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/.
26 let _profiler = <:profiler<_profiler>>;;
30 (* set to false to disable paramodulation inside auto_tac *)
32 let connect_to_auto = true;;
35 (* profiling statistics... *)
36 let infer_time = ref 0.;;
37 let forward_simpl_time = ref 0.;;
38 let forward_simpl_new_time = ref 0.;;
39 let backward_simpl_time = ref 0.;;
40 let passive_maintainance_time = ref 0.;;
42 (* limited-resource-strategy related globals *)
43 let processed_clauses = ref 0;; (* number of equalities selected so far... *)
44 let time_limit = ref 0.;; (* in seconds, settable by the user... *)
45 let start_time = ref 0.;; (* time at which the execution started *)
46 let elapsed_time = ref 0.;;
47 (* let maximal_weight = ref None;; *)
48 let maximal_retained_equality = ref None;;
50 (* equality-selection related globals *)
51 let use_fullred = ref true;;
52 let weight_age_ratio = ref 6 (* 5 *);; (* settable by the user *)
53 let weight_age_counter = ref !weight_age_ratio ;;
54 let symbols_ratio = ref 0 (* 3 *);;
55 let symbols_counter = ref 0;;
57 (* non-recursive Knuth-Bendix term ordering by default *)
58 (* Utils.compare_terms := Utils.rpo;; *)
59 (* Utils.compare_terms := Utils.nonrec_kbo;; *)
60 (* Utils.compare_terms := Utils.ao;; *)
63 let derived_clauses = ref 0;;
64 let kept_clauses = ref 0;;
66 (* index of the greatest Cic.Meta created - TODO: find a better way! *)
69 (* varbiables controlling the search-space *)
70 let maxdepth = ref 3;;
71 let maxwidth = ref 3;;
74 Equality.goal_proof * Equality.proof * int * Subst.substitution * Cic.metasenv
76 | ParamodulationFailure of string
77 | ParamodulationSuccess of new_proof
80 (* type goal = Equality.goal_proof * Cic.metasenv * Cic.term;; *)
82 type theorem = Cic.term * Cic.term * Cic.metasenv;;
84 let symbols_of_equality equality =
85 let (_, _, (_, left, right, _), _,_) = Equality.open_equality equality in
86 let m1 = Utils.symbols_of_term left in
91 let c = Utils.TermMap.find k res in
92 Utils.TermMap.add k (c+v) res
94 Utils.TermMap.add k v res)
95 (Utils.symbols_of_term right) m1
101 module OrderedEquality = struct
102 type t = Equality.equality
104 let compare eq1 eq2 =
105 match Equality.meta_convertibility_eq eq1 eq2 with
108 let w1, _, (ty,left, right, _), m1,_ = Equality.open_equality eq1 in
109 let w2, _, (ty',left', right', _), m2,_ = Equality.open_equality eq2 in
110 match Pervasives.compare w1 w2 with
112 let res = (List.length m1) - (List.length m2) in
113 if res <> 0 then res else
114 Equality.compare eq1 eq2
118 module EqualitySet = Set.Make(OrderedEquality);;
120 exception Empty_list;;
122 type passives = Equality.equality list * EqualitySet.t;;
123 type actives = Equality.equality list * Indexing.Index.t;;
125 (* initializes the passive set of equalities
126 * XXX I think EqualitySet.elements should be ok (to eliminate duplicates)
128 let make_passive pos =
130 List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty pos
132 (*EqualitySet.elements*) pos, set
135 let make_active () = [], Indexing.empty ;;
136 let size_of_passive (passive_list, _) = List.length passive_list;;
137 let size_of_active (active_list, _) = List.length active_list;;
138 let passive_is_empty = function
139 | [], s when EqualitySet.is_empty s -> true
140 | [], s -> assert false (* the set and the list should be in sync *)
144 type goals = Equality.goal list * Equality.goal list
146 let no_more_passive_goals g = match g with | _,[] -> true | _ -> false;;
149 let age_factor = 0.01;;
152 selects one equality from passive. The selection strategy is a combination
153 of weight, age and goal-similarity
156 let rec select env (goals,_) passive =
157 processed_clauses := !processed_clauses + 1;
159 match (List.rev goals) with goal::_ -> goal | _ -> assert false
161 let pos_list, pos_set = passive in
162 let remove eq l = List.filter (fun e -> Equality.compare e eq <> 0) l in
163 if !weight_age_ratio > 0 then
164 weight_age_counter := !weight_age_counter - 1;
165 match !weight_age_counter with
167 weight_age_counter := !weight_age_ratio;
168 let rec skip_giant pos_list pos_set =
170 | (hd:EqualitySet.elt)::tl ->
171 let w,_,_,_,_ = Equality.open_equality hd in
172 let pos_set = EqualitySet.remove hd pos_set in
177 ("+++ skipping giant of size "^string_of_int w^" +++");
178 skip_giant tl pos_set)
181 skip_giant pos_list pos_set)
182 | _ when (!symbols_counter > 0) ->
183 (symbols_counter := !symbols_counter - 1;
184 let cardinality map =
185 Utils.TermMap.fold (fun k v res -> res + v) map 0
188 let _, _, term = goal in
189 Utils.symbols_of_term term
191 let card = cardinality symbols in
192 let foldfun k v (r1, r2) =
193 if Utils.TermMap.mem k symbols then
194 let c = Utils.TermMap.find k symbols in
195 let c1 = abs (c - v) in
201 let f equality (i, e) =
203 Utils.TermMap.fold foldfun (symbols_of_equality equality) (0, 0)
205 let c = others + (abs (common - card)) in
206 if c < i then (c, equality)
209 let e1 = EqualitySet.min_elt pos_set in
212 Utils.TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
214 (others + (abs (common - card))), e1
216 let _, current = EqualitySet.fold f pos_set initial in
218 (remove current pos_list, EqualitySet.remove current pos_set))
220 symbols_counter := !symbols_ratio;
222 let w1,_,_,_,_ = Equality.open_equality e1 in
223 let w2,_,_,_,_ = Equality.open_equality e2 in
224 if w1 < w2 then e1 else e2
226 let rec my_min_elt min = function
228 | hd::tl -> my_min_elt (my_min hd min) tl
230 (* let current = EqualitySet.min_elt pos_set in *)
231 let current = my_min_elt (List.hd pos_list) (List.tl pos_list) in
232 current,(remove current pos_list, EqualitySet.remove current pos_set)
236 let filter_dependent passive id =
237 let pos_list, pos_set = passive in
238 let passive,no_pruned =
240 (fun eq ((list,set),no) ->
241 if Equality.depend eq id then
242 (list, EqualitySet.remove eq set), no + 1
245 pos_list (([],pos_set),0)
247 if no_pruned > 0 then
248 prerr_endline ("+++ pruning "^ string_of_int no_pruned ^" passives +++");
253 (* adds to passive a list of equalities new_pos *)
254 let add_to_passive passive new_pos preferred =
255 let pos_list, pos_set = passive in
256 let ok set equality = not (EqualitySet.mem equality set) in
257 let pos = List.filter (ok pos_set) new_pos in
258 let add set equalities =
259 List.fold_left (fun s e -> EqualitySet.add e s) set equalities
261 let pos_head, pos_tail =
263 (fun e -> List.exists (fun x -> Equality.compare x e = 0) preferred)
266 assert(pos_head = []);
267 pos_head @ pos_list @ pos_tail, add pos_set pos
271 (* removes from passive equalities that are estimated impossible to activate
272 within the current time limit *)
273 let prune_passive howmany (active, _) passive =
274 let (pl, ps), tbl = passive in
275 let howmany = float_of_int howmany
276 and ratio = float_of_int !weight_age_ratio in
279 int_of_float (if t -. v < 0.5 then t else v)
281 let in_weight = round (howmany *. ratio /. (ratio +. 1.))
282 and in_age = round (howmany /. (ratio +. 1.)) in
284 (lazy (Printf.sprintf "in_weight: %d, in_age: %d\n" in_weight in_age));
285 let counter = ref !symbols_ratio in
290 counter := !counter - 1;
291 if !counter = 0 then counter := !symbols_ratio in
292 let e = EqualitySet.min_elt ps in
293 let ps' = pickw (w-1) (EqualitySet.remove e ps) in
294 EqualitySet.add e ps'
296 let e = EqualitySet.min_elt ps in
297 let ps' = pickw (w-1) (EqualitySet.remove e ps) in
298 EqualitySet.add e ps'
302 let ps = pickw in_weight ps in
303 let rec picka w s l =
307 | hd::tl when not (EqualitySet.mem hd s) ->
308 let w, s, l = picka (w-1) s tl in
309 w, EqualitySet.add hd s, hd::l
311 let w, s, l = picka w s tl in
316 let _, ps, pl = picka in_age ps pl in
317 if not (EqualitySet.is_empty ps) then
318 maximal_retained_equality := Some (EqualitySet.max_elt ps);
321 (fun e tbl -> Indexing.index tbl e) ps Indexing.empty
327 (** inference of new equalities between current and some in active *)
328 let infer eq_uri env current (active_list, active_table) =
330 if Utils.debug_metas then
331 (ignore(Indexing.check_target c current "infer1");
332 ignore(List.map (function current -> Indexing.check_target c current "infer2") active_list));
334 let maxm, copy_of_current = Equality.fix_metas !maxmeta current in
336 let active_table = Indexing.index active_table copy_of_current in
337 let _ = <:start<current contro active>> in
339 Indexing.superposition_right eq_uri !maxmeta env active_table current
341 let _ = <:stop<current contro active>> in
342 if Utils.debug_metas then
345 Indexing.check_target c current "sup0") res);
347 let rec infer_positive table = function
351 Indexing.superposition_right
352 ~subterms_only:true eq_uri !maxmeta env table equality
355 if Utils.debug_metas then
359 Indexing.check_target c current "sup2") res);
360 let pos = infer_positive table tl in
364 let maxm, copy_of_current = Equality.fix_metas !maxmeta current in
367 let curr_table = Indexing.index Indexing.empty current in
368 let _ = <:start<active contro current>> in
369 let pos = infer_positive curr_table ((*copy_of_current::*)active_list) in
370 let _ = <:stop<active contro current>> in
371 if Utils.debug_metas then
374 Indexing.check_target c current "sup3") pos);
377 derived_clauses := !derived_clauses + (List.length new_pos);
378 match !maximal_retained_equality with
381 ignore(assert false);
382 (* if we have a maximal_retained_equality, we can discard all equalities
383 "greater" than it, as they will never be reached... An equality is
384 greater than maximal_retained_equality if it is bigger
385 wrt. OrderedEquality.compare and it is less similar than
386 maximal_retained_equality to the current goal *)
387 List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos
390 let check_for_deep_subsumption env active_table eq =
391 let _,_,(eq_ty, left, right, order),metas,id = Equality.open_equality eq in
392 let check_subsumed deep l r =
394 Equality.mk_tmp_equality(0,(eq_ty,l,r,Utils.Incomparable),metas)in
395 match Indexing.subsumption env active_table eqtmp with
399 let rec aux b (ok_so_far, subsumption_used) t1 t2 =
401 | t1, t2 when not ok_so_far -> ok_so_far, subsumption_used
402 | t1, t2 when subsumption_used -> t1 = t2, subsumption_used
403 | Cic.Appl (h1::l),Cic.Appl (h2::l') ->
404 let rc = check_subsumed b t1 t2 in
410 (fun (ok_so_far, subsumption_used) t t' ->
411 aux true (ok_so_far, subsumption_used) t t')
412 (ok_so_far, subsumption_used) l l'
413 with Invalid_argument _ -> false,subsumption_used)
415 false, subsumption_used
416 | _ -> false, subsumption_used
418 fst (aux false (true,false) left right)
421 (** simplifies current using active and passive *)
422 let forward_simplify eq_uri env current (active_list, active_table) =
423 let _, context, _ = env in
424 let demodulate table current =
425 let newmeta, newcurrent =
426 Indexing.demodulation_equality eq_uri !maxmeta env table current
429 if Equality.is_identity env newcurrent then None else Some newcurrent
431 let rec demod current =
432 if Utils.debug_metas then
433 ignore (Indexing.check_target context current "demod0");
434 let res = demodulate active_table current in
435 if Utils.debug_metas then
436 ignore ((function None -> () | Some x ->
437 ignore (Indexing.check_target context x "demod1");()) res);
440 let res = demod current in
444 if Indexing.in_index active_table c ||
445 check_for_deep_subsumption env active_table c
452 (** simplifies new using active and passive *)
453 let forward_simplify_new eq_uri env new_pos active =
454 if Utils.debug_metas then
458 (fun current -> Indexing.check_target c current "forward new pos")
461 let active_list, active_table = active in
462 let demodulate table target =
463 let newmeta, newtarget =
464 Indexing.demodulation_equality eq_uri !maxmeta env table target
469 (* we could also demodulate using passive. Currently we don't *)
470 let new_pos = List.map (demodulate active_table) new_pos in
474 if not (Equality.is_identity env e) then
477 EqualitySet.empty new_pos
479 let new_pos = EqualitySet.elements new_pos_set in
481 let subs e = Indexing.subsumption env active_table e = None in
482 let is_duplicate e = not (Indexing.in_index active_table e) in
483 List.filter subs (List.filter is_duplicate new_pos)
487 (** simplifies a goal with equalities in active and passive *)
488 let rec simplify_goal env goal (active_list, active_table) =
489 let demodulate table goal = Indexing.demodulation_goal env table goal in
490 let changed, goal = demodulate active_table goal in
495 snd (simplify_goal env goal (active_list, active_table))
499 let simplify_goals env goals active =
500 let a_goals, p_goals = goals in
501 let p_goals = List.map (fun g -> snd (simplify_goal env g active)) p_goals in
502 let a_goals = List.map (fun g -> snd (simplify_goal env g active)) a_goals in
507 (** simplifies active usign new *)
508 let backward_simplify_active eq_uri env new_pos new_table min_weight active =
509 let active_list, active_table = active in
510 let active_list, newa, pruned =
512 (fun equality (res, newn,pruned) ->
513 let ew, _, _, _,id = Equality.open_equality equality in
514 if ew < min_weight then
515 equality::res, newn,pruned
518 forward_simplify eq_uri env equality (new_pos, new_table)
520 | None -> res, newn, id::pruned
522 if Equality.compare equality e = 0 then
525 res, e::newn, pruned)
526 active_list ([], [],[])
529 List.exists (Equality.meta_convertibility_eq eq1) where
532 let _, _, _, _,id = Equality.open_equality eq in id
534 let ((active1,pruned),tbl), newa =
536 (fun eq ((res,pruned), tbl) ->
537 if List.mem eq res then
538 (res, (id_of_eq eq)::pruned),tbl
539 else if (Equality.is_identity env eq) || (find eq res) then (
540 (res, (id_of_eq eq)::pruned),tbl
543 (eq::res,pruned), Indexing.index tbl eq)
544 active_list (([],pruned), Indexing.empty),
547 if (Equality.is_identity env eq) then p
552 | [] -> (active1,tbl), None, pruned
553 | _ -> (active1,tbl), Some newa, pruned
557 (** simplifies passive using new *)
558 let backward_simplify_passive eq_uri env new_pos new_table min_weight passive =
559 let (pl, ps), passive_table = passive in
560 let f equality (resl, ress, newn) =
561 let ew, _, _, _ , _ = Equality.open_equality equality in
562 if ew < min_weight then
563 equality::resl, ress, newn
566 forward_simplify eq_uri env equality (new_pos, new_table)
568 | None -> resl, EqualitySet.remove equality ress, newn
571 equality::resl, ress, newn
573 let ress = EqualitySet.remove equality ress in
576 let pl, ps, newp = List.fold_right f pl ([], ps, []) in
579 (fun tbl e -> Indexing.index tbl e) Indexing.empty pl
582 | [] -> ((pl, ps), passive_table), None
583 | _ -> ((pl, ps), passive_table), Some (newp)
586 let build_table equations =
589 let ew, _, _, _ , _ = Equality.open_equality e in
590 e::l, Indexing.index t e, min ew w)
591 ([], Indexing.empty, 1000000) equations
595 let backward_simplify eq_uri env new' active =
596 let new_pos, new_table, min_weight = build_table new' in
597 let active, newa, pruned =
598 backward_simplify_active eq_uri env new_pos new_table min_weight active
600 active, newa, None, pruned
603 let close eq_uri env new' given =
604 let new_pos, new_table, min_weight =
607 let ew, _, _, _ , _ = Equality.open_equality e in
608 e::l, Indexing.index t e, min ew w)
609 ([], Indexing.empty, 1000000) (snd new')
613 let pos = infer eq_uri env c (new_pos,new_table) in
618 let is_commutative_law eq =
619 let w, proof, (eq_ty, left, right, order), metas , _ =
620 Equality.open_equality eq
622 match left,right with
623 Cic.Appl[f1;Cic.Meta _ as a1;Cic.Meta _ as b1],
624 Cic.Appl[f2;Cic.Meta _ as a2;Cic.Meta _ as b2] ->
625 f1 = f2 && a1 = b2 && a2 = b1
629 let prova eq_uri env new' active =
630 let given = List.filter is_commutative_law (fst active) in
634 (Printf.sprintf "symmetric:\n%s\n"
637 (fun e -> Equality.string_of_equality ~env e)
639 close eq_uri env new' given
642 (* returns an estimation of how many equalities in passive can be activated
643 within the current time limit *)
644 let get_selection_estimate () =
645 elapsed_time := (Unix.gettimeofday ()) -. !start_time;
646 (* !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *)
648 ceil ((float_of_int !processed_clauses) *.
649 ((!time_limit (* *. 2. *)) /. !elapsed_time -. 1.)))
653 (** initializes the set of goals *)
654 let make_goals goal =
656 and passive = [0, [goal]] in
660 let make_goal_set goal =
664 (** initializes the set of theorems *)
665 let make_theorems theorems =
670 let activate_goal (active, passive) =
673 | goal_conj::tl -> true, (goal_conj::active, tl)
674 | [] -> false, (active, passive)
676 true, (active,passive)
680 let activate_theorem (active, passive) =
682 | theorem::tl -> true, (theorem::active, tl)
683 | [] -> false, (active, passive)
688 let simplify_theorems env theorems ?passive (active_list, active_table) =
689 let pl, passive_table =
692 | Some ((pn, _), (pp, _), pt) -> pn @ pp, Some pt
694 let a_theorems, p_theorems = theorems in
695 let demodulate table theorem =
696 let newmeta, newthm =
697 Indexing.demodulation_theorem !maxmeta env table theorem in
699 theorem != newthm, newthm
701 let foldfun table (a, p) theorem =
702 let changed, theorem = demodulate table theorem in
703 if changed then (a, theorem::p) else (theorem::a, p)
705 let mapfun table theorem = snd (demodulate table theorem) in
706 match passive_table with
708 let p_theorems = List.map (mapfun active_table) p_theorems in
709 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems
710 | Some passive_table ->
711 let p_theorems = List.map (mapfun active_table) p_theorems in
712 let p_theorems, a_theorems =
713 List.fold_left (foldfun active_table) ([], p_theorems) a_theorems in
714 let p_theorems = List.map (mapfun passive_table) p_theorems in
715 List.fold_left (foldfun passive_table) ([], p_theorems) a_theorems
719 let rec simpl eq_uri env e others others_simpl =
720 let active = others @ others_simpl in
723 (fun t e -> Indexing.index t e)
724 Indexing.empty active
726 let res = forward_simplify eq_uri env e (active, tbl) in
730 | None -> simpl eq_uri env hd tl others_simpl
731 | Some e -> simpl eq_uri env hd tl (e::others_simpl)
735 | None -> others_simpl
736 | Some e -> e::others_simpl
740 let simplify_equalities eq_uri env equalities =
743 (Printf.sprintf "equalities:\n%s\n"
745 (List.map Equality.string_of_equality equalities))));
746 Utils.debug_print (lazy "SIMPLYFYING EQUALITIES...");
747 match equalities with
751 List.rev (simpl eq_uri env hd tl [])
755 (Printf.sprintf "equalities AFTER:\n%s\n"
757 (List.map Equality.string_of_equality res))));
761 let print_goals goals =
768 (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl
770 Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
773 let pp_goal_set msg goals names =
774 let active_goals, passive_goals = goals in
775 prerr_endline ("////" ^ msg);
776 prerr_endline ("ACTIVE G: " ^
777 (String.concat "\n " (List.map (fun (_,_,g) -> CicPp.pp g names)
779 prerr_endline ("PASSIVE G: " ^
780 (String.concat "\n " (List.map (fun (_,_,g) -> CicPp.pp g names)
784 let check_if_goal_is_subsumed ((_,ctx,_) as env) table (goalproof,menv,ty) =
785 let names = Utils.names_of_context ctx in
787 | Cic.Appl[Cic.MutInd(uri,_,_);eq_ty;left;right]
788 when LibraryObjects.is_eq_URI uri ->
791 (0,Equality.Exact (Cic.Implicit None),(eq_ty,left,right,Utils.Eq),menv)
793 (* match Indexing.subsumption env table goal_equation with*)
794 match Indexing.unification env table goal_equation with
795 | Some (subst, equality, swapped ) ->
797 ("GOAL SUBSUMED IS: " ^ Equality.string_of_equality goal_equation ~env);
799 ("GOAL IS SUBSUMED BY: " ^ Equality.string_of_equality equality ~env);
800 prerr_endline ("SUBST:" ^ Subst.ppsubst ~names subst);
801 let (_,p,(ty,l,r,_),m,id) = Equality.open_equality equality in
802 let cicmenv = Subst.apply_subst_metasenv subst (m @ menv) in
805 Equality.symmetric eq_ty l id uri m
809 Some (goalproof, p, id, subst, cicmenv)
814 let check_if_goal_is_identity env = function
815 | (goalproof,m,Cic.Appl[Cic.MutInd(uri,_,ens);eq_ty;left;right])
816 when left = right && LibraryObjects.is_eq_URI uri ->
817 let reflproof = Equality.Exact (Equality.refl_proof uri eq_ty left) in
818 Some (goalproof, reflproof, 0, Subst.empty_subst,m)
819 | (goalproof,m,Cic.Appl[Cic.MutInd(uri,_,ens);eq_ty;left;right])
820 when LibraryObjects.is_eq_URI uri ->
821 (let _,context,_ = env in
824 Inference.unification m m context left right CicUniv.empty_ugraph
826 let reflproof = Equality.Exact (Equality.refl_proof uri eq_ty left) in
827 let m = Subst.apply_subst_metasenv s m in
828 Some (goalproof, reflproof, 0, s,m)
833 let rec check goal = function
837 | None -> check goal tl
838 | (Some p) as ok -> ok
841 let simplify_goal_set env goals active =
842 let active_goals, passive_goals = goals in
843 let find (_,_,g) where =
844 List.exists (fun (_,_,g1) -> Equality.meta_convertibility g g1) where
847 (fun (acc_a,acc_p) goal ->
848 match simplify_goal env goal active with
851 if find g acc_p then acc_a,acc_p else acc_a,g::acc_p
853 if find g acc_a then acc_a,acc_p else g::acc_a,acc_p)
854 ([],passive_goals) active_goals
857 let check_if_goals_set_is_solved env active goals =
858 let active_goals, passive_goals = goals in
865 check_if_goal_is_identity env;
866 check_if_goal_is_subsumed env (snd active)])
870 let infer_goal_set env active goals =
871 let active_goals, passive_goals = goals in
872 let rec aux = function
873 | [] -> active_goals, []
875 let changed,selected = simplify_goal env hd active in
877 prerr_endline ("--------------- goal semplificato");
878 let (_,_,t1) = selected in
880 List.exists (fun (_,_,t) -> Equality.meta_convertibility t t1)
886 let passive_goals = tl in
887 let new_passive_goals =
888 if Utils.metas_of_term t1 = [] then passive_goals
890 let newmaxmeta,new' =
891 Indexing.superposition_left env (snd active) selected
894 maxmeta := newmaxmeta;
897 selected::active_goals, new_passive_goals
902 let infer_goal_set_with_current env current goals active =
903 let active_goals, passive_goals =
904 simplify_goal_set env goals active
906 let l,table,_ = build_table [current] in
910 let newmaxmeta, new' = Indexing.superposition_left env table g !maxmeta in
911 maxmeta := newmaxmeta;
913 passive_goals active_goals
918 let ids = List.map (fun _,_,i,_,_ -> i) p in
922 let ids_of_goal_set (ga,gp) =
923 List.flatten (List.map ids_of_goal ga) @
924 List.flatten (List.map ids_of_goal gp)
927 let size_of_goal_set_a (l,_) = List.length l;;
928 let size_of_goal_set_p (_,l) = List.length l;;
930 let pp_goals label goals context =
931 let names = Utils.names_of_context context in
935 (Printf.sprintf "Current goal: %s = %s\n" label (CicPp.pp g names)))
940 (Printf.sprintf "PASSIVE goal: %s = %s\n" label (CicPp.pp g names)))
944 (** given-clause algorithm with full reduction strategy: NEW implementation *)
945 (* here goals is a set of goals in OR *)
947 eq_uri ((_,context,_) as env) goals theorems passive active max_iterations max_time
949 let initial_time = Unix.gettimeofday () in
950 let iterations_left iterno =
951 let now = Unix.gettimeofday () in
952 let time_left = max_time -. now in
953 let time_spent_until_now = now -. initial_time in
954 let iteration_medium_cost =
955 time_spent_until_now /. (float_of_int iterno)
957 let iterations_left = time_left /. iteration_medium_cost in
958 int_of_float iterations_left
960 let rec step goals theorems passive active iterno =
961 pp_goals "xxx" goals context;
962 if iterno > max_iterations then
963 (ParamodulationFailure "No more iterations to spend")
964 else if Unix.gettimeofday () > max_time then
965 (ParamodulationFailure "No more time to spend")
968 let _ = prerr_endline "simpl goal with active" in
969 let _ = <:start<simplify goal set active>> in
970 let goals = simplify_goal_set env goals passive active in
971 let _ = <:stop<simplify goal set active>> in
975 (Printf.sprintf "%d #ACTIVES: %d #PASSIVES: %d #GOALSET: %d(%d)\n"
976 iterno (size_of_active active) (size_of_passive passive)
977 (size_of_goal_set_a goals) (size_of_goal_set_p goals))
979 (* PRUNING OF PASSIVE THAT WILL NEVER BE PROCESSED *)
981 let selection_estimate = iterations_left iterno in
982 let kept = size_of_passive passive in
983 if kept > selection_estimate then
985 (*Printf.eprintf "Too many passive equalities: pruning...";
986 prune_passive selection_estimate active*) passive
991 kept_clauses := (size_of_passive passive) + (size_of_active active);
992 let goals = infer_goal_set env active goals in
993 match check_if_goals_set_is_solved env active goals with
996 (Printf.sprintf "Found a proof in: %f\n"
997 (Unix.gettimeofday() -. initial_time));
998 ParamodulationSuccess p
1001 if passive_is_empty passive then
1002 if no_more_passive_goals goals then
1003 ParamodulationFailure "No more passive equations/goals"
1004 (*maybe this is a success! *)
1006 step goals theorems passive active (iterno+1)
1009 (* COLLECTION OF GARBAGED EQUALITIES *)
1010 if iterno mod 40 = 0 then
1012 let active = List.map Equality.id_of (fst active) in
1013 let passive = List.map Equality.id_of (fst passive) in
1014 let goal = ids_of_goal_set goals in
1015 Equality.collect active passive goal
1017 let current, passive = select env goals passive in
1018 (* SIMPLIFICATION OF CURRENT *)
1021 Equality.string_of_equality ~env current);
1023 forward_simplify eq_uri env current active
1026 | None -> step goals theorems passive active (iterno+1)
1030 ("Selected simpl: " ^
1031 Equality.string_of_equality ~env current);
1033 (* GENERATION OF NEW EQUATIONS *)
1034 prerr_endline "infer";
1035 let new' = infer eq_uri env current active in
1036 prerr_endline "infer goal";
1038 match check_if_goals_set_is_solved env active goals with
1041 (Printf.sprintf "Found a proof in: %f\n"
1042 (Unix.gettimeofday() -. initial_time));
1043 ParamodulationSuccess p
1047 let al, tbl = active in
1048 al @ [current], Indexing.index tbl current
1051 infer_goal_set_with_current env current goals active
1053 (* FORWARD AND BACKWARD SIMPLIFICATION *)
1054 prerr_endline "fwd/back simpl";
1055 let rec simplify new' active passive head =
1057 forward_simplify_new eq_uri env new' active
1059 let active, newa, retained, pruned =
1060 backward_simplify eq_uri env new' active
1063 List.fold_left filter_dependent passive pruned
1065 match newa, retained with
1066 | None, None -> active, passive, new', head
1068 | None, Some p -> simplify (new' @ p) active passive head
1069 | Some p, Some rp ->
1070 simplify (new' @ p @ rp) active passive (head @ p)
1072 let active, passive, new', head =
1073 simplify new' active passive []
1075 prerr_endline "simpl goal with new";
1077 let a,b,_ = build_table new' in
1078 let _ = <:start<simplify_goal_set new>> in
1079 let rc = simplify_goal_set env goals (a,b) in
1080 let _ = <:stop<simplify_goal_set new>> in
1083 let passive = add_to_passive passive new' head in
1084 step goals theorems passive active (iterno+1)
1087 step goals theorems passive active 1
1090 let rec saturate_equations eq_uri env goal accept_fun passive active =
1091 elapsed_time := Unix.gettimeofday () -. !start_time;
1092 if !elapsed_time > !time_limit then
1095 let current, passive = select env ([goal],[]) passive in
1096 let res = forward_simplify eq_uri env current active in
1099 saturate_equations eq_uri env goal accept_fun passive active
1101 Utils.debug_print (lazy (Printf.sprintf "selected: %s"
1102 (Equality.string_of_equality ~env current)));
1103 let new' = infer eq_uri env current active in
1105 if Equality.is_identity env current then active
1107 let al, tbl = active in
1108 al @ [current], Indexing.index tbl current
1110 (* alla fine new' contiene anche le attive semplificate!
1111 * quindi le aggiungo alle passive insieme alle new *)
1112 let rec simplify new' active passive =
1113 let new' = forward_simplify_new eq_uri env new' active in
1114 let active, newa, retained, pruned =
1115 backward_simplify eq_uri env new' active in
1117 List.fold_left filter_dependent passive pruned in
1118 match newa, retained with
1119 | None, None -> active, passive, new'
1121 | None, Some p -> simplify (new' @ p) active passive
1122 | Some p, Some rp -> simplify (new' @ p @ rp) active passive
1124 let active, passive, new' = simplify new' active passive in
1128 (Printf.sprintf "active:\n%s\n"
1131 (fun e -> Equality.string_of_equality ~env e)
1137 (Printf.sprintf "new':\n%s\n"
1140 (fun e -> "Negative " ^
1141 (Equality.string_of_equality ~env e)) new'))))
1143 let new' = List.filter accept_fun new' in
1144 let passive = add_to_passive passive new' [] in
1145 saturate_equations eq_uri env goal accept_fun passive active
1148 let default_depth = !maxdepth
1149 and default_width = !maxwidth;;
1153 symbols_counter := 0;
1154 weight_age_counter := !weight_age_ratio;
1155 processed_clauses := 0;
1158 maximal_retained_equality := None;
1160 forward_simpl_time := 0.;
1161 forward_simpl_new_time := 0.;
1162 backward_simpl_time := 0.;
1163 passive_maintainance_time := 0.;
1164 derived_clauses := 0;
1169 let eq_of_goal = function
1170 | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri ->
1172 | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
1175 let eq_and_ty_of_goal = function
1176 | Cic.Appl [Cic.MutInd(uri,0,_);t;_;_] when LibraryObjects.is_eq_URI uri ->
1178 | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
1183 dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status =
1184 let module C = Cic in
1186 Indexing.init_index ();
1189 (* CicUnification.unif_ty := false;*)
1190 let proof, goalno = status in
1191 let uri, metasenv, meta_proof, term_to_prove = proof in
1192 let _, context, type_of_goal = CicUtil.lookup_meta goalno metasenv in
1193 let eq_uri = eq_of_goal type_of_goal in
1194 let cleaned_goal = Utils.remove_local_context type_of_goal in
1195 Utils.set_goal_symbols cleaned_goal;
1196 let names = Utils.names_of_context context in
1197 let eq_indexes, equalities, maxm = Inference.find_equalities context proof in
1198 let ugraph = CicUniv.empty_ugraph in
1199 let env = (metasenv, context, ugraph) in
1200 let goal = [], List.filter (fun (i,_,_)->i<>goalno) metasenv, cleaned_goal in
1202 let t1 = Unix.gettimeofday () in
1203 let lib_eq_uris, library_equalities, maxm =
1204 Inference.find_library_equalities caso_strano dbd context (proof, goalno) (maxm+2)
1206 let library_equalities = List.map snd library_equalities in
1207 let t2 = Unix.gettimeofday () in
1210 simplify_equalities eq_uri env (equalities@library_equalities)
1214 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)));
1215 let t1 = Unix.gettimeofday () in
1218 let thms = Inference.find_library_theorems dbd env (proof, goalno) lib_eq_uris in
1219 let context_hyp = Inference.find_context_hypotheses env eq_indexes in
1220 context_hyp @ thms, []
1222 let refl_equal = LibraryObjects.eq_refl_URI ~eq:eq_uri in
1223 let t = CicUtil.term_of_uri refl_equal in
1224 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
1227 let t2 = Unix.gettimeofday () in
1232 "Theorems:\n-------------------------------------\n%s\n"
1237 "Term: %s, type: %s"
1238 (CicPp.ppterm t) (CicPp.ppterm ty))
1242 (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1)));
1244 let active = make_active () in
1245 let passive = make_passive equalities in
1246 let start = Unix.gettimeofday () in
1249 let goals = make_goals goal in
1250 given_clause_fullred dbd env goals theorems passive active
1252 let goals = make_goal_set goal in
1253 let max_iterations = 10000 in
1254 let max_time = Unix.gettimeofday () +. 600. (* minutes *) in
1256 eq_uri env goals theorems passive active max_iterations max_time
1258 let finish = Unix.gettimeofday () in
1259 (res, finish -. start)
1262 | ParamodulationFailure s ->
1263 raise (ProofEngineTypes.Fail (lazy ("NO proof found: " ^ s)))
1264 | ParamodulationSuccess
1265 (goalproof,newproof,subsumption_id,subsumption_subst, proof_menv) ->
1266 prerr_endline "OK, found a proof!";
1268 (Equality.pp_proof names goalproof newproof subsumption_subst
1269 subsumption_id type_of_goal);
1270 prerr_endline "ENDOFPROOFS";
1271 (* generation of the CIC proof *)
1273 List.filter (fun i -> i <> goalno)
1274 (ProofEngineHelpers.compare_metasenvs
1275 ~newmetasenv:metasenv ~oldmetasenv:proof_menv)
1277 let goal_proof, side_effects_t =
1278 let initial = Equality.add_subst subsumption_subst newproof in
1279 Equality.build_goal_proof
1280 eq_uri goalproof initial type_of_goal side_effects
1283 prerr_endline ("PROOF: " ^ CicPp.pp goal_proof names);
1284 let goal_proof = Subst.apply_subst subsumption_subst goal_proof in
1285 let metas_still_open_in_proof = Utils.metas_of_term goal_proof in
1286 (*prerr_endline (CicPp.pp goal_proof names);*)
1288 let goal_proof = (* Subst.apply_subst subsumption_subst *) goal_proof in
1289 let side_effects_t =
1290 List.map (Subst.apply_subst subsumption_subst) side_effects_t
1292 (* replacing fake mets with real ones *)
1293 prerr_endline "replacing metas...";
1294 let irl=CicMkImplicit.identity_relocation_list_for_metavariable context in
1295 let goal_proof_menv, what, with_what,free_meta =
1297 (fun (acc1,acc2,acc3,uniq) (i,_,ty) ->
1300 acc1, (Cic.Meta(i,[]))::acc2, m::acc3, uniq
1302 [i,context,ty], (Cic.Meta(i,[]))::acc2,
1303 (Cic.Meta(i,irl)) ::acc3,Some (Cic.Meta(i,irl)))
1306 (fun (i,_,_) -> List.mem i metas_still_open_in_proof)
1310 (* we need this fake equality since the metas of the hypothesis may be
1311 * with a real local context *)
1312 ProofEngineReduction.replace_lifting
1313 ~equality:(fun x y ->
1314 match x,y with Cic.Meta(i,_),Cic.Meta(j,_) -> i=j | _-> false)
1315 ~what ~with_what ~where
1317 let goal_proof = replace goal_proof in
1318 (* ok per le meta libere... ma per quelle che c'erano e sono rimaste?
1319 * what mi pare buono, sostituisce solo le meta farlocche *)
1320 let side_effects_t = List.map replace side_effects_t in
1322 List.filter (fun i -> i <> goalno)
1323 (ProofEngineHelpers.compare_metasenvs
1324 ~oldmetasenv:metasenv ~newmetasenv:goal_proof_menv)
1326 prerr_endline ("freemetas: " ^ String.concat "," (List.map string_of_int free_metas) );
1327 (* check/refine/... build the new proof *)
1329 ProofEngineReduction.replace
1330 ~what:side_effects ~with_what:side_effects_t
1331 ~equality:(fun i t -> match t with Cic.Meta(j,_)->j=i|_->false)
1334 let subst_side_effects,real_menv,_ =
1335 let fail t s = raise (ProofEngineTypes.Fail (lazy (t^Lazy.force s))) in
1336 let free_metas_menv =
1337 List.map (fun i -> CicUtil.lookup_meta i goal_proof_menv) free_metas
1340 CicUnification.fo_unif_subst [] context (metasenv @ free_metas_menv)
1341 replaced_goal type_of_goal CicUniv.empty_ugraph
1343 | CicUnification.UnificationFailure s
1344 | CicUnification.Uncertain s
1345 | CicUnification.AssertFailure s ->
1346 fail "Maybe the local context of metas in the goal was not an IRL" s
1349 (goalno,(context,goal_proof,type_of_goal))::subst_side_effects
1351 prerr_endline ("MENVreal_menv: " ^ CicMetaSubst.ppmetasenv [] real_menv);
1354 CicTypeChecker.type_of_aux' real_menv context goal_proof
1355 CicUniv.empty_ugraph
1357 | CicUtil.Meta_not_found _
1358 | CicTypeChecker.TypeCheckerFailure _
1359 | CicTypeChecker.AssertFailure _
1360 | Invalid_argument "list_fold_left2" as exn ->
1361 prerr_endline "THE PROOF DOES NOT TYPECHECK!";
1362 prerr_endline (CicPp.pp goal_proof names);
1363 prerr_endline "THE PROOF DOES NOT TYPECHECK!";
1366 let proof, real_metasenv =
1367 ProofEngineHelpers.subst_meta_and_metasenv_in_proof
1368 proof goalno (CicMetaSubst.apply_subst final_subst) real_menv
1371 match free_meta with Some(Cic.Meta(m,_)) when m<>goalno ->[m] | _ ->[]
1374 "GOALS APERTI: %s\nMETASENV PRIMA:\n%s\nMETASENV DOPO:\n%s\n"
1375 (String.concat ", " (List.map string_of_int open_goals))
1376 (CicMetaSubst.ppmetasenv [] metasenv)
1377 (CicMetaSubst.ppmetasenv [] real_metasenv);
1378 prerr_endline (Printf.sprintf "\nTIME NEEDED: %8.2f" time);
1382 let main _ _ _ _ _ = () ;;
1384 let retrieve_and_print dbd term metasenv ugraph =
1385 let module C = Cic in
1386 let module T = CicTypeChecker in
1387 let module PET = ProofEngineTypes in
1388 let module PP = CicPp in
1389 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
1390 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
1391 let proof, goals = status in
1392 let goal' = List.nth goals 0 in
1393 let uri, metasenv, meta_proof, term_to_prove = proof in
1394 let _, context, type_of_goal = CicUtil.lookup_meta goal' metasenv in
1395 let eq_uri = eq_of_goal type_of_goal in
1396 let eq_indexes, equalities, maxm = Inference.find_equalities context proof in
1397 let ugraph = CicUniv.empty_ugraph in
1398 let env = (metasenv, context, ugraph) in
1399 let t1 = Unix.gettimeofday () in
1400 let lib_eq_uris, library_equalities, maxm =
1401 Inference.find_library_equalities false dbd context (proof, goal') (maxm+2) in
1402 let t2 = Unix.gettimeofday () in
1404 let equalities = (* equalities @ *) library_equalities in
1407 (Printf.sprintf "\n\nequalities:\n%s\n"
1411 (* Printf.sprintf "%s: %s" *)
1412 (UriManager.string_of_uri u)
1413 (* (string_of_equality e) *)
1416 Utils.debug_print (lazy "RETR: SIMPLYFYING EQUALITIES...");
1417 let rec simpl e others others_simpl =
1419 let active = (others @ others_simpl) in
1422 (fun t (_, e) -> Indexing.index t e)
1423 Indexing.empty active
1425 let res = forward_simplify eq_uri env e (active, tbl) in
1429 | None -> simpl hd tl others_simpl
1430 | Some e -> simpl hd tl ((u, e)::others_simpl)
1434 | None -> others_simpl
1435 | Some e -> (u, e)::others_simpl
1439 match equalities with
1442 let others = tl in (* List.map (fun e -> (Utils.Positive, e)) tl in *)
1444 List.rev (simpl (*(Positive,*) hd others [])
1448 (Printf.sprintf "\nequalities AFTER:\n%s\n"
1452 Printf.sprintf "%s: %s"
1453 (UriManager.string_of_uri u)
1454 (Equality.string_of_equality e)
1460 (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1)))
1464 let main_demod_equalities dbd term metasenv ugraph =
1465 let module C = Cic in
1466 let module T = CicTypeChecker in
1467 let module PET = ProofEngineTypes in
1468 let module PP = CicPp in
1469 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
1470 let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
1471 let proof, goals = status in
1472 let goal' = List.nth goals 0 in
1473 let _, metasenv, meta_proof, _ = proof in
1474 let _, context, goal = CicUtil.lookup_meta goal' metasenv in
1475 let eq_uri = eq_of_goal goal in
1476 let eq_indexes, equalities, maxm = Inference.find_equalities context proof in
1477 let lib_eq_uris, library_equalities, maxm =
1478 Inference.find_library_equalities false dbd context (proof, goal') (maxm+2)
1480 let library_equalities = List.map snd library_equalities in
1481 maxmeta := maxm+2; (* TODO ugly!! *)
1482 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
1483 let new_meta_goal, metasenv, type_of_goal =
1484 let _, context, ty = CicUtil.lookup_meta goal' metasenv in
1487 (Printf.sprintf "\n\nTRYING TO INFER EQUALITIES MATCHING: %s\n\n"
1488 (CicPp.ppterm ty)));
1489 Cic.Meta (maxm+1, irl),
1490 (maxm+1, context, ty)::metasenv,
1493 let env = (metasenv, context, ugraph) in
1495 let goal = [], [], goal
1498 simplify_equalities eq_uri env (equalities@library_equalities)
1500 let active = make_active () in
1501 let passive = make_passive equalities in
1502 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
1503 Printf.printf "\nmetasenv:\n%s\n" (Utils.print_metasenv metasenv);
1504 Printf.printf "\nequalities:\n%s\n"
1507 (Equality.string_of_equality ~env) equalities));
1508 print_endline "--------------------------------------------------";
1509 print_endline "GO!";
1510 start_time := Unix.gettimeofday ();
1511 if !time_limit < 1. then time_limit := 60.;
1513 saturate_equations eq_uri env goal (fun e -> true) passive active
1517 List.fold_left (fun s e -> EqualitySet.add e s)
1518 EqualitySet.empty equalities
1521 if not (EqualitySet.mem e initial) then EqualitySet.add e s else s
1527 EqualitySet.elements (List.fold_left addfun EqualitySet.empty p)
1531 EqualitySet.elements (List.fold_left addfun EqualitySet.empty l)
1533 Printf.printf "\n\nRESULTS:\nActive:\n%s\n\nPassive:\n%s\n"
1534 (String.concat "\n" (List.map (Equality.string_of_equality ~env) active))
1535 (* (String.concat "\n"
1536 (List.map (fun e -> CicPp.ppterm (term_of_equality e)) active)) *)
1537 (* (String.concat "\n" (List.map (string_of_equality ~env) passive)); *)
1540 (fun e -> CicPp.ppterm (Equality.term_of_equality eq_uri e))
1545 Utils.debug_print (lazy ("EXCEPTION: " ^ (Printexc.to_string e)))
1549 let demodulate_tac ~dbd ((proof,goal)(*s initialstatus*)) =
1550 let curi,metasenv,pbo,pty = proof in
1551 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
1552 let eq_uri = eq_of_goal ty in
1553 let eq_indexes, equalities, maxm =
1554 Inference.find_equalities context proof
1556 let lib_eq_uris, library_equalities, maxm =
1557 Inference.find_library_equalities false dbd context (proof, goal) (maxm+2) in
1558 if library_equalities = [] then prerr_endline "VUOTA!!!";
1559 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
1560 let library_equalities = List.map snd library_equalities in
1561 let initgoal = [], [], ty in
1562 let env = (metasenv, context, CicUniv.empty_ugraph) in
1564 simplify_equalities eq_uri env (equalities@library_equalities)
1568 (fun tbl eq -> Indexing.index tbl eq)
1569 Indexing.empty equalities
1571 let changed,(newproof,newmetasenv, newty) =
1572 Indexing.demodulation_goal
1573 (metasenv,context,CicUniv.empty_ugraph) table initgoal
1577 let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
1579 Equality.build_goal_proof
1580 eq_uri newproof opengoal ty [] context metasenv
1582 let extended_metasenv = (maxm,context,newty)::metasenv in
1583 let extended_status =
1584 (curi,extended_metasenv,pbo,pty),goal in
1585 let (status,newgoals) =
1586 ProofEngineTypes.apply_tactic
1587 (PrimitiveTactics.apply_tac ~term:proofterm)
1589 (status,maxm::newgoals)
1591 else (* if newty = ty then *)
1592 raise (ProofEngineTypes.Fail (lazy "no progress"))
1593 (*else ProofEngineTypes.apply_tactic
1594 (ReductionTactics.simpl_tac
1595 ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
1598 let demodulate_tac ~dbd = ProofEngineTypes.mk_tactic (demodulate_tac ~dbd);;
1600 let rec find_in_ctx i name = function
1601 | [] -> raise (ProofEngineTypes.Fail (lazy ("Hypothesis not found: " ^ name)))
1602 | Some (Cic.Name name', _)::tl when name = name' -> i
1603 | _::tl -> find_in_ctx (i+1) name tl
1606 let rec position_of i x = function
1607 | [] -> assert false
1608 | j::tl when j <> x -> position_of (i+1) x tl
1613 * auto superposition target = NAME
1614 * [table = NAME_LIST] [demod_table = NAME_LIST] [subterms_only]
1616 * - if table is omitted no superposition will be performed
1617 * - if demod_table is omitted no demodulation will be prformed
1618 * - subterms_only is passed to Indexing.superposition_right
1620 * lists are coded using _ (example: H_H1_H2)
1623 let superposition_tac ~target ~table ~subterms_only ~demod_table status =
1625 Indexing.init_index ();
1626 let proof,goalno = status in
1627 let curi,metasenv,pbo,pty = proof in
1628 let metano,context,ty = CicUtil.lookup_meta goalno metasenv in
1629 let eq_uri,tty = eq_and_ty_of_goal ty in
1630 let env = (metasenv, context, CicUniv.empty_ugraph) in
1631 let names = Utils.names_of_context context in
1632 let eq_index, equalities, maxm = Inference.find_equalities context proof in
1634 let what = find_in_ctx 1 target context in
1635 List.nth equalities (position_of 0 what eq_index)
1640 let others = Str.split (Str.regexp "_") table in
1641 List.map (fun other -> find_in_ctx 1 other context) others
1644 (fun other -> List.nth equalities (position_of 0 other eq_index))
1649 let index = List.fold_left Indexing.index Indexing.empty eq_other in
1651 if table = "" then maxm,[eq_what] else
1652 Indexing.superposition_right
1653 ~subterms_only eq_uri maxm env index eq_what
1655 prerr_endline ("Superposition right:");
1656 prerr_endline ("\n eq: " ^ Equality.string_of_equality eq_what ~env);
1657 prerr_endline ("\n table: ");
1658 List.iter (fun e -> prerr_endline (" " ^ Equality.string_of_equality e ~env)) eq_other;
1659 prerr_endline ("\n result: ");
1660 List.iter (fun e -> prerr_endline (Equality.string_of_equality e ~env)) eql;
1661 prerr_endline ("\n result (cut&paste): ");
1664 let t = Equality.term_of_equality eq_uri e in
1665 prerr_endline (CicPp.pp t names))
1667 prerr_endline ("\n result proofs: ");
1669 prerr_endline (let _,p,_,_,_ = Equality.open_equality e in
1670 let s = match p with Equality.Exact _ -> Subst.empty_subst | Equality.Step (s,_) -> s in
1671 Subst.ppsubst s ^ "\n" ^
1672 CicPp.pp (Equality.build_proof_term eq_uri [] 0 p) names)) eql;
1673 if demod_table <> "" then
1676 if eql = [] then [eq_what] else eql
1679 let demod = Str.split (Str.regexp "_") demod_table in
1680 List.map (fun other -> find_in_ctx 1 other context) demod
1684 (fun demod -> List.nth equalities (position_of 0 demod eq_index))
1687 let table = List.fold_left Indexing.index Indexing.empty eq_demod in
1690 (fun (maxm,acc) e ->
1692 Indexing.demodulation_equality eq_uri maxm env table e
1697 let eql = List.rev eql in
1698 prerr_endline ("\n result [demod]: ");
1700 (fun e -> prerr_endline (Equality.string_of_equality e ~env)) eql;
1701 prerr_endline ("\n result [demod] (cut&paste): ");
1704 let t = Equality.term_of_equality eq_uri e in
1705 prerr_endline (CicPp.pp t names))
1712 <:show<Saturation.>> ^ Indexing.get_stats () ^ Inference.get_stats () ^
1713 Equality.get_stats ()