1 (* Copyright (C) 2002, 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/.
31 if debug then prerr_endline (Lazy.force s);;
34 let mk_irl ctx = CicMkImplicit.identity_relocation_list_for_metavariable ctx;;
35 let ugraph = CicUniv.oblivion_ugraph;;
36 let typeof = CicTypeChecker.type_of_aux';;
38 let names = List.map (function None -> None | Some (x,_) -> Some x) ctx in
41 let is_propositional context sort =
42 match CicReduction.whd context sort with
44 | Cic.Sort (Cic.CProp _) -> true
47 let is_in_prop context subst metasenv ty =
48 let sort,u = typeof ~subst metasenv context ty CicUniv.oblivion_ugraph in
49 is_propositional context sort
52 exception NotConvertible;;
54 let check_proof_is_valid proof metasenv context goalty =
58 let ty,u = typeof metasenv context proof CicUniv.oblivion_ugraph in
59 let b,_ = CicReduction.are_convertible context ty goalty u in
60 if not b then raise NotConvertible else b
63 List.map (function None -> None | Some (x,_) -> Some x) context
65 debug_print (lazy ("PROOF:" ^ CicPp.pp proof names));
66 (* debug_print (lazy ("PROOFTY:" ^ CicPp.pp ty names)); *)
67 debug_print (lazy ("GOAL:" ^ CicPp.pp goalty names));
68 debug_print (lazy ("MENV:" ^ CicMetaSubst.ppmetasenv [] metasenv));
74 let assert_proof_is_valid proof metasenv context goalty =
75 assert (check_proof_is_valid proof metasenv context goalty)
78 let assert_subst_are_disjoint subst subst' =
81 (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst')
86 let split_goals_in_prop metasenv subst gl =
89 let _,context,ty = CicUtil.lookup_meta g metasenv in
91 let sort,u = typeof ~subst metasenv context ty ugraph in
92 is_propositional context sort
94 | CicTypeChecker.AssertFailure s
95 | CicTypeChecker.TypeCheckerFailure s ->
97 (lazy ("NON TIPA" ^ ppterm context (CicMetaSubst.apply_subst subst ty)));
100 (* FIXME... they should type! *)
104 let split_goals_with_metas metasenv subst gl =
107 let _,context,ty = CicUtil.lookup_meta g metasenv in
108 let ty = CicMetaSubst.apply_subst subst ty in
109 CicUtil.is_meta_closed ty)
113 let order_new_goals metasenv subst open_goals ppterm =
114 let prop,rest = split_goals_in_prop metasenv subst open_goals in
115 let closed_prop, open_prop = split_goals_with_metas metasenv subst prop in
116 let closed_type, open_type = split_goals_with_metas metasenv subst rest in
118 (List.map (fun x -> x,P) (open_prop @ closed_prop))
120 (List.map (fun x -> x,T) (open_type @ closed_type))
125 let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty,sort) open_goals
127 debug_print (lazy (" OPEN: "^
131 | (i,t,P) -> string_of_int i ^ ":"^ppterm t^ "Prop"
132 | (i,t,T) -> string_of_int i ^ ":"^ppterm t^ "Type")
137 let is_an_equational_goal = function
138 | Cic.Appl [Cic.MutInd(u,_,_);_;_;_] when LibraryObjects.is_eq_URI u -> true
142 type auto_params = Cic.term list * (string * string) list
144 let elems = ref [] ;;
146 (* closing a term w.r.t. its metavariables
147 very naif version: it does not take dependencies properly into account *)
149 let naif_closure ?(prefix_name="xxx_") t metasenv context =
150 let in_term t (i,_,_) =
151 List.exists (fun (j,_) -> j=i) (CicUtil.metas_of_term t)
153 let metasenv = List.filter (in_term t) metasenv in
154 let metasenv = ProofEngineHelpers.sort_metasenv metasenv in
155 let n = List.length metasenv in
156 let what = List.map (fun (i,cc,ty) -> Cic.Meta(i,[])) metasenv in
159 (fun (i,acc) (_,cc,ty) -> (i-1,Cic.Rel i::acc))
162 let t = CicSubstitution.lift n t in
164 ProofEngineReduction.replace_lifting
165 ~equality:(fun c t1 t2 ->
167 | Cic.Meta(i,_),Cic.Meta(j,_) -> i = j
169 ~context ~what ~with_what ~where:t
173 (fun (n,t) (_,cc,ty) ->
174 n-1, Cic.Lambda(Cic.Name (prefix_name^string_of_int n),
175 CicSubstitution.lift n ty,t))
178 t, List.length metasenv
181 let lambda_close ?prefix_name t menv ctx =
182 let t, num_lambdas = naif_closure ?prefix_name t menv ctx in
184 (fun (t,i) -> function
185 | None -> CicSubstitution.subst (Cic.Implicit None) t,i (* delift *)
186 | Some (name, Cic.Decl ty) -> Cic.Lambda (name, ty, t),i+1
187 | Some (name, Cic.Def (bo, ty)) -> Cic.LetIn (name, bo, ty, t),i+1)
191 (* functions for retrieving theorems *)
194 exception FillingFailure of AutoCache.cache * AutomationCache.tables
196 let rec unfold context = function
197 | Cic.Prod(name,s,t) ->
198 let t' = unfold ((Some (name,Cic.Decl s))::context) t in
200 | t -> ProofEngineReduction.unfold context t
202 let find_library_theorems dbd proof goal =
203 let univ = MetadataQuery.universe_of_goal ~dbd false proof goal in
204 let terms = List.map CicUtil.term_of_uri univ in
207 (t,fst(CicTypeChecker.type_of_aux' [] [] t CicUniv.oblivion_ugraph)))
210 let find_context_theorems context metasenv =
213 (fun (res,i) ctxentry ->
215 | Some (_,Cic.Decl t) ->
216 (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
217 | Some (_,Cic.Def (_,t)) ->
218 (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
223 let rec is_an_equality = function
224 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
225 when (LibraryObjects.is_eq_URI uri) -> true
226 | Cic.Prod (_, _, t) -> is_an_equality t
230 let partition_equalities =
231 List.partition (fun (_,ty) -> is_an_equality ty)
234 let default_auto tables _ cache _ _ _ _ = [],cache,tables ;;
236 (* giusto per provare che succede
237 let is_unit_equation context metasenv oldnewmeta term =
238 let head, metasenv, args, newmeta =
239 TermUtil.saturate_term oldnewmeta metasenv context term 0
242 List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv
244 Some (args,metasenv,newmetas,head,newmeta) *)
246 let is_unit_equation context metasenv oldnewmeta term =
247 let head, metasenv, args, newmeta =
248 TermUtil.saturate_term oldnewmeta metasenv context term 0
250 let propositional_args =
254 let _,_,mt = CicUtil.lookup_meta i metasenv in
256 CicTypeChecker.type_of_aux' metasenv context mt
257 CicUniv.oblivion_ugraph
259 if is_propositional context sort then Some i else None
263 if propositional_args = [] then
265 List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv
267 Some (args,metasenv,newmetas,head,newmeta)
271 let get_candidates skip_trie_filtering universe cache t =
272 let t = if skip_trie_filtering then Cic.Meta(0,[]) else t in
274 (Universe.get_candidates universe t)@(AutoCache.get_candidates cache t)
277 (lazy ("candidates for " ^ (CicPp.ppterm t) ^ " = " ^
278 (String.concat "\n" (List.map CicPp.ppterm candidates)))) in
279 debug_print debug_msg;
283 let only signature context metasenv t =
286 CicTypeChecker.type_of_aux' metasenv context t CicUniv.oblivion_ugraph
288 let consts = MetadataConstraints.constants_of ty in
289 let b = MetadataConstraints.UriManagerSet.subset consts signature in
290 (* if b then (prerr_endline ("keeping " ^ (CicPp.ppterm t)); b) *)
293 let ty' = unfold context ty in
294 let consts' = MetadataConstraints.constants_of ty' in
295 let b = MetadataConstraints.UriManagerSet.subset consts' signature in
297 if not b then prerr_endline ("filtering " ^ (CicPp.ppterm t))
298 else prerr_endline ("keeping " ^ (CicPp.ppterm t));
302 | CicTypeChecker.TypeCheckerFailure _ -> assert false
303 | ProofEngineTypes.Fail _ -> false (* unfold may fail *)
306 let not_default_eq_term t =
308 let uri = CicUtil.uri_of_term t in
309 not (LibraryObjects.in_eq_URIs uri)
310 with Invalid_argument _ -> true
312 let retrieve_equations dont_filter signature universe cache context metasenv =
313 match LibraryObjects.eq_URI() with
316 let eq_uri = UriManager.strip_xpointer eq_uri in
317 let fake= Cic.Meta(-1,[]) in
318 let fake_eq = Cic.Appl [Cic.MutInd (eq_uri,0, []);fake;fake;fake] in
319 let candidates = get_candidates false universe cache fake_eq in
320 if dont_filter then candidates
321 else let eq_uri = UriManager.uri_of_uriref eq_uri 0 None in
322 (* let candidates = List.filter not_default_eq_term candidates in *)
324 (only (MetadataConstraints.UriManagerSet.add eq_uri signature)
325 context metasenv) candidates
327 let build_equality bag head args proof newmetas =
329 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] ->
331 if args = [] then proof else Cic.Appl (proof::args)
333 let o = !Utils.compare_terms t1 t2 in
334 let stat = (ty,t1,t2,o) in
335 (* let w = compute_equality_weight stat in *)
337 let proof = Equality.Exact p in
338 let bag, e = Equality.mk_equality bag (w, proof, stat, newmetas) in
339 (* to clean the local context of metas *)
340 Equality.fix_metas bag e
344 let partition_unit_equalities context metasenv newmeta bag equations =
346 (fun (bag,units,other,maxmeta)(t,ty) ->
347 if not (CicUtil.is_meta_closed t && CicUtil.is_meta_closed ty) then
350 ("Skipping " ^ CicMetaSubst.ppterm_in_context ~metasenv [] t context
351 ^ " since it is not meta closed")
353 bag, units,(t,ty)::other,maxmeta
355 match is_unit_equation context metasenv maxmeta ty with
356 | Some (args,metasenv,newmetas,head,newmeta') ->
358 build_equality bag head args t newmetas in
359 bag, equality::units,other,maxmeta
361 bag, units,(t,ty)::other,maxmeta)
362 (bag,[],[],newmeta) equations
365 let init_cache_and_tables
366 ?dbd ~use_library ~use_context
367 automation_cache restricted_univ (proof, goal)
369 let _, metasenv, subst, _, _, _ = proof in
370 let _,context,_ = CicUtil.lookup_meta goal metasenv in
371 let is_prop m s c t =
373 CicTypeChecker.type_of_aux' m ~subst:s c t CicUniv.oblivion_ugraph
376 CicTypeChecker.type_of_aux' m ~subst:s c ty CicUniv.oblivion_ugraph
378 match CicReduction.whd ~subst c sort with
379 | Cic.Sort Cic.Prop | Cic.Sort (Cic.CProp _) -> true
382 if restricted_univ = [] then
384 if use_context then find_context_theorems context metasenv else []
387 match use_library, dbd with
388 | true, Some dbd -> find_library_theorems dbd metasenv goal
391 let cache = AutoCache.cache_empty in
392 let cache = cache_add_list cache context (ct@lt) in
393 let automation_cache, _ =
395 (fun (c,maxmeta) (t,ty) ->
396 let head, metasenv, args, maxmeta =
397 TermUtil.saturate_term maxmeta metasenv context ty 0
399 if List.exists (is_prop metasenv subst context) args then
402 let st = if args = [] then t else Cic.Appl (t::args) in
403 AutomationCache.add_term_to_active
404 c metasenv [] context st (Some head), maxmeta)
405 (automation_cache,CicMkImplicit.new_meta metasenv subst) ct
407 (* AutomationCache.pp_cache automation_cache; *)
408 automation_cache.AutomationCache.univ,
409 automation_cache.AutomationCache.tables,
412 let metasenv, t_ty, s_t_ty, _ =
414 (fun (metasenv as orig,acc, sacc, maxmeta) t ->
416 CicTypeChecker.type_of_aux'
417 metasenv ~subst:[] context t CicUniv.oblivion_ugraph
419 let head, metasenv, args, maxmeta =
420 TermUtil.saturate_term maxmeta metasenv context ty 0
422 if List.exists (is_prop metasenv subst context) args then
423 orig, (t,ty)::acc, sacc, maxmeta
425 let st = if args = [] then t else Cic.Appl (t::args) in
426 metasenv, (t, ty)::acc, (st,head)::sacc, maxmeta)
427 (metasenv, [],[], CicMkImplicit.new_meta metasenv subst) restricted_univ
429 let automation_cache = AutomationCache.empty () in
430 let automation_cache =
431 let universe = automation_cache.AutomationCache.univ in
433 Universe.index_list universe context t_ty
435 { automation_cache with AutomationCache.univ = universe }
437 let automation_cache =
440 AutomationCache.add_term_to_active c metasenv [] context t (Some ty))
441 automation_cache s_t_ty
443 (* AutomationCache.pp_cache automation_cache; *)
444 automation_cache.AutomationCache.univ,
445 automation_cache.AutomationCache.tables,
446 cache_add_list cache_empty context t_ty
449 (* let signature = MetadataQuery.signature_of metasenv goal in *)
450 (* let newmeta = CicMkImplicit.new_meta metasenv [] in *)
452 retrieve_equations dont_filter (* true *) signature universe cache context metasenv
455 (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
460 CicTypeChecker.type_of_aux'
461 metasenv context t CicUniv.oblivion_ugraph
463 (* retrieve_equations could also return flexible terms *)
464 if is_an_equality ty then Some(t,ty)
467 let ty' = unfold context ty in
468 if is_an_equality ty' then Some(t,ty') else None
469 with ProofEngineTypes.Fail _ -> None)
472 let bag = Equality.mk_equality_bag () in
473 let units, other_equalities, newmeta =
474 partition_unit_equalities context metasenv newmeta bag eqs_and_types
476 (* SIMPLIFICATION STEP
478 let env = (metasenv, context, CicUniv.oblivion_ugraph) in
479 let eq_uri = HExtlib.unopt (LibraryObjects.eq_URI()) in
480 Saturation.simplify_equalities bag eq_uri env units
483 let passive = Saturation.make_passive units in
484 let no = List.length units in
485 let active = Saturation.make_active [] in
486 let active,passive,newmeta =
487 if paramod then active,passive,newmeta
489 Saturation.pump_actives
490 context bag newmeta active passive (no+1) infinity
492 (active,passive,bag),cache,newmeta
495 let fill_hypothesis context metasenv term tables (universe:Universe.universe) cache auto fast =
496 let actives, passives, bag = tables in
497 let bag, head, metasenv, args =
498 Equality.saturate_term bag metasenv context term
500 let tables = actives, passives, bag in
501 let propositional_args =
505 let _,_,mt = CicUtil.lookup_meta i metasenv in
507 CicTypeChecker.type_of_aux' metasenv context mt
508 CicUniv.oblivion_ugraph
510 if is_propositional context sort then Some i else None
514 let results,cache,tables =
515 if propositional_args = [] then
516 let _,_,bag = tables in
517 let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
518 [args,metasenv,newmetas,head],cache,tables
522 None,metasenv,term,term (* term non e' significativo *)
526 {AutoTypes.default_flags() with
527 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
528 maxwidth = 2;maxdepth = 2;
529 use_paramod=true;use_only_paramod=false}
531 {AutoTypes.default_flags() with
532 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
533 maxwidth = 2;maxdepth = 4;
534 use_paramod=true;use_only_paramod=false}
536 match auto tables universe cache context metasenv propositional_args flags with
537 | [],cache,tables -> raise (FillingFailure (cache,tables))
538 | substs,cache,tables ->
539 let actives, passaives, bag = tables in
542 (fun subst (bag,acc) ->
544 CicMetaSubst.apply_subst_metasenv subst metasenv
546 let head = CicMetaSubst.apply_subst subst head in
547 let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
548 let args = List.map (CicMetaSubst.apply_subst subst) args in
549 let newm = CicMkImplicit.new_meta metasenv subst in
550 let bag = Equality.push_maxmeta bag newm in
551 bag, ((args,metasenv,newmetas,head) :: acc))
554 let tables = actives, passives, bag in
560 let build_equalities auto context metasenv tables universe cache equations =
562 (fun (tables,facts,cache) (t,ty) ->
563 (* in any case we add the equation to the cache *)
564 let cache = AutoCache.cache_add_list cache context [(t,ty)] in
566 let saturated, cache, tables =
567 fill_hypothesis context metasenv ty tables universe cache auto true
571 (fun (acc, tables) (args,metasenv,newmetas,head) ->
572 let actives, passives, bag = tables in
574 build_equality bag head args t newmetas
576 let tables = actives, passives, bag in
577 equality::acc,tables)
578 ([],tables) saturated
580 (tables, eqs@facts, cache)
581 with FillingFailure (cache,tables) ->
582 (* if filling hypothesis fails we add the equation to
586 (tables,[],cache) equations
588 let close_more tables context status auto universe cache =
589 let proof, goalno = status in
590 let _, metasenv,_subst,_,_, _ = proof in
591 let signature = MetadataQuery.signature_of metasenv goalno in
593 retrieve_equations false signature universe cache context metasenv
599 CicTypeChecker.type_of_aux' metasenv context t
600 CicUniv.oblivion_ugraph in
601 (* retrieve_equations could also return flexible terms *)
602 if is_an_equality ty then Some(t,ty) else None)
604 let tables, units, cache =
605 build_equalities auto context metasenv tables universe cache eqs_and_types
607 let active,passive,bag = tables in
608 let passive = Saturation.add_to_passive units passive in
609 let no = List.length units in
610 let active, passive, bag =
611 Saturation.pump_actives context bag active passive (no+1) infinity
613 (active,passive,bag), cache
616 let find_context_equalities dbd tables context proof (universe:Universe.universe) cache
618 let module C = Cic in
619 let module S = CicSubstitution in
620 let module T = CicTypeChecker in
621 let _,metasenv,_subst,_,_, _ = proof in
622 (* if use_auto is true, we try to close the hypothesis of equational
623 statements using auto; a naif, and probably wrong approach *)
624 let rec aux tables cache index = function
625 | [] -> tables, [], cache
626 | (Some (_, C.Decl (term)))::tl ->
629 (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term)));
630 let do_find tables context term =
632 | C.Prod (name, s, t) when is_an_equality t ->
634 let term = S.lift index term in
635 let saturated, cache, tables =
636 fill_hypothesis context metasenv term
637 tables universe cache default_auto false
639 let actives, passives, bag = tables in
642 (fun (bag,acc) (args,metasenv,newmetas,head) ->
644 build_equality bag head args (Cic.Rel index) newmetas
649 let tables = actives, passives, bag in
651 with FillingFailure (cache,tables) ->
653 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
654 when LibraryObjects.is_eq_URI uri ->
655 let term = S.lift index term in
656 let actives, passives, bag = tables in
658 build_equality bag term [] (Cic.Rel index) []
660 let tables = actives, passives, bag in
662 | _ -> tables, [], cache
664 let tables, eqs, cache = do_find tables context term in
665 let tables, rest, cache = aux tables cache (index+1) tl in
666 tables, List.map (fun x -> index,x) eqs @ rest, cache
668 aux tables cache (index+1) tl
670 let tables, il, cache = aux tables cache 1 context in
671 let indexes, equalities = List.split il in
672 tables, indexes, equalities, cache
675 (********** PARAMETERS PASSING ***************)
677 let bool params name default =
679 let s = List.assoc name params in
680 if s = "" || s = "1" || s = "true" || s = "yes" || s = "on" then true
681 else if s = "0" || s = "false" || s = "no" || s= "off" then false
683 let msg = "Unrecognized value for parameter "^name^"\n" in
684 let msg = msg^"Accepted values are 1,true,yes,on and 0,false,no,off" in
685 raise (ProofEngineTypes.Fail (lazy msg))
686 with Not_found -> default
689 let string params name default =
690 try List.assoc name params with
691 | Not_found -> default
694 let int params name default =
695 try int_of_string (List.assoc name params) with
696 | Not_found -> default
698 raise (ProofEngineTypes.Fail (lazy (name ^ " must be an integer")))
701 let flags_of_params params ?(for_applyS=false) () =
702 let int = int params in
703 let bool = bool params in
704 let close_more = bool "close_more" false in
705 let use_paramod = bool "use_paramod" true in
706 let skip_trie_filtering = bool "skip_trie_filtering" false in
707 let skip_context = bool "skip_context" false in
708 let use_only_paramod =
709 if for_applyS then true else bool "paramodulation" false in
710 let use_library = bool "library"
711 ((AutoTypes.default_flags()).AutoTypes.use_library) in
712 let depth = int "depth" ((AutoTypes.default_flags()).AutoTypes.maxdepth) in
713 let width = int "width" ((AutoTypes.default_flags()).AutoTypes.maxwidth) in
714 let size = int "size" ((AutoTypes.default_flags()).AutoTypes.maxsize) in
715 let gsize = int "gsize" ((AutoTypes.default_flags()).AutoTypes.maxgoalsizefactor) in
716 let do_type = bool "type" false in
717 let timeout = int "timeout" 0 in
718 { AutoTypes.maxdepth =
719 if use_only_paramod then 2 else depth;
720 AutoTypes.maxwidth = width;
721 AutoTypes.maxsize = size;
724 if for_applyS then Unix.gettimeofday () +. 30.0
728 Unix.gettimeofday() +. (float_of_int timeout);
729 AutoTypes.use_library = use_library;
730 AutoTypes.use_paramod = use_paramod;
731 AutoTypes.use_only_paramod = use_only_paramod;
732 AutoTypes.close_more = close_more;
733 AutoTypes.dont_cache_failures = false;
734 AutoTypes.maxgoalsizefactor = gsize;
735 AutoTypes.do_types = do_type;
736 AutoTypes.skip_trie_filtering = skip_trie_filtering;
737 AutoTypes.skip_context = skip_context;
741 let eq_of_goal = function
742 | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri ->
744 | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
747 (* performs steps of rewrite with the universe, obtaining if possible
749 let solve_rewrite ~automation_cache ~params:(univ,params) (proof,goal)=
750 let steps = int_of_string (string params "steps" "4") in
751 let use_context = bool params "use_context" true in
752 let universe, tables, cache =
753 init_cache_and_tables ~use_library:false ~use_context
754 automation_cache univ (proof,goal)
756 let actives, passives, bag = tables in
757 let pa,metasenv,subst,pb,pc,pd = proof in
758 let _,context,ty = CicUtil.lookup_meta goal metasenv in
759 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
760 let context = CicMetaSubst.apply_subst_context subst context in
761 let ty = CicMetaSubst.apply_subst subst ty in
762 let eq_uri = eq_of_goal ty in
763 let initgoal = [], metasenv, ty in
765 let equalities = (Saturation.list_of_passive passives) in
766 List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd actives) equalities
768 let env = metasenv,context,CicUniv.oblivion_ugraph in
769 debug_print (lazy ("demod to solve: " ^ CicPp.ppterm ty));
770 match Indexing.solve_demodulating bag env table initgoal steps with
771 | Some (bag, gproof, metasenv, sub_subst, proof) ->
772 let subst_candidates,extra_infos =
776 if i <> goal && c = context then Some (i,(c,ty)) else None)
779 let proofterm,proto_subst =
780 let proof = Equality.add_subst sub_subst proof in
781 Equality.build_goal_proof
782 bag eq_uri gproof proof ty subst_candidates context metasenv
784 let proofterm = Subst.apply_subst sub_subst proofterm in
787 (fun (i,((c,ty),t)) ->
789 | Cic.Meta (j,_) when i=j -> None
790 | _ -> Some (i,(c,t,ty)))
791 (List.combine subst_candidates
792 (List.combine extra_infos proto_subst))
794 let subst = subst @ extrasubst in
795 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
796 let proofterm, _, metasenv,subst, _ =
797 CicRefine.type_of metasenv subst context proofterm
798 CicUniv.oblivion_ugraph
800 let status = (pa,metasenv,subst,pb,pc,pd), goal in
801 ProofEngineTypes.apply_tactic
802 (PrimitiveTactics.apply_tac ~term:proofterm) status
805 (ProofEngineTypes.Fail (lazy
806 ("Unable to solve with " ^ string_of_int steps ^ " demodulations")))
809 (* Demodulate thorem *)
810 let open_type ty bo =
811 let rec open_type_aux context ty k args =
813 | Cic.Prod (n,s,t) ->
815 FreshNamesGenerator.mk_fresh_name [] context n ~typ:s ~subst:[] in
816 let entry = match n' with
817 | Cic.Name _ -> Some (n',(Cic.Decl s))
818 | Cic.Anonymous -> None
820 open_type_aux (entry::context) t (k+1) ((Cic.Rel k)::args)
821 | Cic.LetIn (n,s,sty,t) ->
822 let entry = Some (n,(Cic.Def (s,sty)))
824 open_type_aux (entry::context) t (k+1) args
825 | _ -> context, ty, args
827 let context, ty, args = open_type_aux [] ty 1 [] in
829 | [] -> context, ty, bo
830 | _ -> context, ty, Cic.Appl (bo::args)
833 let rec close_type bo ty context =
835 | [] -> assert_proof_is_valid bo [] [] ty; (bo,ty)
836 | Some (n,(Cic.Decl s))::tl ->
837 close_type (Cic.Lambda (n,s,bo)) (Cic.Prod (n,s,ty)) tl
838 | Some (n,(Cic.Def (s,sty)))::tl ->
839 close_type (Cic.LetIn (n,s,sty,bo)) (Cic.LetIn (n,s,sty,ty)) tl
843 let is_subsumed univ context ty =
844 let candidates = Universe.get_candidates univ ty in
848 | Some found -> Some found
852 CicMkImplicit.identity_relocation_list_for_metavariable in
853 let metasenv = [(0,context,ty)] in
855 None,metasenv,[] , (lazy (Cic.Meta(0,mk_irl context))),ty,[]
857 let (_,metasenv,subst,_,_,_), open_goals =
858 ProofEngineTypes.apply_tactic
859 (PrimitiveTactics.apply_tac ~term:cand)
862 let prop_goals, other =
863 split_goals_in_prop metasenv subst open_goals
865 if prop_goals = [] then Some cand else None
867 | ProofEngineTypes.Fail s -> None
868 | CicUnification.Uncertain s -> None
872 let demodulate_theorem ~automation_cache uri =
874 match LibraryObjects.eq_URI () with
876 | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
877 let obj,_ = CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
881 | Cic.Constant(n, _, ty ,_, _) -> open_type ty (Cic.Const(uri,[]))
882 | _ -> raise (ProofEngineTypes.Fail (lazy "not a theorem"))
884 if CicUtil.is_closed ty then
885 raise (ProofEngineTypes.Fail (lazy ("closed term: dangerous reduction")));
886 let initgoal = [], [], ty in
887 (* compute the signature *)
889 let ty_set = MetadataConstraints.constants_of ty in
890 let hyp_set = MetadataQuery.signature_of_hypothesis context [] in
891 let set = MetadataConstraints.UriManagerSet.union ty_set hyp_set in
892 MetadataQuery.close_with_types set [] context
894 (* retrieve equations from the universe universe *)
895 (* XXX automation_cache *)
896 let universe = automation_cache.AutomationCache.univ in
898 retrieve_equations true signature universe AutoCache.cache_empty context []
901 (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
906 CicTypeChecker.type_of_aux' [] context t CicUniv.oblivion_ugraph
908 (* retrieve_equations could also return flexible terms *)
909 if is_an_equality ty then Some(t,ty)
912 let ty' = unfold context ty in
913 if is_an_equality ty' then Some(t,ty') else None
914 with ProofEngineTypes.Fail _ -> None)
917 let bag = Equality.mk_equality_bag () in
919 let bag, units, _, newmeta =
920 partition_unit_equalities context [] (CicMkImplicit.new_meta [] []) bag eqs_and_types
924 (fun tbl eq -> Indexing.index tbl eq)
927 let changed,(newproof,newmetasenv, newty) =
929 ([],context,CicUniv.oblivion_ugraph) table initgoal in
932 let oldproof = Equality.Exact bo in
934 Equality.build_goal_proof (~contextualize:false) (~forward:true) bag
935 eq_uri newproof oldproof ty [] context newmetasenv
937 if newmetasenv <> [] then
938 raise (ProofEngineTypes.Fail (lazy ("metasenv not empty")))
941 assert_proof_is_valid proofterm newmetasenv context newty;
942 match is_subsumed universe context newty with
944 (ProofEngineTypes.Fail (lazy ("subsumed by " ^ CicPp.ppterm t)))
945 | None -> close_type proofterm newty context
948 else (* if newty = ty then *)
949 raise (ProofEngineTypes.Fail (lazy "no progress"))
950 (*else ProofEngineTypes.apply_tactic
951 (ReductionTactics.simpl_tac
952 ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
957 let demodulate ~dbd ~automation_cache ~params:(univ, params) (proof,goal)=
958 let universe, tables, cache =
959 init_cache_and_tables
960 ~dbd ~use_library:false ~use_context:true
961 automation_cache univ (proof,goal)
964 match LibraryObjects.eq_URI () with
966 | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
967 let active, passive, bag = tables in
968 let curi,metasenv,subst,pbo,pty, attrs = proof in
969 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
970 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
971 let initgoal = [], metasenv, ty in
972 let equalities = (Saturation.list_of_passive passive) in
973 (* we demodulate using both actives passives *)
974 let env = metasenv,context,CicUniv.empty_ugraph in
975 debug_print (lazy ("PASSIVES:" ^ string_of_int(List.length equalities)));
976 List.iter (fun e -> debug_print (lazy (Equality.string_of_equality ~env e)))
980 (fun tbl eq -> Indexing.index tbl eq)
981 (snd active) equalities
983 let changed,(newproof,newmetasenv, newty) =
984 (* Indexing.demodulation_goal bag *)
986 (metasenv,context,CicUniv.oblivion_ugraph) table initgoal
990 let maxm = CicMkImplicit.new_meta metasenv subst in
991 let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
992 let subst_candidates = List.map (fun (i,_,_) -> i) metasenv in
993 let subst_candidates = List.filter (fun x-> x <> goal) subst_candidates in
994 let proofterm, proto_subst =
995 Equality.build_goal_proof (~contextualize:false) bag
996 eq_uri newproof opengoal ty subst_candidates context metasenv
998 (* XXX understan what to do with proto subst *)
999 let metasenv = (maxm,context,newty)::metasenv in
1000 let proofterm, _, metasenv, subst, _ =
1001 CicRefine.type_of metasenv subst context proofterm
1002 CicUniv.oblivion_ugraph
1004 let extended_status = (curi,metasenv,subst,pbo,pty, attrs),goal in
1006 ProofEngineTypes.apply_tactic
1007 (PrimitiveTactics.apply_tac ~term:proofterm) extended_status
1012 raise (ProofEngineTypes.Fail (lazy "no progress"))
1015 let demodulate_tac ~dbd ~params:(_,flags as params) ~automation_cache =
1016 ProofEngineTypes.mk_tactic
1018 let all = bool flags "all" false in
1020 solve_rewrite ~params ~automation_cache status
1022 demodulate ~dbd ~params ~automation_cache status)
1024 (***************** applyS *******************)
1027 dbd automation_cache params proof goal newmeta' metasenv' subst
1028 context term' ty termty goal_arity
1030 let consthead,newmetasenv,arguments,_ =
1031 TermUtil.saturate_term newmeta' metasenv' context termty goal_arity in
1033 match arguments with
1035 | _ -> Cic.Appl (term'::arguments)
1038 let rec aux t = function
1040 let t = CicReduction.normalize ~delta:false context t in
1042 | Cic.Appl (hd1::_), Cic.Appl (hd2::_) when hd1 <> hd2 ->
1043 let t = ProofEngineReduction.unfold context t in
1045 | Cic.Appl (hd1'::_) when hd1' = hd2 -> t
1046 | _ -> raise (ProofEngineTypes.Fail (lazy "incompatible head")))
1049 match CicReduction.whd context t with
1050 | Cic.Prod (_,_,tgt) ->
1051 aux (CicSubstitution.subst arg tgt) tl
1054 aux termty arguments
1056 let goal_for_paramod =
1057 match LibraryObjects.eq_URI () with
1059 Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Implicit (Some `Type); consthead; ty]
1060 | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined"))
1063 let goal_for_paramod, _, newmetasenv, subst, _ =
1064 CicRefine.type_of newmetasenv subst context goal_for_paramod
1065 CicUniv.oblivion_ugraph
1067 let newmeta = CicMkImplicit.new_meta newmetasenv subst in
1068 let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in
1070 let uri,_,_,p,ty, attrs = proof in
1071 uri,metasenv_for_paramod,subst,p,ty, attrs
1073 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
1075 prerr_endline ("------ prima di rewrite su ------ " ^ string_of_int goal);
1076 prerr_endline ("menv:\n"^CicMetaSubst.ppmetasenv [] metasenv_for_paramod);
1077 prerr_endline ("subst:\n"^CicMetaSubst.ppsubst
1078 ~metasenv:(metasenv_for_paramod)
1082 let (proof''',goals) =
1083 ProofEngineTypes.apply_tactic
1084 (EqualityTactics.rewrite_tac ~direction:`RightToLeft
1085 ~pattern:(ProofEngineTypes.conclusion_pattern None)
1086 (Cic.Meta(newmeta,irl)) []) (proof'',goal)
1088 let goal = match goals with [g] -> g | _ -> assert false in
1090 ProofEngineTypes.apply_tactic
1091 (PrimitiveTactics.apply_tac term'')
1094 let (_,m,_,_,_,_ as p),_ =
1095 solve_rewrite ~params ~automation_cache (proof'''',newmeta)
1098 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv' ~newmetasenv:m
1102 CicRefine.RefineFailure msg ->
1103 raise (ProofEngineTypes.Fail msg)
1107 ~dbd ~term ~automation_cache ~params (proof, goal)
1109 let module T = CicTypeChecker in
1110 let module R = CicReduction in
1111 let module C = Cic in
1112 let (_,metasenv,subst,_,_, _) = proof in
1113 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
1114 let newmeta = CicMkImplicit.new_meta metasenv subst in
1115 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
1117 C.Var (uri,exp_named_subst) ->
1118 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
1119 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
1122 exp_named_subst_diff,newmeta',newmetasenvfragment,
1123 C.Var (uri,exp_named_subst')
1124 | C.Const (uri,exp_named_subst) ->
1125 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
1126 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
1129 exp_named_subst_diff,newmeta',newmetasenvfragment,
1130 C.Const (uri,exp_named_subst')
1131 | C.MutInd (uri,tyno,exp_named_subst) ->
1132 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
1133 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
1136 exp_named_subst_diff,newmeta',newmetasenvfragment,
1137 C.MutInd (uri,tyno,exp_named_subst')
1138 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
1139 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
1140 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
1143 exp_named_subst_diff,newmeta',newmetasenvfragment,
1144 C.MutConstruct (uri,tyno,consno,exp_named_subst')
1145 | _ -> [],newmeta,[],term
1147 let metasenv' = metasenv@newmetasenvfragment in
1149 CicTypeChecker.type_of_aux'
1150 metasenv' ~subst context term' CicUniv.oblivion_ugraph
1152 let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in
1154 let rec count_prods context ty =
1155 match CicReduction.whd ~subst context ty with
1156 | Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
1159 count_prods context ty
1161 apply_smart_aux dbd automation_cache params proof goal
1162 newmeta' metasenv' subst context term' ty termty goal_arity
1165 let applyS_tac ~dbd ~term ~params ~automation_cache =
1166 ProofEngineTypes.mk_tactic
1169 apply_smart ~dbd ~term ~params ~automation_cache status
1171 | CicUnification.UnificationFailure msg
1172 | CicTypeChecker.TypeCheckerFailure msg ->
1173 raise (ProofEngineTypes.Fail msg))
1177 (****************** AUTO ********************)
1179 let calculate_timeout flags =
1180 if flags.timeout = 0. then
1181 (debug_print (lazy "AUTO WITH NO TIMEOUT");
1182 {flags with timeout = infinity})
1186 let is_equational_case goalty flags =
1187 let ensure_equational t =
1188 if is_an_equational_goal t then true
1191 (flags.use_paramod && is_an_equational_goal goalty) ||
1192 (flags.use_only_paramod && ensure_equational goalty)
1195 type menv = Cic.metasenv
1196 type subst = Cic.substitution
1197 type goal = ProofEngineTypes.goal * int * AutoTypes.sort
1198 let candidate_no = ref 0;;
1199 type candidate = int * Cic.term Lazy.t
1200 type cache = AutoCache.cache
1203 (* the goal (mainly for depth) and key of the goal *)
1204 goal * AutoCache.cache_key
1206 (* goal has to be proved *)
1208 (* goal has to be cached as a success obtained using candidate as the first
1210 | S of goal * AutoCache.cache_key * candidate * int
1212 (* menv, subst, size, operations done (only S), operations to do, failures to cache if any op fails *)
1213 menv * subst * int * op list * op list * fail list
1215 (* list of computations that may lead to the solution: all op list will
1216 * end with the same (S(g,_)) *)
1219 (* menv, subst, alternatives, tables, cache *)
1220 | Proved of menv * subst * elem list * AutomationCache.tables * cache
1221 | Gaveup of AutomationCache.tables * cache
1224 (* the status exported to the external observer *)
1226 (* context, (goal,candidate) list, and_list, history *)
1227 Cic.context * (int * Cic.term * bool * int * (int * Cic.term Lazy.t) list) list *
1228 (int * Cic.term * int) list * Cic.term Lazy.t list
1231 let rec aux acc = function
1232 | (D g)::tl -> aux (acc@[g]) tl
1238 List.filter (function (_,_,P) -> true | _ -> false) l
1242 let rec aux acc = function
1243 | (D g)::tl -> aux (acc@[g]) tl
1244 | (S _)::tl -> aux acc tl
1250 let calculate_goal_ty (goalno,_,_) s m =
1252 let _,cc,goalty = CicUtil.lookup_meta goalno m in
1253 (* XXX applicare la subst al contesto? *)
1254 Some (cc, CicMetaSubst.apply_subst s goalty)
1255 with CicUtil.Meta_not_found i when i = goalno -> None
1258 let calculate_closed_goal_ty (goalno,_,_) s =
1260 let cc,_,goalty = List.assoc goalno s in
1261 (* XXX applicare la subst al contesto? *)
1262 Some (cc, CicMetaSubst.apply_subst s goalty)
1267 let pp_status ctx status =
1269 let names = Utils.names_of_context ctx in
1272 ProofEngineReduction.replace
1273 ~equality:(fun a b -> match b with Cic.Meta _ -> true | _ -> false)
1274 ~what:[Cic.Rel 1] ~with_what:[Cic.Implicit None] ~where:x
1278 let string_of_do m s (gi,_,_ as g) d =
1279 match calculate_goal_ty g s m with
1280 | Some (_,gty) -> Printf.sprintf "D(%d, %s, %d)" gi (pp gty) d
1281 | None -> Printf.sprintf "D(%d, _, %d)" gi d
1283 let string_of_s m su k (ci,ct) gi =
1284 Printf.sprintf "S(%d, %s, %s, %d)" gi (pp k) (pp (Lazy.force ct)) ci
1286 let string_of_ol m su l =
1290 | D (g,d,s) -> string_of_do m su (g,d,s) d
1291 | S ((gi,_,_),k,c,_) -> string_of_s m su k c gi)
1294 let string_of_fl m s fl =
1296 (List.map (fun ((i,_,_),ty) ->
1297 Printf.sprintf "(%d, %s)" i (pp ty)) fl)
1299 let rec aux = function
1301 | (m,s,_,_,ol,fl)::tl ->
1302 Printf.eprintf "< [%s] ;;; [%s]>\n"
1303 (string_of_ol m s ol) (string_of_fl m s fl);
1306 Printf.eprintf "-------------------------- status -------------------\n";
1308 Printf.eprintf "-----------------------------------------------------\n";
1311 let auto_status = ref [] ;;
1312 let auto_context = ref [];;
1313 let in_pause = ref false;;
1314 let pause b = in_pause := b;;
1315 let cond = Condition.create ();;
1316 let mutex = Mutex.create ();;
1317 let hint = ref None;;
1318 let prune_hint = ref [];;
1320 let step _ = Condition.signal cond;;
1321 let give_hint n = hint := Some n;;
1322 let give_prune_hint hint =
1323 prune_hint := hint :: !prune_hint
1330 Condition.wait cond mutex;
1335 let get_auto_status _ =
1336 let status = !auto_status in
1337 let and_list,elems,last =
1340 | (m,s,_,don,gl,fail)::tl ->
1343 (fun (id,d,_ as g) ->
1344 match calculate_goal_ty g s m with
1345 | Some (_,x) -> Some (id,x,d) | None -> None)
1349 (* these are the S goalsin the or list *)
1352 (fun (m,s,_,don,gl,fail) ->
1354 (function S (g,k,c,_) -> Some (g,k,c) | _ -> None)
1355 (List.rev don @ gl))
1358 (* this function eats id from a list l::[id,x] returning x, l *)
1359 let eat_tail_if_eq id l =
1360 let rec aux (s, l) = function
1362 | ((id1,_,_),k1,c)::tl when id = id1 ->
1364 | None -> aux (Some c,l) tl
1365 | Some _ -> assert false)
1366 | ((id1,_,_),k1,c as e)::tl -> aux (s, e::l) tl
1368 let c, l = aux (None, []) l in
1371 let eat_in_parallel id l =
1372 let rec aux (b,eaten, new_l as acc) l =
1376 match eat_tail_if_eq id l with
1377 | None, l -> aux (b@[false], eaten, new_l@[l]) tl
1378 | Some t,l -> aux (b@[true],eaten@[t], new_l@[l]) tl
1382 let rec eat_all rows l =
1386 match List.rev elem with
1387 | ((to_eat,depth,_),k,_)::next_lunch ->
1388 let b, eaten, l = eat_in_parallel to_eat l in
1389 let eaten = HExtlib.list_uniq eaten in
1390 let eaten = List.rev eaten in
1391 let b = true (* List.hd (List.rev b) *) in
1392 let rows = rows @ [to_eat,k,b,depth,eaten] in
1394 | [] -> eat_all rows or_list
1396 eat_all [] (List.rev orlist)
1400 (function (S (_,_,(_,c),_)) -> Some c | _ -> None)
1403 (* let rows = List.filter (fun (_,l) -> l <> []) rows in *)
1404 and_list, rows, history
1406 !auto_context, elems, and_list, last
1409 (* Works if there is no dependency over proofs *)
1410 let is_a_green_cut goalty =
1411 CicUtil.is_meta_closed goalty
1413 let rec first_s = function
1414 | (D _)::tl -> first_s tl
1415 | (S (g,k,c,s))::tl -> Some ((g,k,c,s),tl)
1418 let list_union l1 l2 =
1419 (* TODO ottimizzare compare *)
1420 HExtlib.list_uniq (List.sort compare (l1 @ l1))
1422 let rec eq_todo l1 l2 =
1424 | (D g1) :: tl1,(D g2) :: tl2 when g1=g2 -> eq_todo tl1 tl2
1425 | (S (g1,k1,(c1,lt1),i1)) :: tl1, (S (g2,k2,(c2,lt2),i2)) :: tl2
1426 when i1 = i2 && g1 = g2 && k1 = k2 && c1 = c2 ->
1427 if Lazy.force lt1 = Lazy.force lt2 then eq_todo tl1 tl2 else false
1431 let eat_head todo id fl orlist =
1432 let rec aux acc = function
1434 | (m, s, _, _, todo1, fl1)::tl as orlist ->
1435 let rec aux1 todo1 =
1436 match first_s todo1 with
1437 | None -> orlist, acc
1438 | Some (((gno,_,_),_,_,_), todo11) ->
1439 (* TODO confronto tra todo da ottimizzare *)
1440 if gno = id && eq_todo todo11 todo then
1441 aux (list_union fl1 acc) tl
1449 let close_proof p ty menv context =
1451 List.map fst (CicUtil.metas_of_term p @ CicUtil.metas_of_term ty)
1453 let menv = List.filter (fun (i,_,_) -> List.exists ((=)i) metas) menv in
1454 naif_closure p menv context
1456 (* XXX capire bene quando aggiungere alla cache *)
1457 let add_to_cache_and_del_from_orlist_if_green_cut
1458 g s m cache key todo orlist fl ctx size minsize
1460 let cache = cache_remove_underinspection cache key in
1461 (* prima per fare la irl usavamo il contesto vero e proprio e non quello
1463 match calculate_closed_goal_ty g s with
1464 | None -> assert false
1465 | Some (canonical_ctx , gty) ->
1466 let goalno,depth,sort = g in
1467 let irl = mk_irl canonical_ctx in
1468 let goal = Cic.Meta(goalno, irl) in
1469 let proof = CicMetaSubst.apply_subst s goal in
1470 let green_proof, closed_proof =
1471 let b = is_a_green_cut proof in
1473 b, (* close_proof proof gty m ctx *) proof
1477 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm key));
1478 if is_a_green_cut key then
1479 (* if the initia goal was closed, we cut alternatives *)
1480 let _ = debug_print (lazy ("MANGIO: " ^ string_of_int goalno)) in
1481 let orlist, fl = eat_head todo goalno fl orlist in
1483 if size < minsize then
1484 (debug_print (lazy ("NO CACHE: 2 (size <= minsize)"));cache)
1486 (* if the proof is closed we cache it *)
1487 if green_proof then cache_add_success cache key proof
1488 else (* cache_add_success cache key closed_proof *)
1489 (debug_print (lazy ("NO CACHE: (no gree proof)"));cache)
1491 cache, orlist, fl, true
1494 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm gty));
1495 if size < minsize then
1496 (debug_print (lazy ("NO CACHE: (size <= minsize)")); cache) else
1497 (* if the substituted goal and the proof are closed we cache it *)
1498 if is_a_green_cut gty then
1499 if green_proof then cache_add_success cache gty proof
1500 else (* cache_add_success cache gty closed_proof *)
1501 (debug_print (lazy ("NO CACHE: (no green proof (gty))"));cache)
1505 CicTypeChecker.type_of_aux' ~subst:s
1506 m ctx closed_proof CicUniv.oblivion_ugraph
1508 if is_a_green_cut ty then
1509 cache_add_success cache ty closed_proof
1512 | CicTypeChecker.TypeCheckerFailure _ ->*)
1513 (debug_print (lazy ("NO CACHE: (no green gty )"));cache)
1515 cache, orlist, fl, false
1517 let close_failures (fl : fail list) (cache : cache) =
1519 (fun cache ((gno,depth,_),gty) ->
1520 if CicUtil.is_meta_closed gty then
1521 ( debug_print (lazy ("FAIL: INDUCED: " ^ string_of_int gno));
1522 cache_add_failure cache gty depth)
1527 let put_in_subst subst metasenv (goalno,_,_) canonical_ctx t ty =
1528 let entry = goalno, (canonical_ctx, t,ty) in
1529 assert_subst_are_disjoint subst [entry];
1530 let subst = entry :: subst in
1532 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
1537 let mk_fake_proof metasenv subst (goalno,_,_) goalty context =
1538 None,metasenv,subst ,(lazy (Cic.Meta(goalno,mk_irl context))),goalty, []
1542 tables cache depth fake_proof goalno goalty subst context
1545 let active,passive,bag = tables in
1546 let ppterm = ppterm context in
1547 let status = (fake_proof,goalno) in
1548 if flags.use_only_paramod then
1550 debug_print (lazy ("PARAMODULATION SU: " ^
1551 string_of_int goalno ^ " " ^ ppterm goalty ));
1552 let goal_steps, saturation_steps, timeout =
1553 max_int,max_int,flags.timeout
1556 Saturation.given_clause bag status active passive
1557 goal_steps saturation_steps timeout
1559 | None, active, passive, bag ->
1560 [], (active,passive,bag), cache, flags
1561 | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
1563 assert_subst_are_disjoint subst subst';
1564 let subst = subst@subst' in
1566 order_new_goals metasenv subst open_goals ppterm
1569 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1572 [(!candidate_no,proof),metasenv,subst,open_goals],
1573 (active,passive,bag), cache, flags
1577 let params = ([],["use_context","false"]) in
1578 let automation_cache = {
1579 AutomationCache.tables = tables ;
1580 AutomationCache.univ = Universe.empty; }
1583 let ((_,metasenv,subst,_,_,_),open_goals) =
1584 solve_rewrite ~params ~automation_cache
1585 (fake_proof, goalno)
1587 let proof = lazy (Cic.Meta (-1,[])) in
1588 [(!candidate_no,proof),metasenv,subst,[]],tables, cache, flags
1589 with ProofEngineTypes.Fail _ -> [], tables, cache, flags
1591 let res = Saturation.all_subsumed bag status active passive in
1594 (fun (subst',(_,metasenv,_subst,proof,_, _),open_goals) ->
1595 assert_subst_are_disjoint subst subst';
1596 let subst = subst@subst' in
1598 order_new_goals metasenv subst open_goals ppterm
1601 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1604 (!candidate_no,proof),metasenv,subst,open_goals)
1607 res', (active,passive,bag), cache, flags
1612 let sort_new_elems =
1613 List.sort (fun (_,_,_,l1) (_,_,_,l2) ->
1614 let p1 = List.length (prop_only l1) in
1615 let p2 = List.length (prop_only l2) in
1616 if p1 = p2 then List.length l1 - List.length l2 else p1-p2)
1620 let try_candidate dbd
1621 goalty tables subst fake_proof goalno depth context cand
1623 let ppterm = ppterm context in
1625 let actives, passives, bag = tables in
1626 let (_,metasenv,subst,_,_,_), open_goals =
1627 ProofEngineTypes.apply_tactic
1628 (PrimitiveTactics.apply_tac ~term:cand)
1631 let tables = actives, passives,
1632 Equality.push_maxmeta bag
1633 (max (Equality.maxmeta bag) (CicMkImplicit.new_meta metasenv subst))
1635 debug_print (lazy (" OK: " ^ ppterm cand));
1636 let metasenv = CicRefine.pack_coercion_metasenv metasenv in
1637 let open_goals = order_new_goals metasenv subst open_goals ppterm in
1638 let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
1640 Some ((!candidate_no,lazy cand),metasenv,subst,open_goals), tables
1642 | ProofEngineTypes.Fail s -> None,tables
1643 | CicUnification.Uncertain s -> None,tables
1646 let applicative_case dbd
1647 tables depth subst fake_proof goalno goalty metasenv context universe
1652 | Cic.Appl (hd::tl) ->
1653 Cic.Appl (hd :: HExtlib.mk_list (Cic.Meta (0,[])) (List.length tl))
1657 get_candidates flags.skip_trie_filtering universe cache goalty_aux
1661 (fun (tables,elems) cand ->
1663 try_candidate dbd goalty
1664 tables subst fake_proof goalno depth context cand
1666 | None, tables -> tables, elems
1667 | Some x, tables -> tables, x::elems)
1668 (tables,[]) candidates
1670 let elems = sort_new_elems elems in
1671 elems, tables, cache
1674 let try_smart_candidate dbd
1675 goalty tables subst fake_proof goalno depth context cand
1677 let ppterm = ppterm context in
1679 let params = ([],[]) in
1680 let automation_cache = {
1681 AutomationCache.tables = tables ;
1682 AutomationCache.univ = Universe.empty; }
1684 debug_print (lazy ("candidato per " ^ string_of_int goalno
1685 ^ ": " ^ CicPp.ppterm cand));
1687 let (_,metasenv,subst,_,_,_) = fake_proof in
1688 prerr_endline ("metasenv:\n" ^ CicMetaSubst.ppmetasenv [] metasenv);
1689 prerr_endline ("subst:\n" ^ CicMetaSubst.ppsubst ~metasenv subst);
1691 let ((_,metasenv,subst,_,_,_),open_goals) =
1692 apply_smart ~dbd ~term:cand ~params ~automation_cache
1693 (fake_proof, goalno)
1695 let metasenv = CicRefine.pack_coercion_metasenv metasenv in
1696 let open_goals = order_new_goals metasenv subst open_goals ppterm in
1697 let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
1699 Some ((!candidate_no,lazy cand),metasenv,subst,open_goals), tables
1701 | ProofEngineTypes.Fail s -> None,tables
1702 | CicUnification.Uncertain s -> None,tables
1705 let smart_applicative_case dbd
1706 tables depth subst fake_proof goalno goalty metasenv context universe
1709 let signature = MetadataQuery.signature_of metasenv goalno in
1712 | Cic.Appl (hd::tl) ->
1713 Cic.Appl (hd :: HExtlib.mk_list (Cic.Meta (0,[])) (List.length tl))
1716 let smart_candidates =
1717 get_candidates flags.skip_trie_filtering universe cache goalty_aux
1720 get_candidates flags.skip_trie_filtering universe cache goalty
1722 let smart_candidates =
1724 (fun x -> not(List.mem x candidates)) smart_candidates
1726 let candidates = List.filter (only signature context metasenv) candidates in
1727 let smart_candidates =
1728 List.filter (only signature context metasenv) smart_candidates
1731 let penalty cand depth =
1732 if only signature context metasenv cand then depth else ((prerr_endline (
1733 "penalizzo " ^ CicPp.ppterm cand));depth -1)
1738 (fun (tables,elems) cand ->
1740 try_candidate dbd goalty
1741 tables subst fake_proof goalno depth context cand
1743 | None, tables -> tables, elems
1744 | Some x, tables -> tables, x::elems)
1745 (tables,[]) candidates
1747 let tables, smart_elems =
1749 (fun (tables,elems) cand ->
1751 try_smart_candidate dbd goalty
1752 tables subst fake_proof goalno depth context cand
1754 | None, tables -> tables, elems
1755 | Some x, tables -> tables, x::elems)
1756 (tables,[]) smart_candidates
1758 let elems = sort_new_elems (elems @ smart_elems) in
1759 elems, tables, cache
1762 let equational_and_applicative_case dbd
1763 universe flags m s g gty tables cache context
1765 let goalno, depth, sort = g in
1766 let fake_proof = mk_fake_proof m s g gty context in
1767 if is_equational_case gty flags then
1768 let elems,tables,cache, flags =
1769 equational_case tables cache
1770 depth fake_proof goalno gty s context flags
1772 let more_elems, tables, cache =
1773 if flags.use_only_paramod then
1776 applicative_case dbd
1777 tables depth s fake_proof goalno
1778 gty m context universe cache flags
1780 elems@more_elems, tables, cache, flags
1782 let elems, tables, cache =
1783 match LibraryObjects.eq_URI () with
1785 smart_applicative_case dbd tables depth s fake_proof goalno
1786 gty m context universe cache flags
1788 applicative_case dbd tables depth s fake_proof goalno
1789 gty m context universe cache flags
1791 elems, tables, cache, flags
1793 let rec condition_for_hint i = function
1795 | S (_,_,(j,_),_):: tl -> j <> i (* && condition_for_hint i tl *)
1796 | _::tl -> condition_for_hint i tl
1798 let remove_s_from_fl (id,_,_) (fl : fail list) =
1799 let rec aux = function
1801 | ((id1,_,_),_)::tl when id = id1 -> tl
1802 | hd::tl -> hd :: aux tl
1807 let prunable_for_size flags s m todo =
1808 let rec aux b = function
1809 | (S _)::tl -> aux b tl
1810 | (D (_,_,T))::tl -> aux b tl
1812 (match calculate_goal_ty g s m with
1814 | Some (canonical_ctx, gty) ->
1816 Utils.weight_of_term
1817 ~consider_metas:false ~count_metas_occurrences:true gty in
1818 let newb = b || gsize > flags.maxgoalsizefactor in
1825 let prunable ty todo =
1826 let rec aux b = function
1827 | (S(_,k,_,_))::tl -> aux (b || Equality.meta_convertibility k ty) tl
1828 | (D (_,_,T))::tl -> aux b tl
1836 let prunable menv subst ty todo =
1837 let rec aux = function
1838 | (S(_,k,_,_))::tl ->
1839 (match Equality.meta_convertibility_subst k ty menv with
1842 no_progress variant tl (* || aux tl*))
1843 | (D (_,_,T))::tl -> aux tl
1845 and no_progress variant = function
1846 | [] -> (*prerr_endline "++++++++++++++++++++++++ no_progress";*) true
1847 | D ((n,_,P) as g)::tl ->
1848 (match calculate_goal_ty g subst menv with
1849 | None -> no_progress variant tl
1851 (match calculate_goal_ty g variant menv with
1852 | None -> assert false
1854 if gty = gty' then no_progress variant tl
1856 (prerr_endline (string_of_int n);
1857 prerr_endline (CicPp.ppterm gty);
1858 prerr_endline (CicPp.ppterm gty');
1859 prerr_endline "---------- subst";
1860 prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv subst);
1861 prerr_endline "---------- variant";
1862 prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv variant);
1863 prerr_endline "---------- menv";
1864 prerr_endline (CicMetaSubst.ppmetasenv [] menv);
1865 no_progress variant tl) *)
1867 | _::tl -> no_progress variant tl
1872 let condition_for_prune_hint prune (m, s, size, don, todo, fl) =
1874 HExtlib.filter_map (function S (_,_,(c,_),_) -> Some c | _ -> None) todo
1876 List.for_all (fun i -> List.for_all (fun j -> i<>j) prune) s
1878 let filter_prune_hint c l =
1879 let prune = !prune_hint in
1880 prune_hint := []; (* possible race... *)
1881 if prune = [] then c,l
1883 cache_reset_underinspection c,
1884 List.filter (condition_for_prune_hint prune) l
1886 let auto_main dbd tables context flags universe cache elems =
1887 auto_context := context;
1888 let rec aux tables flags cache (elems : status) =
1889 pp_status context elems;
1890 (* DEBUGGING CODE: uncomment these two lines to stop execution at each iteration
1891 auto_status := elems;
1894 let cache, elems = filter_prune_hint cache elems in
1896 | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
1897 debug_print (lazy "skip");
1899 | Some i when condition_for_hint i todo ->
1900 aux tables flags cache orlist
1903 aux tables flags cache elems)
1905 (* complete failure *)
1906 debug_print (lazy "give up");
1907 Gaveup (tables, cache)
1908 | (m, s, _, _, [],_)::orlist ->
1909 (* complete success *)
1910 debug_print (lazy "success");
1911 Proved (m, s, orlist, tables, cache)
1912 | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist
1913 when not flags.AutoTypes.do_types ->
1914 (* skip since not Prop, don't even check if closed by side-effect *)
1915 debug_print (lazy "skip existential goal");
1916 aux tables flags cache ((m, s, size, don, todo, fl)::orlist)
1917 | (m, s, size, don, (S(g, key, c,minsize) as op)::todo, fl)::orlist ->
1918 (* partial success, cache g and go on *)
1919 let cache, orlist, fl, sibling_pruned =
1920 add_to_cache_and_del_from_orlist_if_green_cut
1921 g s m cache key todo orlist fl context size minsize
1923 debug_print (lazy (AutoCache.cache_print context cache));
1924 let fl = remove_s_from_fl g fl in
1925 let don = if sibling_pruned then don else op::don in
1926 aux tables flags cache ((m, s, size, don, todo, fl)::orlist)
1927 | (m, s, size, don, todo, fl)::orlist
1928 when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
1929 debug_print (lazy ("FAIL: WIDTH"));
1930 (* too many goals in and generated by last th *)
1931 let cache = close_failures fl cache in
1932 aux tables flags cache orlist
1933 | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize ->
1935 (lazy ("FAIL: SIZE: "^string_of_int size ^
1936 " > " ^ string_of_int flags.maxsize ));
1937 (* we already have a too large proof term *)
1938 let cache = close_failures fl cache in
1939 aux tables flags cache orlist
1940 | _ when Unix.gettimeofday () > flags.timeout ->
1942 debug_print (lazy ("FAIL: TIMEOUT"));
1943 Gaveup (tables, cache)
1944 | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status ->
1946 debug_print (lazy "attack goal");
1947 match calculate_goal_ty g s m with
1949 (* closed by side effect *)
1950 debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
1951 aux tables flags cache ((m,s,size,don,todo, fl)::orlist)
1952 | Some (canonical_ctx, gty) ->
1954 Utils.weight_of_term ~consider_metas:false ~count_metas_occurrences:true gty
1956 if gsize > flags.maxgoalsizefactor then
1957 (debug_print (lazy ("FAIL: SIZE: goal: "^string_of_int gsize));
1958 aux tables flags cache orlist)
1959 else if prunable_for_size flags s m todo then
1960 (debug_print (lazy ("POTO at depth: "^(string_of_int depth)));
1961 aux tables flags cache orlist)
1963 (* still to be proved *)
1964 (debug_print (lazy ("EXAMINE: "^CicPp.ppterm gty));
1965 match cache_examine cache gty with
1966 | Failed_in d when d >= depth ->
1968 debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
1969 let cache = close_failures fl cache in
1970 aux tables flags cache orlist
1971 | UnderInspection ->
1973 debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
1974 let cache = close_failures fl cache in
1975 aux tables flags cache orlist
1977 debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
1978 let s, m = put_in_subst s m g canonical_ctx t gty in
1979 aux tables flags cache ((m, s, size, don,todo, fl)::orlist)
1981 | Failed_in _ when depth > 0 ->
1982 ( (* more depth or is the first time we see the goal *)
1983 if prunable m s gty todo then
1985 "FAIL: LOOP: one father is equal"));
1986 aux tables flags cache orlist)
1988 let cache = cache_add_underinspection cache gty depth in
1989 auto_status := status;
1992 (lazy ("INSPECTING: " ^
1993 string_of_int gno ^ "("^ string_of_int size ^ "): "^
1995 (* elems are possible computations for proving gty *)
1996 let elems, tables, cache, flags =
1997 equational_and_applicative_case dbd
1998 universe flags m s g gty tables cache context
2001 (* this goal has failed *)
2002 let cache = close_failures ((g,gty)::fl) cache in
2003 aux tables flags cache orlist
2005 (* elems = (cand,m,s,gl) *)
2006 let size_gl l = List.length
2007 (List.filter (function (_,_,P) -> true | _ -> false) l)
2010 let inj_gl gl = List.map (fun g -> D g) gl in
2011 let rec map = function
2012 | [] -> assert false
2013 | (cand,m,s,gl)::[] ->
2014 (* in the last one we add the failure *)
2016 inj_gl gl @ (S(g,gty,cand,size+1))::todo
2018 (* we are the last in OR, we fail on g and
2019 * also on all failures implied by g *)
2020 (m,s, size + size_gl gl, don, todo, (g,gty)::fl)
2022 | (cand,m,s,gl)::tl ->
2023 (* we add the S step after gl and before todo *)
2025 inj_gl gl @ (S(g,gty,cand,size+1))::todo
2027 (* since we are not the last in OR, we do not
2029 (m,s, size + size_gl gl, don, todo, []) :: map tl
2033 aux tables flags cache elems)
2036 debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
2037 let cache = close_failures fl cache in
2038 aux tables flags cache orlist)
2040 (aux tables flags cache elems : auto_result)
2045 auto_all_solutions dbd tables universe cache context metasenv gl flags
2047 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
2050 (fun (x,s) -> D (x,flags.maxdepth,s)) goals
2052 let elems = [metasenv,[],1,[],goals,[]] in
2053 let rec aux tables solutions cache elems flags =
2054 match auto_main dbd tables context flags universe cache elems with
2055 | Gaveup (tables,cache) ->
2056 solutions,cache, tables
2057 | Proved (metasenv,subst,others,tables,cache) ->
2058 if Unix.gettimeofday () > flags.timeout then
2059 ((subst,metasenv)::solutions), cache, tables
2061 aux tables ((subst,metasenv)::solutions) cache others flags
2063 let rc = aux tables [] cache elems flags in
2065 | [],cache,tables -> [],cache,tables
2066 | solutions, cache,tables ->
2069 (fun (subst,newmetasenv) ->
2071 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv ~newmetasenv
2073 if opened = [] then Some subst else None)
2076 solutions,cache,tables
2079 (******************* AUTO ***************)
2081 let auto dbd flags metasenv tables universe cache context metasenv gl =
2082 let initial_time = Unix.gettimeofday() in
2083 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
2084 let goals = List.map (fun (x,s) -> D(x,flags.maxdepth,s)) goals in
2085 let elems = [metasenv,[],1,[],goals,[]] in
2086 match auto_main dbd tables context flags universe cache elems with
2087 | Proved (metasenv,subst,_, tables,cache) ->
2089 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
2090 Some (subst,metasenv), cache
2091 | Gaveup (tables,cache) ->
2093 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
2097 let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~automation_cache (proof, goal) =
2098 let flags = flags_of_params params () in
2099 let use_library = flags.use_library in
2100 let universe, tables, cache =
2101 init_cache_and_tables
2102 ~dbd ~use_library ~use_context:(not flags.skip_context)
2103 automation_cache univ (proof, goal)
2105 let _,metasenv,subst,_,_, _ = proof in
2106 let _,context,goalty = CicUtil.lookup_meta goal metasenv in
2108 if flags.close_more then
2110 tables context (proof, goal)
2111 (auto_all_solutions dbd) universe cache
2112 else tables,cache in
2113 let initial_time = Unix.gettimeofday() in
2114 let (_,oldmetasenv,_,_,_, _) = proof in
2117 metasenv,subst,1,[],[D (goal,flags.maxdepth,P)],[]
2119 match auto_main dbd tables context flags universe cache [elem] with
2120 | Proved (metasenv,subst,_, tables,cache) ->
2122 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
2123 let proof,metasenv =
2124 ProofEngineHelpers.subst_meta_and_metasenv_in_proof
2125 proof goal subst metasenv
2128 ProofEngineHelpers.compare_metasenvs ~oldmetasenv
2129 ~newmetasenv:metasenv
2132 | Gaveup (tables,cache) ->
2135 string_of_float(Unix.gettimeofday()-.initial_time)));
2136 raise (ProofEngineTypes.Fail (lazy "Auto gave up"))
2139 let auto_tac ~dbd ~params ~automation_cache =
2140 ProofEngineTypes.mk_tactic (auto_tac ~params ~dbd ~automation_cache);;
2142 let pp_proofterm = Equality.pp_proofterm;;
2144 let revision = "$Revision$";;
2145 let size_and_depth context metasenv t = 100, 100