in
2100 let active = make_active () in
2101 let passive = make_passive [] equalities in
2102 Printf.printf "\ncurrent goal: %s\n"
2103 (let _, _, g = goal in CicPp.ppterm g);
2104 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
2105 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
2106 Printf.printf "\nequalities:\n%s\n"
2109 (string_of_equality ~env) equalities));
2110 (* (equalities @ library_equalities))); *)
2111 print_endline "--------------------------------------------------";
2112 let start = Unix.gettimeofday () in
2113 print_endline "GO!";
2114 start_time := Unix.gettimeofday ();
2116 let goals = make_goals goal in
2117 (if !use_fullred then given_clause_fullred else given_clause)
2118 dbd env goals theorems passive active
2120 let finish = Unix.gettimeofday () in
2123 | ParamodulationFailure ->
2124 Printf.printf "NO proof found! :-(\n\n"
2125 | ParamodulationSuccess (Some proof, env) ->
2126 let proof = Inference.build_proof_term proof in
2127 Printf.printf "OK, found a proof!\n";
2128 (* REMEMBER: we have to instantiate meta_proof, we should use
2129 apply the "apply" tactic to proof and status
2131 let names = names_of_context context in
2132 print_endline (PP.pp proof names);
2135 (fun m (_, _, _, menv, _) -> m @ menv) metasenv equalities
2140 CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
2142 print_endline (string_of_float (finish -. start));
2144 "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n\n"
2145 (CicPp.pp type_of_goal names) (CicPp.pp ty names)
2147 (fst (CicReduction.are_convertible
2148 context type_of_goal ty ug)));
2150 Printf.printf "\nEXCEPTION!!! %s\n" (Printexc.to_string e);
2151 Printf.printf "MAXMETA USED: %d\n" !maxmeta;
2152 print_endline (string_of_float (finish -. start));*)
2156 | ParamodulationSuccess (None, env) ->
2157 Printf.printf "Success, but no proof?!?\n\n"
2162 ((Printf.sprintf ("infer_time: %.9f\nforward_simpl_time: %.9f\n" ^^
2163 "forward_simpl_new_time: %.9f\n" ^^
2164 "backward_simpl_time: %.9f\n")
2165 !infer_time !forward_simpl_time !forward_simpl_new_time
2166 !backward_simpl_time) ^
2167 (Printf.sprintf "beta_expand_time: %.9f\n"
2168 !Indexing.beta_expand_time) ^
2169 (Printf.sprintf "passive_maintainance_time: %.9f\n"
2170 !passive_maintainance_time) ^
2171 (Printf.sprintf " successful unification/matching time: %.9f\n"
2172 !Indexing.match_unif_time_ok) ^
2173 (Printf.sprintf " failed unification/matching time: %.9f\n"
2174 !Indexing.match_unif_time_no) ^
2175 (Printf.sprintf " indexing retrieval time: %.9f\n"
2176 !Indexing.indexing_retrieval_time) ^
2177 (Printf.sprintf " demodulate_term.build_newtarget_time: %.9f\n"
2178 !Indexing.build_newtarget_time) ^
2179 (Printf.sprintf "derived %d clauses, kept %d clauses.\n"
2180 !derived_clauses !kept_clauses))
2184 print_endline ("EXCEPTION: " ^ (Printexc.to_string exc));
2190 let default_depth = !maxdepth
2191 and default_width = !maxwidth;;
2195 Indexing.local_max := 100;
2196 symbols_counter := 0;
2197 weight_age_counter := !weight_age_ratio;
2198 processed_clauses := 0;
2201 maximal_retained_equality := None;
2203 forward_simpl_time := 0.;
2204 forward_simpl_new_time := 0.;
2205 backward_simpl_time := 0.;
2206 passive_maintainance_time := 0.;
2207 derived_clauses := 0;
2209 Indexing.beta_expand_time := 0.;
2210 Inference.metas_of_proof_time := 0.;
2214 dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status =
2215 let module C = Cic in
2217 Indexing.init_index ();
2220 let proof, goal = status in
2222 let uri, metasenv, meta_proof, term_to_prove = proof in
2223 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2224 let eq_indexes, equalities, maxm = find_equalities context proof in
2225 let new_meta_goal, metasenv, type_of_goal =
2227 CicMkImplicit.identity_relocation_list_for_metavariable context in
2228 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2230 (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty)));
2231 Cic.Meta (maxm+1, irl),
2232 (maxm+1, context, ty)::metasenv,
2235 let ugraph = CicUniv.empty_ugraph in
2236 let env = (metasenv, context, ugraph) in
2237 let goal = Inference.BasicProof new_meta_goal, [], goal in
2239 let t1 = Unix.gettimeofday () in
2240 let lib_eq_uris, library_equalities, maxm =
2241 find_library_equalities dbd context (proof, goal') (maxm+2)
2243 let library_equalities = List.map snd library_equalities in
2244 let t2 = Unix.gettimeofday () in
2246 let equalities = simplify_equalities env (equalities@library_equalities) in
2249 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)));
2250 let t1 = Unix.gettimeofday () in
2253 let thms = find_library_theorems dbd env (proof, goal') lib_eq_uris in
2254 let context_hyp = find_context_hypotheses env eq_indexes in
2255 context_hyp @ thms, []
2258 let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
2259 UriManager.uri_of_string (us ^ "#xpointer(1/1/1)")
2261 let t = CicUtil.term_of_uri refl_equal in
2262 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
2265 let t2 = Unix.gettimeofday () in
2270 "Theorems:\n-------------------------------------\n%s\n"
2275 "Term: %s, type: %s"
2276 (CicPp.ppterm t) (CicPp.ppterm ty))
2280 (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
2282 let active = make_active () in
2283 let passive = make_passive [] equalities in
2284 let start = Unix.gettimeofday () in
2286 let goals = make_goals goal in
2287 given_clause_fullred dbd env goals theorems passive active
2289 let finish = Unix.gettimeofday () in
2290 (res, finish -. start)
2293 | ParamodulationSuccess (Some proof, env) ->
2294 debug_print (lazy "OK, found a proof!");
2295 let proof = Inference.build_proof_term proof in
2296 let names = names_of_context context in
2299 match new_meta_goal with
2300 | C.Meta (i, _) -> i | _ -> assert false
2302 List.filter (fun (i, _, _) -> i <> i1 && i <> goal') metasenv
2307 CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
2309 debug_print (lazy (CicPp.pp proof [](* names *)));
2313 "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n"
2314 (CicPp.pp type_of_goal names) (CicPp.pp ty names)
2316 (fst (CicReduction.are_convertible
2317 context type_of_goal ty ug)))));
2318 let equality_for_replace i t1 =
2320 | C.Meta (n, _) -> n = i
2324 ProofEngineReduction.replace
2325 ~equality:equality_for_replace
2326 ~what:[goal'] ~with_what:[proof]
2331 (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n"
2332 (match uri with Some uri -> UriManager.string_of_uri uri
2334 (print_metasenv newmetasenv)
2335 (CicPp.pp real_proof [](* names *))
2336 (CicPp.pp term_to_prove names)));
2337 ((uri, newmetasenv, real_proof, term_to_prove), [])
2338 with CicTypeChecker.TypeCheckerFailure _ ->
2339 debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
2340 debug_print (lazy (CicPp.pp proof names));
2341 raise (ProofEngineTypes.Fail
2342 (lazy "Found a proof, but it doesn't typecheck"))
2344 let tall = fs_time_info.build_all in
2345 let tdemodulate = fs_time_info.demodulate in
2346 let tsubsumption = fs_time_info.subsumption in
2350 (Printf.sprintf "\nTIME NEEDED: %.9f" time) ^
2351 (Printf.sprintf "\ntall: %.9f" tall) ^
2352 (Printf.sprintf "\ntdemod: %.9f" tdemodulate) ^
2353 (Printf.sprintf "\ntsubsumption: %.9f" tsubsumption) ^
2354 (Printf.sprintf "\ninfer_time: %.9f" !infer_time) ^
2355 (Printf.sprintf "\nbeta_expand_time: %.9f\n"
2356 !Indexing.beta_expand_time) ^
2357 (Printf.sprintf "\nmetas_of_proof: %.9f\n"
2358 !Inference.metas_of_proof_time) ^
2359 (Printf.sprintf "\nforward_simpl_times: %.9f" !forward_simpl_time) ^
2360 (Printf.sprintf "\nforward_simpl_new_times: %.9f"
2361 !forward_simpl_new_time) ^
2362 (Printf.sprintf "\nbackward_simpl_times: %.9f" !backward_simpl_time) ^
2363 (Printf.sprintf "\npassive_maintainance_time: %.9f"
2364 !passive_maintainance_time))
2368 raise (ProofEngineTypes.Fail (lazy "NO proof found"))
2371 (* dummy function called within matita to trigger linkage *)
2375 let retrieve_and_print dbd term metasenv ugraph =
2376 let module C = Cic in
2377 let module T = CicTypeChecker in
2378 let module PET = ProofEngineTypes in
2379 let module PP = CicPp in
2380 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2381 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2382 let proof, goals = status in
2383 let goal' = List.nth goals 0 in
2384 let uri, metasenv, meta_proof, term_to_prove = proof in
2385 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2386 let eq_indexes, equalities, maxm = find_equalities context proof in
2387 let new_meta_goal, metasenv, type_of_goal =
2389 CicMkImplicit.identity_relocation_list_for_metavariable context in
2390 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2392 (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty)));
2393 Cic.Meta (maxm+1, irl),
2394 (maxm+1, context, ty)::metasenv,
2397 let ugraph = CicUniv.empty_ugraph in
2398 let env = (metasenv, context, ugraph) in
2399 let t1 = Unix.gettimeofday () in
2400 let lib_eq_uris, library_equalities, maxm =
2401 find_library_equalities dbd context (proof, goal') (maxm+2) in
2402 let t2 = Unix.gettimeofday () in
2404 let equalities = (* equalities @ *) library_equalities in
2407 (Printf.sprintf "\n\nequalities:\n%s\n"
2411 (* Printf.sprintf "%s: %s" *)
2412 (UriManager.string_of_uri u)
2413 (* (string_of_equality e) *)
2416 debug_print (lazy "RETR: SIMPLYFYING EQUALITIES...");
2417 let rec simpl e others others_simpl =
2419 let active = List.map (fun (u, e) -> (Positive, e))
2420 (others @ others_simpl) in
2423 (fun t (_, e) -> Indexing.index t e)
2424 Indexing.empty active
2426 let res = forward_simplify env (Positive, e) (active, tbl) in
2430 | None -> simpl hd tl others_simpl
2431 | Some e -> simpl hd tl ((u, (snd e))::others_simpl)
2435 | None -> others_simpl
2436 | Some e -> (u, (snd e))::others_simpl
2440 match equalities with
2443 let others = tl in (* List.map (fun e -> (Positive, e)) tl in *)
2445 List.rev (simpl (*(Positive,*) hd others [])
2449 (Printf.sprintf "\nequalities AFTER:\n%s\n"
2453 Printf.sprintf "%s: %s"
2454 (UriManager.string_of_uri u)
2455 (string_of_equality e)
2461 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)))
2465 let main_demod_equalities dbd term metasenv ugraph =
2466 let module C = Cic in
2467 let module T = CicTypeChecker in
2468 let module PET = ProofEngineTypes in
2469 let module PP = CicPp in
2470 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
2471 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
2472 let proof, goals = status in
2473 let goal' = List.nth goals 0 in
2474 let _, metasenv, meta_proof, _ = proof in
2475 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
2476 let eq_indexes, equalities, maxm = find_equalities context proof in
2477 let lib_eq_uris, library_equalities, maxm =
2478 find_library_equalities dbd context (proof, goal') (maxm+2)
2480 let library_equalities = List.map snd library_equalities in
2481 maxmeta := maxm+2; (* TODO ugly!! *)
2482 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2483 let new_meta_goal, metasenv, type_of_goal =
2484 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
2487 (Printf.sprintf "\n\nTRYING TO INFER EQUALITIES MATCHING: %s\n\n"
2488 (CicPp.ppterm ty)));
2489 Cic.Meta (maxm+1, irl),
2490 (maxm+1, context, ty)::metasenv,
2493 let env = (metasenv, context, ugraph) in
2495 let goal = Inference.BasicProof new_meta_goal, [], goal in
2496 let equalities = simplify_equalities env (equalities@library_equalities) in
2497 let active = make_active () in
2498 let passive = make_passive [] equalities in
2499 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
2500 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
2501 Printf.printf "\nequalities:\n%s\n"
2504 (string_of_equality ~env) equalities));
2505 print_endline "--------------------------------------------------";
2506 print_endline "GO!";
2507 start_time := Unix.gettimeofday ();
2508 if !time_limit < 1. then time_limit := 60.;
2510 saturate_equations env goal (fun e -> true) passive active
2514 List.fold_left (fun s e -> EqualitySet.add e s)
2515 EqualitySet.empty equalities
2518 if not (EqualitySet.mem e initial) then EqualitySet.add e s else s
2523 | (n, _), (p, _), _ ->
2524 EqualitySet.elements (List.fold_left addfun EqualitySet.empty p)
2527 let l = List.map snd (fst ra) in
2528 EqualitySet.elements (List.fold_left addfun EqualitySet.empty l)
2530 Printf.printf "\n\nRESULTS:\nActive:\n%s\n\nPassive:\n%s\n"
2531 (String.concat "\n" (List.map (string_of_equality ~env) active))
2532 (* (String.concat "\n"
2533 (List.map (fun e -> CicPp.ppterm (term_of_equality e)) active)) *)
2534 (* (String.concat "\n" (List.map (string_of_equality ~env) passive)); *)
2536 (List.map (fun e -> CicPp.ppterm (term_of_equality e)) passive));
2540 debug_print (lazy ("EXCEPTION: " ^ (Printexc.to_string e)))
2544 let demodulate_tac ~dbd ~pattern ((proof,goal) as initialstatus) =
2545 let module I = Inference in
2546 let curi,metasenv,pbo,pty = proof in
2547 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
2548 let eq_indexes, equalities, maxm = I.find_equalities context proof in
2549 let lib_eq_uris, library_equalities, maxm =
2550 I.find_library_equalities dbd context (proof, goal) (maxm+2) in
2551 if library_equalities = [] then prerr_endline "VUOTA!!!";
2552 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
2553 let library_equalities = List.map snd library_equalities in
2554 let goalterm = Cic.Meta (metano,irl) in
2555 let initgoal = Inference.BasicProof goalterm, [], ty in
2556 let env = (metasenv, context, CicUniv.empty_ugraph) in
2557 let equalities = simplify_equalities env (equalities@library_equalities) in
2560 (fun tbl eq -> Indexing.index tbl eq)
2561 Indexing.empty equalities
2563 let newmeta,(newproof,newmetasenv, newty) = Indexing.demodulation_goal
2564 maxm (metasenv,context,CicUniv.empty_ugraph) table initgoal
2566 if newmeta != maxm then
2568 let opengoal = Cic.Meta(maxm,irl) in
2570 Inference.build_proof_term ~noproof:opengoal newproof in
2571 let extended_metasenv = (maxm,context,newty)::metasenv in
2572 let extended_status =
2573 (curi,extended_metasenv,pbo,pty),goal in
2574 let (status,newgoals) =
2575 ProofEngineTypes.apply_tactic
2576 (PrimitiveTactics.apply_tac ~term:proofterm)
2578 (status,maxm::newgoals)
2580 else if newty = ty then
2581 raise (ProofEngineTypes.Fail (lazy "no progress"))
2582 else ProofEngineTypes.apply_tactic
2583 (ReductionTactics.simpl_tac ~pattern)
2587 let demodulate_tac ~dbd ~pattern =
2588 ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~pattern)