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, _, _, _, _ = proof in
370 let _,context,_ = CicUtil.lookup_meta goal metasenv in
371 if restricted_univ = [] then
373 if use_context then find_context_theorems context metasenv else []
376 match use_library, dbd with
377 | true, Some dbd -> find_library_theorems dbd metasenv goal
380 let cache = AutoCache.cache_empty in
381 let cache = cache_add_list cache context (ct@lt) in
383 let env = metasenv, context, CicUniv.oblivion_ugraph in
385 (fun (a,p,b) (t,ty) ->
386 let mes = CicUtil.metas_of_term ty in
387 Saturation.add_to_active b a p env ty t
388 (List.filter (fun (i,_,_) -> List.mem_assoc i mes) metasenv))
389 automation_cache.AutomationCache.tables ct
391 (* AutomationCache.pp_cache { automation_cache with AutomationCache.tables =
393 automation_cache.AutomationCache.univ, tables, cache
395 let metasenv, t_ty, s_t_ty, _ =
397 (fun (metasenv,acc, sacc, maxmeta) t ->
399 CicTypeChecker.type_of_aux'
400 metasenv ~subst:[] context t CicUniv.oblivion_ugraph
402 let head, metasenv, args, maxmeta =
403 TermUtil.saturate_term maxmeta metasenv context ty 0
405 let st = if args = [] then t else Cic.Appl (t::args) in
406 metasenv, (t, ty)::acc, (st,head)::sacc, maxmeta)
407 (metasenv, [],[], CicMkImplicit.new_meta metasenv []) restricted_univ
409 let automation_cache = AutomationCache.empty () in
410 let automation_cache =
411 let universe = automation_cache.AutomationCache.univ in
413 Universe.index_list universe context t_ty
415 { automation_cache with AutomationCache.univ = universe }
417 let automation_cache =
420 AutomationCache.add_term_to_active c metasenv [] context t (Some ty))
421 automation_cache s_t_ty
423 (* AutomationCache.pp_cache automation_cache; *)
424 automation_cache.AutomationCache.univ,
425 automation_cache.AutomationCache.tables,
426 cache_add_list cache_empty context t_ty
429 (* let signature = MetadataQuery.signature_of metasenv goal in *)
430 (* let newmeta = CicMkImplicit.new_meta metasenv [] in *)
432 retrieve_equations dont_filter (* true *) signature universe cache context metasenv
435 (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
440 CicTypeChecker.type_of_aux'
441 metasenv context t CicUniv.oblivion_ugraph
443 (* retrieve_equations could also return flexible terms *)
444 if is_an_equality ty then Some(t,ty)
447 let ty' = unfold context ty in
448 if is_an_equality ty' then Some(t,ty') else None
449 with ProofEngineTypes.Fail _ -> None)
452 let bag = Equality.mk_equality_bag () in
453 let units, other_equalities, newmeta =
454 partition_unit_equalities context metasenv newmeta bag eqs_and_types
456 (* SIMPLIFICATION STEP
458 let env = (metasenv, context, CicUniv.oblivion_ugraph) in
459 let eq_uri = HExtlib.unopt (LibraryObjects.eq_URI()) in
460 Saturation.simplify_equalities bag eq_uri env units
463 let passive = Saturation.make_passive units in
464 let no = List.length units in
465 let active = Saturation.make_active [] in
466 let active,passive,newmeta =
467 if paramod then active,passive,newmeta
469 Saturation.pump_actives
470 context bag newmeta active passive (no+1) infinity
472 (active,passive,bag),cache,newmeta
475 let fill_hypothesis context metasenv term tables (universe:Universe.universe) cache auto fast =
476 let actives, passives, bag = tables in
477 let bag, head, metasenv, args =
478 Equality.saturate_term bag metasenv context term
480 let tables = actives, passives, bag in
481 let propositional_args =
485 let _,_,mt = CicUtil.lookup_meta i metasenv in
487 CicTypeChecker.type_of_aux' metasenv context mt
488 CicUniv.oblivion_ugraph
490 if is_propositional context sort then Some i else None
494 let results,cache,tables =
495 if propositional_args = [] then
496 let _,_,bag = tables in
497 let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
498 [args,metasenv,newmetas,head],cache,tables
502 None,metasenv,term,term (* term non e' significativo *)
506 {AutoTypes.default_flags() with
507 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
508 maxwidth = 2;maxdepth = 2;
509 use_paramod=true;use_only_paramod=false}
511 {AutoTypes.default_flags() with
512 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
513 maxwidth = 2;maxdepth = 4;
514 use_paramod=true;use_only_paramod=false}
516 match auto tables universe cache context metasenv propositional_args flags with
517 | [],cache,tables -> raise (FillingFailure (cache,tables))
518 | substs,cache,tables ->
519 let actives, passaives, bag = tables in
522 (fun subst (bag,acc) ->
524 CicMetaSubst.apply_subst_metasenv subst metasenv
526 let head = CicMetaSubst.apply_subst subst head in
527 let newmetas = Equality.filter_metasenv_gt_maxmeta bag metasenv in
528 let args = List.map (CicMetaSubst.apply_subst subst) args in
529 let newm = CicMkImplicit.new_meta metasenv subst in
530 let bag = Equality.push_maxmeta bag newm in
531 bag, ((args,metasenv,newmetas,head) :: acc))
534 let tables = actives, passives, bag in
540 let build_equalities auto context metasenv tables universe cache equations =
542 (fun (tables,facts,cache) (t,ty) ->
543 (* in any case we add the equation to the cache *)
544 let cache = AutoCache.cache_add_list cache context [(t,ty)] in
546 let saturated, cache, tables =
547 fill_hypothesis context metasenv ty tables universe cache auto true
551 (fun (acc, tables) (args,metasenv,newmetas,head) ->
552 let actives, passives, bag = tables in
554 build_equality bag head args t newmetas
556 let tables = actives, passives, bag in
557 equality::acc,tables)
558 ([],tables) saturated
560 (tables, eqs@facts, cache)
561 with FillingFailure (cache,tables) ->
562 (* if filling hypothesis fails we add the equation to
566 (tables,[],cache) equations
568 let close_more tables context status auto universe cache =
569 let proof, goalno = status in
570 let _, metasenv,_subst,_,_, _ = proof in
571 let signature = MetadataQuery.signature_of metasenv goalno in
573 retrieve_equations false signature universe cache context metasenv
579 CicTypeChecker.type_of_aux' metasenv context t
580 CicUniv.oblivion_ugraph in
581 (* retrieve_equations could also return flexible terms *)
582 if is_an_equality ty then Some(t,ty) else None)
584 let tables, units, cache =
585 build_equalities auto context metasenv tables universe cache eqs_and_types
587 let active,passive,bag = tables in
588 let passive = Saturation.add_to_passive units passive in
589 let no = List.length units in
590 let active, passive, bag =
591 Saturation.pump_actives context bag active passive (no+1) infinity
593 (active,passive,bag), cache
596 let find_context_equalities tables context proof (universe:Universe.universe) cache
598 let module C = Cic in
599 let module S = CicSubstitution in
600 let module T = CicTypeChecker in
601 let _,metasenv,_subst,_,_, _ = proof in
602 (* if use_auto is true, we try to close the hypothesis of equational
603 statements using auto; a naif, and probably wrong approach *)
604 let rec aux tables cache index = function
605 | [] -> tables, [], cache
606 | (Some (_, C.Decl (term)))::tl ->
609 (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term)));
610 let do_find tables context term =
612 | C.Prod (name, s, t) when is_an_equality t ->
614 let term = S.lift index term in
615 let saturated, cache, tables =
616 fill_hypothesis context metasenv term
617 tables universe cache default_auto false
619 let actives, passives, bag = tables in
622 (fun (bag,acc) (args,metasenv,newmetas,head) ->
624 build_equality bag head args (Cic.Rel index) newmetas
629 let tables = actives, passives, bag in
631 with FillingFailure (cache,tables) ->
633 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
634 when LibraryObjects.is_eq_URI uri ->
635 let term = S.lift index term in
636 let actives, passives, bag = tables in
638 build_equality bag term [] (Cic.Rel index) []
640 let tables = actives, passives, bag in
642 | _ -> tables, [], cache
644 let tables, eqs, cache = do_find tables context term in
645 let tables, rest, cache = aux tables cache (index+1) tl in
646 tables, List.map (fun x -> index,x) eqs @ rest, cache
648 aux tables cache (index+1) tl
650 let tables, il, cache = aux tables cache 1 context in
651 let indexes, equalities = List.split il in
652 tables, indexes, equalities, cache
655 (********** PARAMETERS PASSING ***************)
657 let bool params name default =
659 let s = List.assoc name params in
660 if s = "" || s = "1" || s = "true" || s = "yes" || s = "on" then true
661 else if s = "0" || s = "false" || s = "no" || s= "off" then false
663 let msg = "Unrecognized value for parameter "^name^"\n" in
664 let msg = msg^"Accepted values are 1,true,yes,on and 0,false,no,off" in
665 raise (ProofEngineTypes.Fail (lazy msg))
666 with Not_found -> default
669 let string params name default =
670 try List.assoc name params with
671 | Not_found -> default
674 let int params name default =
675 try int_of_string (List.assoc name params) with
676 | Not_found -> default
678 raise (ProofEngineTypes.Fail (lazy (name ^ " must be an integer")))
681 let flags_of_params params ?(for_applyS=false) () =
682 let int = int params in
683 let bool = bool params in
684 let close_more = bool "close_more" false in
685 let use_paramod = bool "use_paramod" true in
686 let skip_trie_filtering = bool "skip_trie_filtering" false in
687 let skip_context = bool "skip_context" false in
688 let use_only_paramod =
689 if for_applyS then true else bool "paramodulation" false in
690 let use_library = bool "library"
691 ((AutoTypes.default_flags()).AutoTypes.use_library) in
692 let depth = int "depth" ((AutoTypes.default_flags()).AutoTypes.maxdepth) in
693 let width = int "width" ((AutoTypes.default_flags()).AutoTypes.maxwidth) in
694 let size = int "size" ((AutoTypes.default_flags()).AutoTypes.maxsize) in
695 let gsize = int "gsize" ((AutoTypes.default_flags()).AutoTypes.maxgoalsizefactor) in
696 let do_type = bool "type" false in
697 let timeout = int "timeout" 0 in
698 { AutoTypes.maxdepth =
699 if use_only_paramod then 2 else depth;
700 AutoTypes.maxwidth = width;
701 AutoTypes.maxsize = size;
704 if for_applyS then Unix.gettimeofday () +. 30.0
708 Unix.gettimeofday() +. (float_of_int timeout);
709 AutoTypes.use_library = use_library;
710 AutoTypes.use_paramod = use_paramod;
711 AutoTypes.use_only_paramod = use_only_paramod;
712 AutoTypes.close_more = close_more;
713 AutoTypes.dont_cache_failures = false;
714 AutoTypes.maxgoalsizefactor = gsize;
715 AutoTypes.do_types = do_type;
716 AutoTypes.skip_trie_filtering = skip_trie_filtering;
717 AutoTypes.skip_context = skip_context;
720 (***************** applyS *******************)
723 dbd flags automation_cache univ proof goal newmeta' metasenv'
724 context term' ty termty goal_arity
726 (* let ppterm = ppterm context in *)
727 let (consthead,newmetasenv,arguments,_) =
728 TermUtil.saturate_term newmeta' metasenv' context termty goal_arity in
730 match arguments with [] -> term' | _ -> Cic.Appl (term'::arguments)
732 let proof',oldmetasenv =
733 let (puri,metasenv,_subst,pbo,pty, attrs) = proof in
734 (puri,newmetasenv,_subst,pbo,pty, attrs),metasenv
736 let goal_for_paramod =
737 match LibraryObjects.eq_URI () with
739 Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Sort Cic.Prop; consthead; ty]
740 | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined"))
742 let newmeta = CicMkImplicit.new_meta newmetasenv (*subst*) [] in
743 let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in
745 let uri,_,_subst,p,ty, attrs = proof' in
746 uri,metasenv_for_paramod,_subst,p,ty, attrs
748 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
750 ProofEngineTypes.apply_tactic
751 (EqualityTactics.rewrite_tac ~direction:`RightToLeft
752 ~pattern:(ProofEngineTypes.conclusion_pattern None)
753 (Cic.Meta(newmeta,irl)) [])
756 let goal = match goals with [g] -> g | _ -> assert false in
758 ProofEngineTypes.apply_tactic
759 (PrimitiveTactics.apply_tac term'')
762 let universe, tables, cache =
763 init_cache_and_tables ~dbd ~use_library:flags.use_library
764 ~use_context:true automation_cache univ (proof'''',newmeta)
766 let active, passive, bag = tables in
768 Saturation.given_clause bag (proof'''',newmeta) active passive
772 raise (ProofEngineTypes.Fail (lazy ("FIXME: propaga le tabelle")))
773 | Some (_,proof''''',_), active,passive,bag ->
775 ProofEngineHelpers.compare_metasenvs ~oldmetasenv
776 ~newmetasenv:(let _,m,_subst,_,_, _ = proof''''' in m), active, passive
780 ("SUBSUMPTION SU: " ^ string_of_int newmeta ^ " " ^ ppterm goal_for_paramod));
782 Saturation.all_subsumed bag maxm (proof'''',newmeta) active passive
785 raise (ProofEngineTypes.Fail (lazy("BUM")))
786 else let (_,proof''''',_) = List.hd res in
787 proof''''',ProofEngineHelpers.compare_metasenvs ~oldmetasenv
788 ~newmetasenv:(let _,m,_subst,_,_, _ = proof''''' in m), active, passive
792 let rec count_prods context ty =
793 match CicReduction.whd context ty with
794 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
798 ~dbd ~term ~subst ~automation_cache ~params:(univ,params) (proof, goal)
800 let module T = CicTypeChecker in
801 let module R = CicReduction in
802 let module C = Cic in
803 let (_,metasenv,_subst,_,_, _) = proof in
804 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
805 let flags = flags_of_params params ~for_applyS:true () in
806 let newmeta = CicMkImplicit.new_meta metasenv subst in
807 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
809 C.Var (uri,exp_named_subst) ->
810 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
811 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
814 exp_named_subst_diff,newmeta',newmetasenvfragment,
815 C.Var (uri,exp_named_subst')
816 | C.Const (uri,exp_named_subst) ->
817 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
818 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
821 exp_named_subst_diff,newmeta',newmetasenvfragment,
822 C.Const (uri,exp_named_subst')
823 | C.MutInd (uri,tyno,exp_named_subst) ->
824 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
825 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
828 exp_named_subst_diff,newmeta',newmetasenvfragment,
829 C.MutInd (uri,tyno,exp_named_subst')
830 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
831 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
832 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
835 exp_named_subst_diff,newmeta',newmetasenvfragment,
836 C.MutConstruct (uri,tyno,consno,exp_named_subst')
837 | _ -> [],newmeta,[],term
839 let metasenv' = metasenv@newmetasenvfragment in
841 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.oblivion_ugraph
843 let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in
844 let goal_arity = count_prods context ty in
845 let proof, gl, active, passive =
846 apply_smart_aux dbd flags automation_cache univ proof goal
847 newmeta' metasenv' context term' ty termty goal_arity
849 proof, gl, active, passive
852 (****************** AUTO ********************)
857 let prop = function (_,depth,P) -> depth < 9 | _ -> false;;
860 let calculate_timeout flags =
861 if flags.timeout = 0. then
862 (debug_print (lazy "AUTO WITH NO TIMEOUT");
863 {flags with timeout = infinity})
867 let is_equational_case goalty flags =
868 let ensure_equational t =
869 if is_an_equational_goal t then true
872 let msg="Not an equational goal.\nYou cant use the paramodulation flag"in
873 raise (ProofEngineTypes.Fail (lazy msg))
876 (flags.use_paramod && is_an_equational_goal goalty) ||
877 (flags.use_only_paramod && ensure_equational goalty)
880 let cache_add_success sort cache k v =
881 if sort = P then cache_add_success cache k v else cache_remove_underinspection
886 type menv = Cic.metasenv
887 type subst = Cic.substitution
888 type goal = ProofEngineTypes.goal * int * AutoTypes.sort
889 let candidate_no = ref 0;;
890 type candidate = int * Cic.term Lazy.t
891 type cache = AutoCache.cache
894 (* the goal (mainly for depth) and key of the goal *)
895 goal * AutoCache.cache_key
897 (* goal has to be proved *)
899 (* goal has to be cached as a success obtained using candidate as the first
901 | S of goal * AutoCache.cache_key * candidate * int
903 (* menv, subst, size, operations done (only S), operations to do, failures to cache if any op fails *)
904 menv * subst * int * op list * op list * fail list
906 (* list of computations that may lead to the solution: all op list will
907 * end with the same (S(g,_)) *)
910 (* menv, subst, alternatives, tables, cache *)
911 | Proved of menv * subst * elem list * AutomationCache.tables * cache
912 | Gaveup of AutomationCache.tables * cache
915 (* the status exported to the external observer *)
917 (* context, (goal,candidate) list, and_list, history *)
918 Cic.context * (int * Cic.term * bool * int * (int * Cic.term Lazy.t) list) list *
919 (int * Cic.term * int) list * Cic.term Lazy.t list
922 let rec aux acc = function
923 | (D g)::tl -> aux (acc@[g]) tl
929 List.filter (function (_,_,P) -> true | _ -> false) l
933 let rec aux acc = function
934 | (D g)::tl -> aux (acc@[g]) tl
935 | (S _)::tl -> aux acc tl
941 let calculate_goal_ty (goalno,_,_) s m =
943 let _,cc,goalty = CicUtil.lookup_meta goalno m in
944 (* XXX applicare la subst al contesto? *)
945 Some (cc, CicMetaSubst.apply_subst s goalty)
946 with CicUtil.Meta_not_found i when i = goalno -> None
949 let calculate_closed_goal_ty (goalno,_,_) s =
951 let cc,_,goalty = List.assoc goalno s in
952 (* XXX applicare la subst al contesto? *)
953 Some (cc, CicMetaSubst.apply_subst s goalty)
954 with Not_found -> None
957 let pp_status ctx status =
959 let names = Utils.names_of_context ctx in
962 ProofEngineReduction.replace
963 ~equality:(fun a b -> match b with Cic.Meta _ -> true | _ -> false)
964 ~what:[Cic.Rel 1] ~with_what:[Cic.Implicit None] ~where:x
968 let string_of_do m s (gi,_,_ as g) d =
969 match calculate_goal_ty g s m with
970 | Some (_,gty) -> Printf.sprintf "D(%d, %s, %d)" gi (pp gty) d
971 | None -> Printf.sprintf "D(%d, _, %d)" gi d
973 let string_of_s m su k (ci,ct) gi =
974 Printf.sprintf "S(%d, %s, %s, %d)" gi (pp k) (pp (Lazy.force ct)) ci
976 let string_of_ol m su l =
980 | D (g,d,s) -> string_of_do m su (g,d,s) d
981 | S ((gi,_,_),k,c,_) -> string_of_s m su k c gi)
984 let string_of_fl m s fl =
986 (List.map (fun ((i,_,_),ty) ->
987 Printf.sprintf "(%d, %s)" i (pp ty)) fl)
989 let rec aux = function
991 | (m,s,_,_,ol,fl)::tl ->
992 Printf.eprintf "< [%s] ;;; [%s]>\n"
993 (string_of_ol m s ol) (string_of_fl m s fl);
996 Printf.eprintf "-------------------------- status -------------------\n";
998 Printf.eprintf "-----------------------------------------------------\n";
1001 let auto_status = ref [] ;;
1002 let auto_context = ref [];;
1003 let in_pause = ref false;;
1004 let pause b = in_pause := b;;
1005 let cond = Condition.create ();;
1006 let mutex = Mutex.create ();;
1007 let hint = ref None;;
1008 let prune_hint = ref [];;
1010 let step _ = Condition.signal cond;;
1011 let give_hint n = hint := Some n;;
1012 let give_prune_hint hint =
1013 prune_hint := hint :: !prune_hint
1020 Condition.wait cond mutex;
1025 let get_auto_status _ =
1026 let status = !auto_status in
1027 let and_list,elems,last =
1030 | (m,s,_,don,gl,fail)::tl ->
1033 (fun (id,d,_ as g) ->
1034 match calculate_goal_ty g s m with
1035 | Some (_,x) -> Some (id,x,d) | None -> None)
1039 (* these are the S goalsin the or list *)
1042 (fun (m,s,_,don,gl,fail) ->
1044 (function S (g,k,c,_) -> Some (g,k,c) | _ -> None)
1045 (List.rev don @ gl))
1048 (* this function eats id from a list l::[id,x] returning x, l *)
1049 let eat_tail_if_eq id l =
1050 let rec aux (s, l) = function
1052 | ((id1,_,_),k1,c)::tl when id = id1 ->
1054 | None -> aux (Some c,l) tl
1055 | Some _ -> assert false)
1056 | ((id1,_,_),k1,c as e)::tl -> aux (s, e::l) tl
1058 let c, l = aux (None, []) l in
1061 let eat_in_parallel id l =
1062 let rec aux (b,eaten, new_l as acc) l =
1066 match eat_tail_if_eq id l with
1067 | None, l -> aux (b@[false], eaten, new_l@[l]) tl
1068 | Some t,l -> aux (b@[true],eaten@[t], new_l@[l]) tl
1072 let rec eat_all rows l =
1076 match List.rev elem with
1077 | ((to_eat,depth,_),k,_)::next_lunch ->
1078 let b, eaten, l = eat_in_parallel to_eat l in
1079 let eaten = HExtlib.list_uniq eaten in
1080 let eaten = List.rev eaten in
1081 let b = true (* List.hd (List.rev b) *) in
1082 let rows = rows @ [to_eat,k,b,depth,eaten] in
1084 | [] -> eat_all rows or_list
1086 eat_all [] (List.rev orlist)
1090 (function (S (_,_,(_,c),_)) -> Some c | _ -> None)
1093 (* let rows = List.filter (fun (_,l) -> l <> []) rows in *)
1094 and_list, rows, history
1096 !auto_context, elems, and_list, last
1099 (* Works if there is no dependency over proofs *)
1100 let is_a_green_cut goalty =
1101 CicUtil.is_meta_closed goalty
1103 let rec first_s = function
1104 | (D _)::tl -> first_s tl
1105 | (S (g,k,c,s))::tl -> Some ((g,k,c,s),tl)
1108 let list_union l1 l2 =
1109 (* TODO ottimizzare compare *)
1110 HExtlib.list_uniq (List.sort compare (l1 @ l1))
1112 let rec eq_todo l1 l2 =
1114 | (D g1) :: tl1,(D g2) :: tl2 when g1=g2 -> eq_todo tl1 tl2
1115 | (S (g1,k1,(c1,lt1),i1)) :: tl1, (S (g2,k2,(c2,lt2),i2)) :: tl2
1116 when i1 = i2 && g1 = g2 && k1 = k2 && c1 = c2 ->
1117 if Lazy.force lt1 = Lazy.force lt2 then eq_todo tl1 tl2 else false
1121 let eat_head todo id fl orlist =
1122 let rec aux acc = function
1124 | (m, s, _, _, todo1, fl1)::tl as orlist ->
1125 let rec aux1 todo1 =
1126 match first_s todo1 with
1127 | None -> orlist, acc
1128 | Some (((gno,_,_),_,_,_), todo11) ->
1129 (* TODO confronto tra todo da ottimizzare *)
1130 if gno = id && eq_todo todo11 todo then
1131 aux (list_union fl1 acc) tl
1139 let close_proof p ty menv context =
1141 List.map fst (CicUtil.metas_of_term p @ CicUtil.metas_of_term ty)
1143 let menv = List.filter (fun (i,_,_) -> List.exists ((=)i) metas) menv in
1144 naif_closure p menv context
1146 (* XXX capire bene quando aggiungere alla cache *)
1147 let add_to_cache_and_del_from_orlist_if_green_cut
1148 g s m cache key todo orlist fl ctx size minsize
1150 let cache = cache_remove_underinspection cache key in
1151 (* prima per fare la irl usavamo il contesto vero e proprio e non quello
1153 match calculate_closed_goal_ty g s with
1154 | None -> assert false
1155 | Some (canonical_ctx , gty) ->
1156 let goalno,depth,sort = g in
1157 let irl = mk_irl canonical_ctx in
1158 let goal = Cic.Meta(goalno, irl) in
1159 let proof = CicMetaSubst.apply_subst s goal in
1160 let green_proof, closed_proof =
1161 let b = is_a_green_cut proof in
1163 b, (* close_proof proof gty m ctx *) proof
1167 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm key));
1168 if is_a_green_cut key then
1169 (* if the initia goal was closed, we cut alternatives *)
1170 let _ = debug_print (lazy ("MANGIO: " ^ string_of_int goalno)) in
1171 let orlist, fl = eat_head todo goalno fl orlist in
1173 if size < minsize then
1174 (debug_print (lazy ("NO CACHE: 2 (size <= minsize)"));cache)
1176 (* if the proof is closed we cache it *)
1177 if green_proof then cache_add_success cache key proof
1178 else (* cache_add_success cache key closed_proof *)
1179 (debug_print (lazy ("NO CACHE: (no gree proof)"));cache)
1181 cache, orlist, fl, true
1184 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm gty));
1185 if size < minsize then
1186 (debug_print (lazy ("NO CACHE: (size <= minsize)")); cache) else
1187 (* if the substituted goal and the proof are closed we cache it *)
1188 if is_a_green_cut gty then
1189 if green_proof then cache_add_success cache gty proof
1190 else (* cache_add_success cache gty closed_proof *)
1191 (debug_print (lazy ("NO CACHE: (no green proof (gty))"));cache)
1195 CicTypeChecker.type_of_aux' ~subst:s
1196 m ctx closed_proof CicUniv.oblivion_ugraph
1198 if is_a_green_cut ty then
1199 cache_add_success cache ty closed_proof
1202 | CicTypeChecker.TypeCheckerFailure _ ->*)
1203 (debug_print (lazy ("NO CACHE: (no green gty )"));cache)
1205 cache, orlist, fl, false
1207 let close_failures (fl : fail list) (cache : cache) =
1209 (fun cache ((gno,depth,_),gty) ->
1210 debug_print (lazy ("FAIL: INDUCED: " ^ string_of_int gno));
1211 cache_add_failure cache gty depth)
1214 let put_in_subst subst metasenv (goalno,_,_) canonical_ctx t ty =
1215 let entry = goalno, (canonical_ctx, t,ty) in
1216 assert_subst_are_disjoint subst [entry];
1217 let subst = entry :: subst in
1219 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
1224 let mk_fake_proof metasenv subst (goalno,_,_) goalty context =
1225 None,metasenv,subst ,(lazy (Cic.Meta(goalno,mk_irl context))),goalty, []
1228 tables cache depth fake_proof goalno goalty subst context
1231 let active,passive,bag = tables in
1232 let ppterm = ppterm context in
1233 let status = (fake_proof,goalno) in
1234 if flags.use_only_paramod then
1236 debug_print (lazy ("PARAMODULATION SU: " ^
1237 string_of_int goalno ^ " " ^ ppterm goalty ));
1238 let goal_steps, saturation_steps, timeout =
1239 max_int,max_int,flags.timeout
1243 Saturation.given_clause bag status active passive
1244 goal_steps saturation_steps timeout
1246 | None, active, passive, bag ->
1247 [], (active,passive,bag), cache, flags
1248 | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
1250 assert_subst_are_disjoint subst subst';
1251 let subst = subst@subst' in
1253 order_new_goals metasenv subst open_goals ppterm
1256 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1259 [(!candidate_no,proof),metasenv,subst,open_goals],
1260 (active,passive,bag), cache, flags
1266 ("SUBSUMPTION SU: " ^ string_of_int goalno ^ " " ^ ppterm goalty));
1267 let res = Saturation.all_subsumed bag status active passive in
1270 (fun (subst',(_,metasenv,_subst,proof,_, _),open_goals) ->
1271 assert_subst_are_disjoint subst subst';
1272 let subst = subst@subst' in
1274 order_new_goals metasenv subst open_goals ppterm
1277 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1280 (!candidate_no,proof),metasenv,subst,open_goals)
1283 res', (active,passive,bag), cache, flags
1288 goalty tables subst fake_proof goalno depth context cand
1290 let ppterm = ppterm context in
1292 let actives, passives, bag = tables in
1293 let subst,((_,metasenv,_,_,_,_), open_goals),maxmeta =
1294 (PrimitiveTactics.apply_with_subst ~subst ~maxmeta:(Equality.maxmeta bag) ~term:cand)
1297 let tables = actives, passives, Equality.push_maxmeta bag maxmeta in
1298 debug_print (lazy (" OK: " ^ ppterm cand));
1299 let metasenv = CicRefine.pack_coercion_metasenv metasenv in
1300 let open_goals = order_new_goals metasenv subst open_goals ppterm in
1301 let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
1303 Some ((!candidate_no,lazy cand),metasenv,subst,open_goals), tables
1305 | ProofEngineTypes.Fail s -> None,tables
1306 | CicUnification.Uncertain s -> None,tables
1309 let sort_new_elems =
1310 List.sort (fun (_,_,_,l1) (_,_,_,l2) ->
1311 List.length (prop_only l1) - List.length (prop_only l2))
1314 let applicative_case
1315 tables depth subst fake_proof goalno goalty metasenv context universe
1318 let candidates = get_candidates flags.skip_trie_filtering universe cache goalty in
1321 (fun (tables,elems) cand ->
1323 try_candidate goalty
1324 tables subst fake_proof goalno depth context cand
1326 | None, tables -> tables, elems
1327 | Some x, tables -> tables, x::elems)
1328 (tables,[]) candidates
1330 let elems = sort_new_elems elems in
1331 elems, tables, cache
1334 let equational_and_applicative_case
1335 universe flags m s g gty tables cache context
1337 let goalno, depth, sort = g in
1338 let fake_proof = mk_fake_proof m s g gty context in
1339 if is_equational_case gty flags then
1340 let elems,tables,cache, flags =
1341 equational_case tables cache
1342 depth fake_proof goalno gty s context flags
1344 let more_elems, tables, cache =
1345 if flags.use_only_paramod then
1349 tables depth s fake_proof goalno
1350 gty m context universe cache flags
1352 elems@more_elems, tables, cache, flags
1354 let elems, tables, cache =
1355 applicative_case tables depth s fake_proof goalno
1356 gty m context universe cache flags
1358 elems, tables, cache, flags
1360 let rec condition_for_hint i = function
1362 | S (_,_,(j,_),_):: tl -> j <> i (* && condition_for_hint i tl *)
1363 | _::tl -> condition_for_hint i tl
1365 let remove_s_from_fl (id,_,_) (fl : fail list) =
1366 let rec aux = function
1368 | ((id1,_,_),_)::tl when id = id1 -> tl
1369 | hd::tl -> hd :: aux tl
1374 let prunable_for_size flags s m todo =
1375 let rec aux b = function
1376 | (S _)::tl -> aux b tl
1377 | (D (_,_,T))::tl -> aux b tl
1379 (match calculate_goal_ty g s m with
1381 | Some (canonical_ctx, gty) ->
1383 Utils.weight_of_term
1384 ~consider_metas:false ~count_metas_occurrences:true gty in
1385 let newb = b || gsize > flags.maxgoalsizefactor in
1392 let prunable ty todo =
1393 let rec aux b = function
1394 | (S(_,k,_,_))::tl -> aux (b || Equality.meta_convertibility k ty) tl
1395 | (D (_,_,T))::tl -> aux b tl
1403 let prunable menv subst ty todo =
1404 let rec aux = function
1405 | (S(_,k,_,_))::tl ->
1406 (match Equality.meta_convertibility_subst k ty menv with
1409 no_progress variant tl (* || aux tl*))
1410 | (D (_,_,T))::tl -> aux tl
1412 and no_progress variant = function
1413 | [] -> (*prerr_endline "++++++++++++++++++++++++ no_progress";*) true
1414 | D ((n,_,P) as g)::tl ->
1415 (match calculate_goal_ty g subst menv with
1416 | None -> no_progress variant tl
1418 (match calculate_goal_ty g variant menv with
1419 | None -> assert false
1421 if gty = gty' then no_progress variant tl
1423 (prerr_endline (string_of_int n);
1424 prerr_endline (CicPp.ppterm gty);
1425 prerr_endline (CicPp.ppterm gty');
1426 prerr_endline "---------- subst";
1427 prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv subst);
1428 prerr_endline "---------- variant";
1429 prerr_endline (CicMetaSubst.ppsubst ~metasenv:menv variant);
1430 prerr_endline "---------- menv";
1431 prerr_endline (CicMetaSubst.ppmetasenv [] menv);
1432 no_progress variant tl) *)
1434 | _::tl -> no_progress variant tl
1439 let condition_for_prune_hint prune (m, s, size, don, todo, fl) =
1441 HExtlib.filter_map (function S (_,_,(c,_),_) -> Some c | _ -> None) todo
1443 List.for_all (fun i -> List.for_all (fun j -> i<>j) prune) s
1445 let filter_prune_hint l =
1446 let prune = !prune_hint in
1447 prune_hint := []; (* possible race... *)
1448 if prune = [] then l
1449 else List.filter (condition_for_prune_hint prune) l
1451 let auto_main tables context flags universe cache elems =
1452 auto_context := context;
1453 let rec aux tables flags cache (elems : status) =
1454 (* pp_status context elems; *)
1455 (* DEBUGGING CODE: uncomment these two lines to stop execution at each iteration
1456 auto_status := elems;
1459 let elems = filter_prune_hint elems in
1461 | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
1462 debug_print (lazy "skip");
1464 | Some i when condition_for_hint i todo ->
1465 aux tables flags cache orlist
1468 aux tables flags cache elems)
1470 (* complete failure *)
1471 debug_print (lazy "give up");
1472 Gaveup (tables, cache)
1473 | (m, s, _, _, [],_)::orlist ->
1474 (* complete success *)
1475 debug_print (lazy "success");
1476 Proved (m, s, orlist, tables, cache)
1477 | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist
1478 when not flags.AutoTypes.do_types ->
1479 (* skip since not Prop, don't even check if closed by side-effect *)
1480 debug_print (lazy "skip existential goal");
1481 aux tables flags cache ((m, s, size, don, todo, fl)::orlist)
1482 | (m, s, size, don, (S(g, key, c,minsize) as op)::todo, fl)::orlist ->
1483 (* partial success, cache g and go on *)
1484 let cache, orlist, fl, sibling_pruned =
1485 add_to_cache_and_del_from_orlist_if_green_cut
1486 g s m cache key todo orlist fl context size minsize
1488 debug_print (lazy (AutoCache.cache_print context cache));
1489 let fl = remove_s_from_fl g fl in
1490 let don = if sibling_pruned then don else op::don in
1491 aux tables flags cache ((m, s, size, don, todo, fl)::orlist)
1492 | (m, s, size, don, todo, fl)::orlist
1493 when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
1494 debug_print (lazy ("FAIL: WIDTH"));
1495 (* too many goals in and generated by last th *)
1496 let cache = close_failures fl cache in
1497 aux tables flags cache orlist
1498 | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize ->
1500 (lazy ("FAIL: SIZE: "^string_of_int size ^
1501 " > " ^ string_of_int flags.maxsize ));
1502 (* we already have a too large proof term *)
1503 let cache = close_failures fl cache in
1504 aux tables flags cache orlist
1505 | _ when Unix.gettimeofday () > flags.timeout ->
1507 debug_print (lazy ("FAIL: TIMEOUT"));
1508 Gaveup (tables, cache)
1509 | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status ->
1511 debug_print (lazy "attack goal");
1512 match calculate_goal_ty g s m with
1514 (* closed by side effect *)
1515 debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
1516 aux tables flags cache ((m,s,size,don,todo, fl)::orlist)
1517 | Some (canonical_ctx, gty) ->
1519 Utils.weight_of_term ~consider_metas:false ~count_metas_occurrences:true gty
1521 if gsize > flags.maxgoalsizefactor then
1522 (debug_print (lazy ("FAIL: SIZE: goal: "^string_of_int gsize));
1523 aux tables flags cache orlist)
1524 else if prunable_for_size flags s m todo then
1525 (debug_print (lazy ("POTO at depth: "^(string_of_int depth)));
1526 aux tables flags cache orlist)
1528 (* still to be proved *)
1529 (debug_print (lazy ("EXAMINE: "^CicPp.ppterm gty));
1530 match cache_examine cache gty with
1531 | Failed_in d when d >= depth ->
1533 debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
1534 let cache = close_failures fl cache in
1535 aux tables flags cache orlist
1536 | UnderInspection ->
1538 debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
1539 let cache = close_failures fl cache in
1540 aux tables flags cache orlist
1542 debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
1543 let s, m = put_in_subst s m g canonical_ctx t gty in
1544 aux tables flags cache ((m, s, size, don,todo, fl)::orlist)
1546 | Failed_in _ when depth > 0 ->
1547 ( (* more depth or is the first time we see the goal *)
1548 if prunable m s gty todo then
1550 "FAIL: LOOP: one father is equal"));
1551 aux tables flags cache orlist)
1553 let cache = cache_add_underinspection cache gty depth in
1554 auto_status := status;
1557 (lazy ("INSPECTING: " ^
1558 string_of_int gno ^ "("^ string_of_int size ^ "): "^
1560 (* elems are possible computations for proving gty *)
1561 let elems, tables, cache, flags =
1562 equational_and_applicative_case
1563 universe flags m s g gty tables cache context
1566 (* this goal has failed *)
1567 let cache = close_failures ((g,gty)::fl) cache in
1568 aux tables flags cache orlist
1570 (* elems = (cand,m,s,gl) *)
1571 let size_gl l = List.length
1572 (List.filter (function (_,_,P) -> true | _ -> false) l)
1575 let inj_gl gl = List.map (fun g -> D g) gl in
1576 let rec map = function
1577 | [] -> assert false
1578 | (cand,m,s,gl)::[] ->
1579 (* in the last one we add the failure *)
1581 inj_gl gl @ (S(g,gty,cand,size+1))::todo
1583 (* we are the last in OR, we fail on g and
1584 * also on all failures implied by g *)
1585 (m,s, size + size_gl gl, don, todo, (g,gty)::fl)
1587 | (cand,m,s,gl)::tl ->
1588 (* we add the S step after gl and before todo *)
1590 inj_gl gl @ (S(g,gty,cand,size+1))::todo
1592 (* since we are not the last in OR, we do not
1594 (m,s, size + size_gl gl, don, todo, []) :: map tl
1598 aux tables flags cache elems)
1601 debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
1602 let cache = close_failures fl cache in
1603 aux tables flags cache orlist)
1605 (aux tables flags cache elems : auto_result)
1610 auto_all_solutions tables universe cache context metasenv gl flags
1612 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
1615 (fun (x,s) -> D (x,flags.maxdepth,s)) goals
1617 let elems = [metasenv,[],1,[],goals,[]] in
1618 let rec aux tables solutions cache elems flags =
1619 match auto_main tables context flags universe cache elems with
1620 | Gaveup (tables,cache) ->
1621 solutions,cache, tables
1622 | Proved (metasenv,subst,others,tables,cache) ->
1623 if Unix.gettimeofday () > flags.timeout then
1624 ((subst,metasenv)::solutions), cache, tables
1626 aux tables ((subst,metasenv)::solutions) cache others flags
1628 let rc = aux tables [] cache elems flags in
1630 | [],cache,tables -> [],cache,tables
1631 | solutions, cache,tables ->
1634 (fun (subst,newmetasenv) ->
1636 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv ~newmetasenv
1638 if opened = [] then Some subst else None)
1641 solutions,cache,tables
1644 (******************* AUTO ***************)
1646 let auto flags metasenv tables universe cache context metasenv gl =
1647 let initial_time = Unix.gettimeofday() in
1648 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
1649 let goals = List.map (fun (x,s) -> D(x,flags.maxdepth,s)) goals in
1650 let elems = [metasenv,[],1,[],goals,[]] in
1651 match auto_main tables context flags universe cache elems with
1652 | Proved (metasenv,subst,_, tables,cache) ->
1654 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
1655 Some (subst,metasenv), cache
1656 | Gaveup (tables,cache) ->
1658 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
1662 let applyS_tac ~dbd ~term ~params ~automation_cache =
1663 ProofEngineTypes.mk_tactic
1667 apply_smart ~dbd ~term ~subst:[] ~params ~automation_cache status
1671 | CicUnification.UnificationFailure msg
1672 | CicTypeChecker.TypeCheckerFailure msg ->
1673 raise (ProofEngineTypes.Fail msg))
1675 let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~automation_cache (proof, goal) =
1676 let flags = flags_of_params params () in
1677 let use_library = flags.use_library in
1678 let universe, tables, cache =
1679 init_cache_and_tables
1680 ~dbd ~use_library ~use_context:(not flags.skip_context)
1681 automation_cache univ (proof, goal)
1683 let _,metasenv,_subst,_,_, _ = proof in
1684 let _,context,goalty = CicUtil.lookup_meta goal metasenv in
1686 if flags.close_more then
1688 tables context (proof, goal)
1689 auto_all_solutions universe cache
1690 else tables,cache in
1691 let initial_time = Unix.gettimeofday() in
1692 let (_,oldmetasenv,_subst,_,_, _) = proof in
1695 metasenv,[],1,[],[D (goal,flags.maxdepth,P)],[]
1697 match auto_main tables context flags universe cache [elem] with
1698 | Proved (metasenv,subst,_, tables,cache) ->
1700 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
1701 let proof,metasenv =
1702 ProofEngineHelpers.subst_meta_and_metasenv_in_proof
1703 proof goal subst metasenv
1706 ProofEngineHelpers.compare_metasenvs ~oldmetasenv
1707 ~newmetasenv:metasenv
1710 | Gaveup (tables,cache) ->
1713 string_of_float(Unix.gettimeofday()-.initial_time)));
1714 raise (ProofEngineTypes.Fail (lazy "Auto gave up"))
1717 let auto_tac ~dbd ~params ~automation_cache =
1718 ProofEngineTypes.mk_tactic (auto_tac ~params ~dbd ~automation_cache);;
1720 let eq_of_goal = function
1721 | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri ->
1723 | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
1726 (* performs steps of rewrite with the universe, obtaining if possible
1728 let solve_rewrite_tac ~automation_cache ~params:(univ,params) (proof,goal)=
1729 let steps = int_of_string (string params "steps" "1") in
1730 let use_context = bool params "use_context" true in
1731 let universe, tables, cache =
1732 init_cache_and_tables ~use_library:false ~use_context
1733 automation_cache univ (proof,goal)
1735 let actives, passives, bag = tables in
1736 let pa,metasenv,_subst,pb,pc,pd = proof in
1737 let _,context,ty = CicUtil.lookup_meta goal metasenv in
1738 let eq_uri = eq_of_goal ty in
1739 let initgoal = [], metasenv, ty in
1741 let equalities = (Saturation.list_of_passive passives) in
1742 List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd actives) equalities
1744 let env = metasenv,context,CicUniv.oblivion_ugraph in
1745 match Indexing.solve_demodulating bag env table initgoal steps with
1746 | Some (proof, metasenv, newty) ->
1749 | Cic.Appl[Cic.MutInd _;eq_ty;left;_] ->
1750 Equality.Exact (Equality.refl_proof eq_uri eq_ty left)
1754 Equality.build_goal_proof
1755 bag eq_uri proof refl newty [] context metasenv
1757 let proofterm, _, metasenv, _ =
1758 CicRefine.type_of_aux' metasenv context proofterm
1759 CicUniv.oblivion_ugraph
1761 let status = (pa,metasenv,_subst,pb,pc,pd), goal in
1762 ProofEngineTypes.apply_tactic
1763 (PrimitiveTactics.apply_tac ~term:proofterm) status
1766 (ProofEngineTypes.Fail (lazy
1767 ("Unable to solve with " ^ string_of_int steps ^ " demodulations")))
1769 let solve_rewrite_tac ~params ~automation_cache () =
1770 ProofEngineTypes.mk_tactic (solve_rewrite_tac ~automation_cache ~params)
1773 (* Demodulate thorem *)
1774 let open_type ty bo =
1775 let rec open_type_aux context ty k args =
1777 | Cic.Prod (n,s,t) ->
1779 FreshNamesGenerator.mk_fresh_name [] context n ~typ:s ~subst:[] in
1780 let entry = match n' with
1781 | Cic.Name _ -> Some (n',(Cic.Decl s))
1782 | Cic.Anonymous -> None
1784 open_type_aux (entry::context) t (k+1) ((Cic.Rel k)::args)
1785 | Cic.LetIn (n,s,sty,t) ->
1786 let entry = Some (n,(Cic.Def (s,sty)))
1788 open_type_aux (entry::context) t (k+1) args
1789 | _ -> context, ty, args
1791 let context, ty, args = open_type_aux [] ty 1 [] in
1793 | [] -> context, ty, bo
1794 | _ -> context, ty, Cic.Appl (bo::args)
1797 let rec close_type bo ty context =
1799 | [] -> assert_proof_is_valid bo [] [] ty; (bo,ty)
1800 | Some (n,(Cic.Decl s))::tl ->
1801 close_type (Cic.Lambda (n,s,bo)) (Cic.Prod (n,s,ty)) tl
1802 | Some (n,(Cic.Def (s,sty)))::tl ->
1803 close_type (Cic.LetIn (n,s,sty,bo)) (Cic.LetIn (n,s,sty,ty)) tl
1807 let is_subsumed univ context ty =
1808 let candidates = Universe.get_candidates univ ty in
1812 | Some found -> Some found
1815 let mk_irl = CicMkImplicit.identity_relocation_list_for_metavariable in
1816 let metasenv = [(0,context,ty)] in
1817 let fake_proof = None,metasenv,[] , (lazy (Cic.Meta(0,mk_irl context))),ty,[] in
1818 let subst,((_,metasenv,_,_,_,_), open_goals),maxmeta =
1819 (PrimitiveTactics.apply_with_subst ~subst:[] ~maxmeta:0 ~term:cand) (fake_proof,0)
1821 let prop_goals, other = split_goals_in_prop metasenv subst open_goals in
1822 if prop_goals = [] then Some cand else None
1824 | ProofEngineTypes.Fail s -> None
1825 | CicUnification.Uncertain s -> None
1829 let demodulate_theorem ~automation_cache uri =
1831 match LibraryObjects.eq_URI () with
1833 | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
1834 let obj,_ = CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
1838 | Cic.Constant(n, _, ty ,_, _) -> open_type ty (Cic.Const(uri,[]))
1839 | _ -> raise (ProofEngineTypes.Fail (lazy "not a theorem"))
1841 if CicUtil.is_closed ty then
1842 raise (ProofEngineTypes.Fail (lazy ("closed term: dangerous reduction")));
1843 let initgoal = [], [], ty in
1844 (* compute the signature *)
1846 let ty_set = MetadataConstraints.constants_of ty in
1847 let hyp_set = MetadataQuery.signature_of_hypothesis context [] in
1848 let set = MetadataConstraints.UriManagerSet.union ty_set hyp_set in
1849 MetadataQuery.close_with_types set [] context
1851 (* retrieve equations from the universe universe *)
1852 (* XXX automation_cache *)
1853 let universe = automation_cache.AutomationCache.univ in
1855 retrieve_equations true signature universe AutoCache.cache_empty context []
1858 (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
1863 CicTypeChecker.type_of_aux' [] context t CicUniv.oblivion_ugraph
1865 (* retrieve_equations could also return flexible terms *)
1866 if is_an_equality ty then Some(t,ty)
1869 let ty' = unfold context ty in
1870 if is_an_equality ty' then Some(t,ty') else None
1871 with ProofEngineTypes.Fail _ -> None)
1874 let bag = Equality.mk_equality_bag () in
1876 let bag, units, _, newmeta =
1877 partition_unit_equalities context [] (CicMkImplicit.new_meta [] []) bag eqs_and_types
1881 (fun tbl eq -> Indexing.index tbl eq)
1882 Indexing.empty units
1884 let changed,(newproof,newmetasenv, newty) =
1886 ([],context,CicUniv.oblivion_ugraph) table initgoal in
1889 let oldproof = Equality.Exact bo in
1891 Equality.build_goal_proof (~contextualize:false) (~forward:true) bag
1892 eq_uri newproof oldproof ty [] context newmetasenv
1894 if newmetasenv <> [] then
1895 raise (ProofEngineTypes.Fail (lazy ("metasenv not empty")))
1898 assert_proof_is_valid proofterm newmetasenv context newty;
1899 match is_subsumed universe context newty with
1901 (ProofEngineTypes.Fail (lazy ("subsumed by " ^ CicPp.ppterm t)))
1902 | None -> close_type proofterm newty context
1905 else (* if newty = ty then *)
1906 raise (ProofEngineTypes.Fail (lazy "no progress"))
1907 (*else ProofEngineTypes.apply_tactic
1908 (ReductionTactics.simpl_tac
1909 ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
1913 (* NEW DEMODULATE *)
1914 let demodulate_tac ~dbd ~automation_cache ~params:(univ, params) (proof,goal)=
1915 let universe, tables, cache =
1916 init_cache_and_tables
1917 ~dbd ~use_library:false ~use_context:true
1918 automation_cache univ (proof,goal)
1921 match LibraryObjects.eq_URI () with
1923 | None -> raise (ProofEngineTypes.Fail (lazy "equality not declared")) in
1924 let active, passive, bag = tables in
1925 let curi,metasenv,_subst,pbo,pty, attrs = proof in
1926 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
1927 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
1928 let initgoal = [], metasenv, ty in
1929 let equalities = (Saturation.list_of_passive passive) in
1930 (* we demodulate using both actives passives *)
1931 let env = metasenv,context,CicUniv.empty_ugraph in
1932 debug_print (lazy ("PASSIVES:" ^ string_of_int(List.length equalities)));
1933 List.iter (fun e -> debug_print (lazy (Equality.string_of_equality ~env e)))
1937 (fun tbl eq -> Indexing.index tbl eq)
1938 (snd active) equalities
1940 let changed,(newproof,newmetasenv, newty) =
1941 (* Indexing.demodulation_goal bag *)
1943 (metasenv,context,CicUniv.oblivion_ugraph) table initgoal
1947 let maxm = CicMkImplicit.new_meta metasenv [] in
1948 let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
1950 Equality.build_goal_proof (~contextualize:false) bag
1951 eq_uri newproof opengoal ty [] context metasenv
1953 let metasenv = (maxm,context,newty)::metasenv in
1954 let proofterm, _, metasenv, _ =
1955 CicRefine.type_of_aux' metasenv context proofterm
1956 CicUniv.oblivion_ugraph
1958 let extended_status =
1959 (curi,metasenv,_subst,pbo,pty, attrs),goal in
1960 let (status,newgoals) =
1961 ProofEngineTypes.apply_tactic
1962 (PrimitiveTactics.apply_tac ~term:proofterm)
1964 (status,maxm::newgoals)
1966 else (* if newty = ty then *)
1967 raise (ProofEngineTypes.Fail (lazy "no progress"))
1968 (*else ProofEngineTypes.apply_tactic
1969 (ReductionTactics.simpl_tac
1970 ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
1973 let demodulate_tac ~dbd ~params ~automation_cache =
1974 ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~params ~automation_cache);;
1976 let demodulate_tac ~dbd ~params:(_,flags as params) ~automation_cache =
1977 let all = bool flags "all" false in
1979 solve_rewrite_tac ~params ~automation_cache ()
1981 demodulate_tac ~dbd ~params ~automation_cache
1984 let pp_proofterm = Equality.pp_proofterm;;
1986 let revision = "$Revision$";;
1987 let size_and_depth context metasenv t = 100, 100