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);;
33 type auto_params = Cic.term list * (string * string) list
37 (* closing a term w.r.t. its metavariables
38 very naif version: it does not take dependencies properly into account *)
40 let naif_closure ?(prefix_name="xxx_") t metasenv context =
41 let metasenv = ProofEngineHelpers.sort_metasenv metasenv in
42 let n = List.length metasenv in
43 let what = List.map (fun (i,cc,ty) -> Cic.Meta(i,[])) metasenv in
46 (fun (i,acc) (_,cc,ty) -> (i-1,Cic.Rel i::acc))
49 let t = CicSubstitution.lift n t in
51 ProofEngineReduction.replace_lifting
52 ~equality:(fun c t1 t2 ->
54 | Cic.Meta(i,_),Cic.Meta(j,_) -> i = j
56 ~context ~what ~with_what ~where:t
60 (fun (n,t) (_,cc,ty) ->
61 n-1, Cic.Lambda(Cic.Name (prefix_name^string_of_int n),
62 CicSubstitution.lift n ty,t))
68 let lambda_close ?prefix_name t menv ctx =
69 let t = naif_closure ?prefix_name t menv ctx in
71 (fun (t,i) -> function
72 | None -> CicSubstitution.subst (Cic.Implicit None) t,i (* delift *)
73 | Some (name, Cic.Decl ty) -> Cic.Lambda (name, ty, t),i+1
74 | Some (name, Cic.Def (bo, ty)) -> Cic.LetIn (name, bo, ty, t),i+1)
75 (t,List.length menv) ctx
78 (* functions for retrieving theorems *)
80 exception FillingFailure of AutoCache.cache * int
82 let rec unfold context = function
83 | Cic.Prod(name,s,t) ->
84 let t' = unfold ((Some (name,Cic.Decl s))::context) t in
86 | t -> ProofEngineReduction.unfold context t
88 let find_library_theorems dbd proof goal =
89 let univ = MetadataQuery.universe_of_goal ~dbd false proof goal in
90 let terms = List.map CicUtil.term_of_uri univ in
93 (t,fst(CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph)))
96 let find_context_theorems context metasenv =
99 (fun (res,i) ctxentry ->
101 | Some (_,Cic.Decl t) ->
102 (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
103 | Some (_,Cic.Def (_,t)) ->
104 (Cic.Rel i, CicSubstitution.lift i t)::res,i+1
109 let rec is_an_equality = function
110 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
111 when (LibraryObjects.is_eq_URI uri) -> true
112 | Cic.Prod (_, _, t) -> is_an_equality t
116 let partition_equalities =
117 List.partition (fun (_,ty) -> is_an_equality ty)
120 let default_auto maxm _ _ cache _ _ _ _ = [],cache,maxm ;;
123 let is_unit_equation context metasenv oldnewmeta term =
124 let head, metasenv, args, newmeta =
125 TermUtil.saturate_term oldnewmeta metasenv context term 0
127 let propositional_args =
131 let _,_,mt = CicUtil.lookup_meta i metasenv in
133 CicTypeChecker.type_of_aux' metasenv context mt
137 CicReduction.are_convertible ~metasenv context
138 sort (Cic.Sort Cic.Prop) u
140 if b then Some i else None
144 if propositional_args = [] then
146 List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv
148 Some (args,metasenv,newmetas,head,newmeta)
152 let get_candidates universe cache t =
154 (Universe.get_candidates universe t)@(AutoCache.get_candidates cache t)
157 (lazy ("candidates for " ^ (CicPp.ppterm t) ^ " = " ^
158 (String.concat "\n" (List.map CicPp.ppterm candidates)))) in
159 debug_print debug_msg;
163 let only signature context metasenv t =
166 CicTypeChecker.type_of_aux' metasenv context t CicUniv.empty_ugraph
168 let consts = MetadataConstraints.constants_of ty in
169 let b = MetadataConstraints.UriManagerSet.subset consts signature in
172 let ty' = unfold context ty in
173 let consts' = MetadataConstraints.constants_of ty' in
174 MetadataConstraints.UriManagerSet.subset consts' signature
176 | CicTypeChecker.TypeCheckerFailure _ -> assert false
177 | ProofEngineTypes.Fail _ -> false (* unfold may fail *)
180 let not_default_eq_term t =
182 let uri = CicUtil.uri_of_term t in
183 not (LibraryObjects.in_eq_URIs uri)
184 with Invalid_argument _ -> true
186 let retrieve_equations dont_filter signature universe cache context metasenv =
187 match LibraryObjects.eq_URI() with
190 let eq_uri = UriManager.strip_xpointer eq_uri in
191 let fake= Cic.Meta(-1,[]) in
192 let fake_eq = Cic.Appl [Cic.MutInd (eq_uri,0, []);fake;fake;fake] in
193 let candidates = get_candidates universe cache fake_eq in
194 if dont_filter then candidates
196 let candidates = List.filter not_default_eq_term candidates in
197 List.filter (only signature context metasenv) candidates
199 let build_equality bag head args proof newmetas maxmeta =
201 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] ->
203 if args = [] then proof else Cic.Appl (proof::args)
205 let o = !Utils.compare_terms t1 t2 in
206 let stat = (ty,t1,t2,o) in
207 (* let w = compute_equality_weight stat in *)
209 let proof = Equality.Exact p in
210 let e = Equality.mk_equality bag (w, proof, stat, newmetas) in
211 (* to clean the local context of metas *)
212 Equality.fix_metas bag maxmeta e
216 let partition_unit_equalities context metasenv newmeta bag equations =
218 (fun (units,other,maxmeta)(t,ty) ->
219 if not (CicUtil.is_meta_closed t && CicUtil.is_meta_closed ty) then
222 ("Skipping " ^ CicMetaSubst.ppterm_in_context ~metasenv [] t context
223 ^ " since it is not meta closed")
225 units,(t,ty)::other,maxmeta
227 match is_unit_equation context metasenv maxmeta ty with
228 | Some (args,metasenv,newmetas,head,newmeta') ->
229 let maxmeta,equality =
230 build_equality bag head args t newmetas newmeta' in
231 equality::units,other,maxmeta
233 units,(t,ty)::other,maxmeta)
234 ([],[],newmeta) equations
237 (Saturation.make_active [],
238 Saturation.make_passive [],
239 Equality.mk_equality_bag)
241 let init_cache_and_tables
242 ?dbd use_library paramod use_context dont_filter universe (proof, goal)
244 (* the local cache in initially empty *)
245 let cache = AutoCache.cache_empty in
246 let _, metasenv, _subst,_, _, _ = proof in
247 let signature = MetadataQuery.signature_of metasenv goal in
248 let newmeta = CicMkImplicit.new_meta metasenv [] in
249 let _,context,_ = CicUtil.lookup_meta goal metasenv in
250 let ct = if use_context then find_context_theorems context metasenv else [] in
252 (lazy ("ho trovato nel contesto " ^ (string_of_int (List.length ct))));
254 match use_library, dbd with
255 | true, Some dbd -> find_library_theorems dbd metasenv goal
259 (lazy ("ho trovato nella libreria " ^ (string_of_int (List.length lt))));
260 let cache = cache_add_list cache context (ct@lt) in
262 retrieve_equations dont_filter signature universe cache context metasenv
265 (lazy ("ho trovato equazioni n. "^(string_of_int (List.length equations))));
270 CicTypeChecker.type_of_aux'
271 metasenv context t CicUniv.empty_ugraph
273 (* retrieve_equations could also return flexible terms *)
274 if is_an_equality ty then Some(t,ty)
277 let ty' = unfold context ty in
278 if is_an_equality ty' then Some(t,ty') else None
279 with ProofEngineTypes.Fail _ -> None)
282 let bag = Equality.mk_equality_bag () in
283 let units, other_equalities, newmeta =
284 partition_unit_equalities context metasenv newmeta bag eqs_and_types
286 (* SIMPLIFICATION STEP
288 let env = (metasenv, context, CicUniv.empty_ugraph) in
289 let eq_uri = HExtlib.unopt (LibraryObjects.eq_URI()) in
290 Saturation.simplify_equalities bag eq_uri env units
293 let passive = Saturation.make_passive units in
294 let no = List.length units in
295 let active = Saturation.make_active [] in
296 let active,passive,newmeta =
297 if paramod then active,passive,newmeta
299 Saturation.pump_actives
300 context bag newmeta active passive (no+1) infinity
302 (active,passive,bag),cache,newmeta
304 let fill_hypothesis context metasenv oldnewmeta term tables (universe:Universe.universe) cache auto fast =
305 let head, metasenv, args, newmeta =
306 TermUtil.saturate_term oldnewmeta metasenv context term 0
308 let propositional_args =
312 let _,_,mt = CicUtil.lookup_meta i metasenv in
314 CicTypeChecker.type_of_aux' metasenv context mt
318 CicReduction.are_convertible ~metasenv context
319 sort (Cic.Sort Cic.Prop) u
321 if b then Some i else None
325 let results,cache,newmeta =
326 if propositional_args = [] then
327 let newmetas = List.filter (fun (i,_,_) -> i >= oldnewmeta) metasenv in
328 [args,metasenv,newmetas,head,newmeta],cache,newmeta
332 None,metasenv,term,term (* term non e' significativo *)
336 {AutoTypes.default_flags() with
337 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
338 maxwidth = 2;maxdepth = 2;
339 use_paramod=true;use_only_paramod=false}
341 {AutoTypes.default_flags() with
342 AutoTypes.timeout = Unix.gettimeofday() +. 1.0;
343 maxwidth = 2;maxdepth = 4;
344 use_paramod=true;use_only_paramod=false}
346 match auto newmeta tables universe cache context metasenv propositional_args flags with
347 | [],cache,newmeta -> raise (FillingFailure (cache,newmeta))
348 | substs,cache,newmeta ->
352 CicMetaSubst.apply_subst_metasenv subst metasenv
354 let head = CicMetaSubst.apply_subst subst head in
356 List.filter (fun (i,_,_) ->i >= oldnewmeta) metasenv
358 let args = List.map (CicMetaSubst.apply_subst subst) args in
359 let newm = CicMkImplicit.new_meta metasenv subst in
360 args,metasenv,newmetas,head,max newm newmeta)
361 substs, cache, newmeta
363 results,cache,newmeta
365 let build_equalities auto context metasenv tables universe cache newmeta equations =
367 (fun (facts,cache,newmeta) (t,ty) ->
368 (* in any case we add the equation to the cache *)
369 let cache = AutoCache.cache_add_list cache context [(t,ty)] in
371 let saturated,cache,newmeta =
372 fill_hypothesis context metasenv newmeta ty tables universe cache auto true
374 let (active,passive,bag) = tables in
375 let eqs,bag,newmeta =
377 (fun (acc,bag,newmeta) (args,metasenv,newmetas,head,newmeta') ->
378 let maxmeta,equality =
379 build_equality bag head args t newmetas newmeta'
381 equality::acc,bag,maxmeta)
382 ([],bag,newmeta) saturated
384 (eqs@facts, cache, newmeta)
385 with FillingFailure (cache,newmeta) ->
386 (* if filling hypothesis fails we add the equation to
388 (facts,cache,newmeta)
390 ([],cache,newmeta) equations
392 let close_more tables maxmeta context status auto universe cache =
393 let (active,passive,bag) = tables in
394 let proof, goalno = status in
395 let _, metasenv,_subst,_,_, _ = proof in
396 let signature = MetadataQuery.signature_of metasenv goalno in
398 retrieve_equations false signature universe cache context metasenv
404 CicTypeChecker.type_of_aux' metasenv context t CicUniv.empty_ugraph in
405 (* retrieve_equations could also return flexible terms *)
406 if is_an_equality ty then Some(t,ty) else None)
408 let units, cache, maxm =
409 build_equalities auto context metasenv tables universe cache maxmeta eqs_and_types in
410 debug_print (lazy (">>>>>>> gained from a new context saturation >>>>>>>>>" ^
411 string_of_int maxm));
413 (fun e -> debug_print (lazy (Equality.string_of_equality e)))
415 debug_print (lazy ">>>>>>>>>>>>>>>>>>>>>>");
416 let passive = Saturation.add_to_passive units passive in
417 let no = List.length units in
418 debug_print (lazy ("No = " ^ (string_of_int no)));
419 let active,passive,newmeta =
420 Saturation.pump_actives context bag maxm active passive (no+1) infinity
422 (active,passive,bag),cache,newmeta
424 let find_context_equalities
425 maxmeta bag context proof (universe:Universe.universe) cache
427 let module C = Cic in
428 let module S = CicSubstitution in
429 let module T = CicTypeChecker in
430 let _,metasenv,_subst,_,_, _ = proof in
431 let newmeta = max (ProofEngineHelpers.new_meta_of_proof ~proof) maxmeta in
432 (* if use_auto is true, we try to close the hypothesis of equational
433 statements using auto; a naif, and probably wrong approach *)
434 let rec aux cache index newmeta = function
435 | [] -> [], newmeta,cache
436 | (Some (_, C.Decl (term)))::tl ->
439 (Printf.sprintf "Examining: %d (%s)" index (CicPp.ppterm term)));
440 let do_find context term =
442 | C.Prod (name, s, t) when is_an_equality t ->
445 let term = S.lift index term in
446 let saturated,cache,newmeta =
447 fill_hypothesis context metasenv newmeta term
448 empty_tables universe cache default_auto false
452 (fun (acc,newmeta) (args,metasenv,newmetas,head,newmeta') ->
453 let newmeta, equality =
455 bag head args (Cic.Rel index) newmetas (max newmeta newmeta')
457 equality::acc, newmeta + 1)
458 ([],newmeta) saturated
461 with FillingFailure (cache,newmeta) ->
463 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
464 when LibraryObjects.is_eq_URI uri ->
465 let term = S.lift index term in
467 build_equality bag term [] (Cic.Rel index) [] newmeta
469 [e], (newmeta+1),cache
470 | _ -> [], newmeta, cache
472 let eqs, newmeta, cache = do_find context term in
473 let rest, newmeta,cache = aux cache (index+1) newmeta tl in
474 List.map (fun x -> index,x) eqs @ rest, newmeta, cache
476 aux cache (index+1) newmeta tl
478 let il, maxm, cache =
479 aux cache 1 newmeta context
481 let indexes, equalities = List.split il in
482 indexes, equalities, maxm, cache
485 (********** PARAMETERS PASSING ***************)
487 let bool params name default =
489 let s = List.assoc name params in
490 if s = "" || s = "1" || s = "true" || s = "yes" || s = "on" then true
491 else if s = "0" || s = "false" || s = "no" || s= "off" then false
493 let msg = "Unrecognized value for parameter "^name^"\n" in
494 let msg = msg^"Accepted values are 1,true,yes,on and 0,false,no,off" in
495 raise (ProofEngineTypes.Fail (lazy msg))
496 with Not_found -> default
499 let string params name default =
500 try List.assoc name params with
501 | Not_found -> default
504 let int params name default =
505 try int_of_string (List.assoc name params) with
506 | Not_found -> default
508 raise (ProofEngineTypes.Fail (lazy (name ^ " must be an integer")))
511 let flags_of_params params ?(for_applyS=false) () =
512 let int = int params in
513 let bool = bool params in
514 let close_more = bool "close_more" false in
515 let use_paramod = bool "use_paramod" true in
516 let use_only_paramod =
517 if for_applyS then true else bool "paramodulation" false in
518 let use_library = bool "library"
519 ((AutoTypes.default_flags()).AutoTypes.use_library) in
520 let depth = int "depth" ((AutoTypes.default_flags()).AutoTypes.maxdepth) in
521 let width = int "width" ((AutoTypes.default_flags()).AutoTypes.maxwidth) in
522 let size = int "size" ((AutoTypes.default_flags()).AutoTypes.maxsize) in
523 let gsize = int "gsize" ((AutoTypes.default_flags()).AutoTypes.maxgoalsizefactor) in
524 let do_type = bool "type" false in
525 let timeout = int "timeout" 0 in
526 { AutoTypes.maxdepth =
527 if use_only_paramod then 2 else depth;
528 AutoTypes.maxwidth = width;
529 AutoTypes.maxsize = size;
532 if for_applyS then Unix.gettimeofday () +. 30.0
536 Unix.gettimeofday() +. (float_of_int timeout);
537 AutoTypes.use_library = use_library;
538 AutoTypes.use_paramod = use_paramod;
539 AutoTypes.use_only_paramod = use_only_paramod;
540 AutoTypes.close_more = close_more;
541 AutoTypes.dont_cache_failures = false;
542 AutoTypes.maxgoalsizefactor = gsize;
543 AutoTypes.do_types = do_type;
546 let universe_of_params metasenv context universe tl =
547 if tl = [] then universe else
551 fst (CicTypeChecker.type_of_aux' metasenv context term
552 CicUniv.oblivion_ugraph))
555 Universe.index_list Universe.empty context (List.combine tl tys)
559 (***************** applyS *******************)
561 let new_metasenv_and_unify_and_t
562 dbd flags universe proof goal ?tables newmeta' metasenv'
563 context term' ty termty goal_arity
565 let (consthead,newmetasenv,arguments,_) =
566 TermUtil.saturate_term newmeta' metasenv' context termty goal_arity in
568 match arguments with [] -> term' | _ -> Cic.Appl (term'::arguments)
570 let proof',oldmetasenv =
571 let (puri,metasenv,_subst,pbo,pty, attrs) = proof in
572 (puri,newmetasenv,_subst,pbo,pty, attrs),metasenv
574 let goal_for_paramod =
575 match LibraryObjects.eq_URI () with
577 Cic.Appl [Cic.MutInd (uri,0,[]); Cic.Sort Cic.Prop; consthead; ty]
578 | None -> raise (ProofEngineTypes.Fail (lazy "No equality defined"))
580 let newmeta = CicMkImplicit.new_meta newmetasenv (*subst*) [] in
581 let metasenv_for_paramod = (newmeta,context,goal_for_paramod)::newmetasenv in
583 let uri,_,_subst,p,ty, attrs = proof' in
584 uri,metasenv_for_paramod,_subst,p,ty, attrs
586 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
588 ProofEngineTypes.apply_tactic
589 (EqualityTactics.rewrite_tac ~direction:`RightToLeft
590 ~pattern:(ProofEngineTypes.conclusion_pattern None)
591 (Cic.Meta(newmeta,irl)) [])
594 let goal = match goals with [g] -> g | _ -> assert false in
596 ProofEngineTypes.apply_tactic
597 (PrimitiveTactics.apply_tac term'')
601 let (active, passive,bag), cache, maxmeta =
602 init_cache_and_tables ~dbd flags.use_library true true false universe
605 Saturation.given_clause bag maxmeta (proof'''',newmeta) active passive
606 max_int max_int flags.timeout
609 raise (ProofEngineTypes.Fail (lazy ("FIXME: propaga le tabelle")))
610 | Some (_,proof''''',_), active,passive,_ ->
612 ProofEngineHelpers.compare_metasenvs ~oldmetasenv
613 ~newmetasenv:(let _,m,_subst,_,_, _ = proof''''' in m), active, passive
616 let rec count_prods context ty =
617 match CicReduction.whd context ty with
618 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
622 ~dbd ~term ~subst ~universe ?tables ~params:(univ,params) (proof, goal)
624 let module T = CicTypeChecker in
625 let module R = CicReduction in
626 let module C = Cic in
627 let (_,metasenv,_subst,_,_, _) = proof in
628 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
629 let flags = flags_of_params params ~for_applyS:true () in
630 let universe = universe_of_params metasenv context universe univ in
631 let newmeta = CicMkImplicit.new_meta metasenv subst in
632 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
634 C.Var (uri,exp_named_subst) ->
635 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
636 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
639 exp_named_subst_diff,newmeta',newmetasenvfragment,
640 C.Var (uri,exp_named_subst')
641 | C.Const (uri,exp_named_subst) ->
642 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
643 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
646 exp_named_subst_diff,newmeta',newmetasenvfragment,
647 C.Const (uri,exp_named_subst')
648 | C.MutInd (uri,tyno,exp_named_subst) ->
649 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
650 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
653 exp_named_subst_diff,newmeta',newmetasenvfragment,
654 C.MutInd (uri,tyno,exp_named_subst')
655 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
656 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
657 PrimitiveTactics.generalize_exp_named_subst_with_fresh_metas context newmeta uri
660 exp_named_subst_diff,newmeta',newmetasenvfragment,
661 C.MutConstruct (uri,tyno,consno,exp_named_subst')
662 | _ -> [],newmeta,[],term
664 let metasenv' = metasenv@newmetasenvfragment in
666 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
668 let termty = CicSubstitution.subst_vars exp_named_subst_diff termty in
669 let goal_arity = count_prods context ty in
670 let proof, gl, active, passive =
671 new_metasenv_and_unify_and_t dbd flags universe proof goal ?tables
672 newmeta' metasenv' context term' ty termty goal_arity
674 proof, gl, active, passive
677 (****************** AUTO ********************)
679 let mk_irl ctx = CicMkImplicit.identity_relocation_list_for_metavariable ctx;;
680 let ugraph = CicUniv.empty_ugraph;;
681 let typeof = CicTypeChecker.type_of_aux';;
683 let names = List.map (function None -> None | Some (x,_) -> Some x) ctx in
686 let is_in_prop context subst metasenv ty =
687 let sort,u = typeof ~subst metasenv context ty CicUniv.empty_ugraph in
688 fst (CicReduction.are_convertible context sort (Cic.Sort Cic.Prop) u)
691 let assert_proof_is_valid proof metasenv context goalty =
694 let ty,u = typeof metasenv context proof CicUniv.empty_ugraph in
695 let b,_ = CicReduction.are_convertible context ty goalty u in
699 List.map (function None -> None | Some (x,_) -> Some x) context
701 debug_print (lazy ("PROOF:" ^ CicPp.pp proof names));
702 debug_print (lazy ("PROOFTY:" ^ CicPp.pp ty names));
703 debug_print (lazy ("GOAL:" ^ CicPp.pp goalty names));
704 debug_print (lazy ("MENV:" ^ CicMetaSubst.ppmetasenv [] metasenv));
711 let assert_subst_are_disjoint subst subst' =
714 (fun (i,_) -> List.for_all (fun (j,_) -> i<>j) subst')
719 let split_goals_in_prop metasenv subst gl =
722 let _,context,ty = CicUtil.lookup_meta g metasenv in
724 let sort,u = typeof ~subst metasenv context ty ugraph in
726 CicReduction.are_convertible
727 ~subst ~metasenv context sort (Cic.Sort Cic.Prop) u in
730 | CicTypeChecker.AssertFailure s
731 | CicTypeChecker.TypeCheckerFailure s ->
733 (lazy ("NON TIPA" ^ ppterm context (CicMetaSubst.apply_subst subst ty)));
736 (* FIXME... they should type! *)
740 let split_goals_with_metas metasenv subst gl =
743 let _,context,ty = CicUtil.lookup_meta g metasenv in
744 let ty = CicMetaSubst.apply_subst subst ty in
745 CicUtil.is_meta_closed ty)
749 let order_new_goals metasenv subst open_goals ppterm =
750 let prop,rest = split_goals_in_prop metasenv subst open_goals in
751 let closed_prop, open_prop = split_goals_with_metas metasenv subst prop in
753 (List.map (fun x -> x,P) (closed_prop @ open_prop))
755 (List.map (fun x -> x,T) rest)
760 let _,_,ty = CicUtil.lookup_meta i metasenv in i,ty,sort) open_goals
762 debug_print (lazy (" OPEN: "^
766 | (i,t,P) -> string_of_int i ^ ":"^ppterm t^ "Prop"
767 | (i,t,T) -> string_of_int i ^ ":"^ppterm t^ "Type")
772 let is_an_equational_goal = function
773 | Cic.Appl [Cic.MutInd(u,_,_);_;_;_] when LibraryObjects.is_eq_URI u -> true
778 let prop = function (_,depth,P) -> depth < 9 | _ -> false;;
781 let calculate_timeout flags =
782 if flags.timeout = 0. then
783 (debug_print (lazy "AUTO WITH NO TIMEOUT");
784 {flags with timeout = infinity})
788 let is_equational_case goalty flags =
789 let ensure_equational t =
790 if is_an_equational_goal t then true
793 let msg="Not an equational goal.\nYou cant use the paramodulation flag"in
794 raise (ProofEngineTypes.Fail (lazy msg))
797 (flags.use_paramod && is_an_equational_goal goalty) ||
798 (flags.use_only_paramod && ensure_equational goalty)
801 let cache_add_success sort cache k v =
802 if sort = P then cache_add_success cache k v else cache_remove_underinspection
807 type menv = Cic.metasenv
808 type subst = Cic.substitution
809 type goal = ProofEngineTypes.goal * int * AutoTypes.sort
810 let candidate_no = ref 0;;
811 type candidate = int * Cic.term
812 type cache = AutoCache.cache
814 Saturation.active_table * Saturation.passive_table * Equality.equality_bag
817 (* the goal (mainly for depth) and key of the goal *)
818 goal * AutoCache.cache_key
820 (* goal has to be proved *)
822 (* goal has to be cached as a success obtained using candidate as the first
824 | S of goal * AutoCache.cache_key * candidate * int
826 (* menv, subst, size, operations done (only S), operations to do, failures to cache if any op fails *)
827 menv * subst * int * op list * op list * fail list
829 (* list of computations that may lead to the solution: all op list will
830 * end with the same (S(g,_)) *)
833 (* menv, subst, alternatives, tables, cache, maxmeta *)
834 | Proved of menv * subst * elem list * tables * cache * int
835 | Gaveup of tables * cache * int
838 (* the status exported to the external observer *)
840 (* context, (goal,candidate) list, and_list, history *)
841 Cic.context * (int * Cic.term * bool * int * (int * Cic.term) list) list *
842 (int * Cic.term * int) list * Cic.term list
845 let rec aux acc = function
846 | (D g)::tl -> aux (acc@[g]) tl
852 List.filter (function (_,_,P) -> true | _ -> false) l
856 let rec aux acc = function
857 | (D g)::tl -> aux (acc@[g]) tl
858 | (S _)::tl -> aux acc tl
863 let calculate_goal_ty (goalno,_,_) s m =
865 let _,cc,goalty = CicUtil.lookup_meta goalno m in
866 (* XXX applicare la subst al contesto? *)
867 Some (cc, CicMetaSubst.apply_subst s goalty)
868 with CicUtil.Meta_not_found i when i = goalno -> None
870 let calculate_closed_goal_ty (goalno,_,_) s =
872 let cc,_,goalty = List.assoc goalno s in
873 (* XXX applicare la subst al contesto? *)
874 Some (cc, CicMetaSubst.apply_subst s goalty)
875 with Not_found -> None
877 let pp_status ctx status =
879 let names = Utils.names_of_context ctx in
882 ProofEngineReduction.replace
883 ~equality:(fun a b -> match b with Cic.Meta _ -> true | _ -> false)
884 ~what:[Cic.Rel 1] ~with_what:[Cic.Implicit None] ~where:x
888 let string_of_do m s (gi,_,_ as g) d =
889 match calculate_goal_ty g s m with
890 | Some (_,gty) -> Printf.sprintf "D(%d, %s, %d)" gi (pp gty) d
891 | None -> Printf.sprintf "D(%d, _, %d)" gi d
893 let string_of_s m su k (ci,ct) gi =
894 Printf.sprintf "S(%d, %s, %s, %d)" gi (pp k) (pp ct) ci
896 let string_of_ol m su l =
900 | D (g,d,s) -> string_of_do m su (g,d,s) d
901 | S ((gi,_,_),k,c,_) -> string_of_s m su k c gi)
904 let string_of_fl m s fl =
906 (List.map (fun ((i,_,_),ty) ->
907 Printf.sprintf "(%d, %s)" i (pp ty)) fl)
909 let rec aux = function
911 | (m,s,_,_,ol,fl)::tl ->
912 Printf.eprintf "< [%s] ;;; [%s]>\n"
913 (string_of_ol m s ol) (string_of_fl m s fl);
916 Printf.eprintf "-------------------------- status -------------------\n";
918 Printf.eprintf "-----------------------------------------------------\n";
921 let auto_status = ref [] ;;
922 let auto_context = ref [];;
923 let in_pause = ref false;;
924 let pause b = in_pause := b;;
925 let cond = Condition.create ();;
926 let mutex = Mutex.create ();;
927 let hint = ref None;;
928 let prune_hint = ref [];;
930 let step _ = Condition.signal cond;;
931 let give_hint n = hint := Some n;;
932 let give_prune_hint hint =
933 prune_hint := hint :: !prune_hint
940 Condition.wait cond mutex;
945 let get_auto_status _ =
946 let status = !auto_status in
947 let and_list,elems,last =
950 | (m,s,_,don,gl,fail)::tl ->
953 (fun (id,d,_ as g) ->
954 match calculate_goal_ty g s m with
955 | Some (_,x) -> Some (id,x,d) | None -> None)
959 (* these are the S goalsin the or list *)
962 (fun (m,s,_,don,gl,fail) ->
964 (function S (g,k,c,_) -> Some (g,k,c) | _ -> None)
968 (* this function eats id from a list l::[id,x] returning x, l *)
969 let eat_tail_if_eq id l =
970 let rec aux (s, l) = function
972 | ((id1,_,_),k1,c)::tl when id = id1 ->
974 | None -> aux (Some c,l) tl
975 | Some _ -> assert false)
976 | ((id1,_,_),k1,c as e)::tl -> aux (s, e::l) tl
978 let c, l = aux (None, []) l in
981 let eat_in_parallel id l =
982 let rec aux (b,eaten, new_l as acc) l =
986 match eat_tail_if_eq id l with
987 | None, l -> aux (b@[false], eaten, new_l@[l]) tl
988 | Some t,l -> aux (b@[true],eaten@[t], new_l@[l]) tl
992 let rec eat_all rows l =
996 match List.rev elem with
997 | ((to_eat,depth,_),k,_)::next_lunch ->
998 let b, eaten, l = eat_in_parallel to_eat l in
999 let eaten = HExtlib.list_uniq eaten in
1000 let eaten = List.rev eaten in
1001 let b = true (* List.hd (List.rev b) *) in
1002 let rows = rows @ [to_eat,k,b,depth,eaten] in
1004 | [] -> eat_all rows or_list
1006 eat_all [] (List.rev orlist)
1010 (function (S (_,_,(_,c),_)) -> Some c | _ -> None)
1013 (* let rows = List.filter (fun (_,l) -> l <> []) rows in *)
1014 and_list, rows, history
1016 !auto_context, elems, and_list, last
1019 (* Works if there is no dependency over proofs *)
1020 let is_a_green_cut goalty =
1021 CicUtil.is_meta_closed goalty
1023 let rec first_s = function
1024 | (D _)::tl -> first_s tl
1025 | (S (g,k,c,s))::tl -> Some ((g,k,c,s),tl)
1028 let list_union l1 l2 =
1029 (* TODO ottimizzare compare *)
1030 HExtlib.list_uniq (List.sort compare (l1 @ l1))
1032 let eat_head todo id fl orlist =
1033 let rec aux acc = function
1035 | (m, s, _, _, todo1, fl1)::tl as orlist ->
1036 let rec aux1 todo1 =
1037 match first_s todo1 with
1038 | None -> orlist, acc
1039 | Some (((gno,_,_),_,_,_), todo11) ->
1040 (* TODO confronto tra todo da ottimizzare *)
1041 if gno = id && todo11 = todo then
1042 aux (list_union fl1 acc) tl
1050 let close_proof p ty menv context =
1052 List.map fst (CicUtil.metas_of_term p @ CicUtil.metas_of_term ty)
1054 let menv = List.filter (fun (i,_,_) -> List.exists ((=)i) metas) menv in
1055 naif_closure p menv context
1057 (* XXX capire bene quando aggiungere alla cache *)
1058 let add_to_cache_and_del_from_orlist_if_green_cut
1059 g s m cache key todo orlist fl ctx size minsize
1061 let cache = cache_remove_underinspection cache key in
1062 (* prima per fare la irl usavamo il contesto vero e proprio e non quello
1064 match calculate_closed_goal_ty g s with
1065 | None -> assert false
1066 | Some (canonical_ctx , gty) ->
1067 let goalno,depth,sort = g in
1068 let irl = mk_irl canonical_ctx in
1069 let goal = Cic.Meta(goalno, irl) in
1070 let proof = CicMetaSubst.apply_subst s goal in
1071 let green_proof, closed_proof =
1072 let b = is_a_green_cut proof in
1074 b, (* close_proof proof gty m ctx *) proof
1078 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm key));
1079 if is_a_green_cut key then
1080 (* if the initia goal was closed, we cut alternatives *)
1081 let _ = debug_print (lazy ("MANGIO: " ^ string_of_int goalno)) in
1082 let orlist, fl = eat_head todo goalno fl orlist in
1084 if size < minsize then
1085 (debug_print (lazy ("NO CACHE: 2 (size <= minsize)"));cache)
1087 (* if the proof is closed we cache it *)
1088 if green_proof then cache_add_success cache key proof
1089 else (* cache_add_success cache key closed_proof *)
1090 (debug_print (lazy ("NO CACHE: (no gree proof)"));cache)
1092 cache, orlist, fl, true
1095 debug_print (lazy ("TENTATIVE CACHE: " ^ CicPp.ppterm gty));
1096 if size < minsize then
1097 (debug_print (lazy ("NO CACHE: (size <= minsize)")); cache) else
1098 (* if the substituted goal and the proof are closed we cache it *)
1099 if is_a_green_cut gty then
1100 if green_proof then cache_add_success cache gty proof
1101 else (* cache_add_success cache gty closed_proof *)
1102 (debug_print (lazy ("NO CACHE: (no green proof (gty))"));cache)
1106 CicTypeChecker.type_of_aux' ~subst:s
1107 m ctx closed_proof CicUniv.oblivion_ugraph
1109 if is_a_green_cut ty then
1110 cache_add_success cache ty closed_proof
1113 | CicTypeChecker.TypeCheckerFailure _ ->*)
1114 (debug_print (lazy ("NO CACHE: (no green gty )"));cache)
1116 cache, orlist, fl, false
1118 let close_failures (fl : fail list) (cache : cache) =
1120 (fun cache ((gno,depth,_),gty) ->
1121 debug_print (lazy ("FAIL: INDUCED: " ^ string_of_int gno));
1122 cache_add_failure cache gty depth)
1125 let put_in_subst subst metasenv (goalno,_,_) canonical_ctx t ty =
1126 let entry = goalno, (canonical_ctx, t,ty) in
1127 assert_subst_are_disjoint subst [entry];
1128 let subst = entry :: subst in
1129 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
1132 let mk_fake_proof metasenv subst (goalno,_,_) goalty context =
1133 None,metasenv,subst ,Cic.Meta(goalno,mk_irl context),goalty, []
1136 tables maxm cache depth fake_proof goalno goalty subst context
1139 let active,passive,bag = tables in
1140 let ppterm = ppterm context in
1141 let status = (fake_proof,goalno) in
1142 if flags.use_only_paramod then
1144 debug_print (lazy ("PARAMODULATION SU: " ^
1145 string_of_int goalno ^ " " ^ ppterm goalty ));
1146 let goal_steps, saturation_steps, timeout =
1147 max_int,max_int,flags.timeout
1150 Saturation.given_clause bag maxm status active passive
1151 goal_steps saturation_steps timeout
1153 | None, active, passive, maxmeta ->
1154 [], (active,passive,bag), cache, maxmeta, flags
1155 | Some(subst',(_,metasenv,_subst,proof,_, _),open_goals),active,
1157 assert_subst_are_disjoint subst subst';
1158 let subst = subst@subst' in
1160 order_new_goals metasenv subst open_goals ppterm
1163 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1166 [(!candidate_no,proof),metasenv,subst,open_goals],
1167 (active,passive,bag),
1168 cache, maxmeta, flags
1174 ("SUBSUMPTION SU: " ^ string_of_int goalno ^ " " ^ ppterm goalty));
1176 Saturation.all_subsumed bag maxm status active passive
1178 assert (maxmeta >= maxm);
1181 (fun (subst',(_,metasenv,_subst,proof,_, _),open_goals) ->
1182 assert_subst_are_disjoint subst subst';
1183 let subst = subst@subst' in
1185 order_new_goals metasenv subst open_goals ppterm
1188 List.map (fun (x,sort) -> x,depth-1,sort) open_goals
1191 (!candidate_no,proof),metasenv,subst,open_goals)
1194 res', (active,passive,bag), cache, maxmeta, flags
1199 goalty tables maxm subst fake_proof goalno depth context cand
1201 let ppterm = ppterm context in
1203 let subst,((_,metasenv,_,_,_,_), open_goals),maxmeta =
1204 (PrimitiveTactics.apply_with_subst ~subst ~maxmeta:maxm ~term:cand)
1207 debug_print (lazy (" OK: " ^ ppterm cand));
1208 let metasenv = CicRefine.pack_coercion_metasenv metasenv in
1209 let open_goals = order_new_goals metasenv subst open_goals ppterm in
1210 let open_goals = List.map (fun (x,sort) -> x,depth-1,sort) open_goals in
1212 Some ((!candidate_no,cand),metasenv,subst,open_goals), tables , maxmeta
1214 | ProofEngineTypes.Fail s -> None,tables, maxm
1215 | CicUnification.Uncertain s -> None,tables, maxm
1218 let sort_new_elems =
1219 List.sort (fun (_,_,_,l1) (_,_,_,l2) ->
1220 List.length (prop_only l1) - List.length (prop_only l2))
1223 let applicative_case
1224 tables maxm depth subst fake_proof goalno goalty metasenv context universe
1227 let candidates = get_candidates universe cache goalty in
1228 let tables, elems, maxm =
1230 (fun (tables,elems,maxm) cand ->
1232 try_candidate goalty
1233 tables maxm subst fake_proof goalno depth context cand
1235 | None, tables,maxm -> tables,elems, maxm
1236 | Some x, tables, maxm -> tables,x::elems, maxm)
1237 (tables,[],maxm) candidates
1239 let elems = sort_new_elems elems in
1240 elems, tables, cache, maxm
1243 let equational_and_applicative_case
1244 universe flags m s g gty tables cache maxm context
1246 let goalno, depth, sort = g in
1247 let fake_proof = mk_fake_proof m s g gty context in
1248 if is_equational_case gty flags then
1249 let elems,tables,cache,maxm1, flags =
1250 equational_case tables maxm cache
1251 depth fake_proof goalno gty s context flags
1254 let more_elems, tables, cache, maxm1 =
1255 if flags.use_only_paramod then
1256 [],tables, cache, maxm
1259 tables maxm depth s fake_proof goalno
1260 gty m context universe cache
1263 elems@more_elems, tables, cache, maxm, flags
1265 let elems, tables, cache, maxm =
1266 applicative_case tables maxm depth s fake_proof goalno
1267 gty m context universe cache
1269 elems, tables, cache, maxm, flags
1271 let rec condition_for_hint i = function
1273 | S (_,_,(j,_),_):: tl -> j <> i (* && condition_for_hint i tl *)
1274 | _::tl -> condition_for_hint i tl
1276 let remove_s_from_fl (id,_,_) (fl : fail list) =
1277 let rec aux = function
1279 | ((id1,_,_),_)::tl when id = id1 -> tl
1280 | hd::tl -> hd :: aux tl
1285 let prunable_for_size flags s m todo =
1286 let rec aux b = function
1287 | (S _)::tl -> aux b tl
1288 | (D (_,_,T))::tl -> aux b tl
1290 (match calculate_goal_ty g s m with
1292 | Some (canonical_ctx, gty) ->
1294 Utils.weight_of_term
1295 ~consider_metas:false ~count_metas_occurrences:true gty in
1296 let newb = b || gsize > flags.maxgoalsizefactor in
1303 let prunable ty todo =
1304 let rec aux b = function
1305 | (S(_,k,_,_))::tl -> aux (b || Equality.meta_convertibility k ty) tl
1306 | (D (_,_,T))::tl -> aux b tl
1314 let prunable menv subst ty todo =
1315 let rec aux = function
1316 | (S(_,k,_,_))::tl ->
1317 (match Equality.meta_convertibility_subst k ty menv with
1320 no_progress variant tl (* || aux tl*))
1321 | (D (_,_,T))::tl -> aux tl
1323 and no_progress variant = function
1324 | [] -> (*prerr_endline "++++++++++++++++++++++++ no_progress";*) true
1325 | D ((n,_,P) as g)::tl ->
1326 (match calculate_goal_ty g subst menv with
1327 | None -> no_progress variant tl
1329 (match calculate_goal_ty g variant menv with
1330 | None -> assert false
1333 no_progress variant tl
1335 | _::tl -> no_progress variant tl
1340 let condition_for_prune_hint prune (m, s, size, don, todo, fl) =
1342 HExtlib.filter_map (function S (_,_,(c,_),_) -> Some c | _ -> None) todo
1344 List.for_all (fun i -> List.for_all (fun j -> i<>j) prune) s
1346 let filter_prune_hint l =
1347 let prune = !prune_hint in
1348 prune_hint := []; (* possible race... *)
1349 if prune = [] then l
1350 else List.filter (condition_for_prune_hint prune) l
1352 let auto_main tables maxm context flags universe cache elems =
1353 auto_context := context;
1354 let rec aux tables maxm flags cache (elems : status) =
1355 (* pp_status context elems; *)
1356 (* DEBUGGING CODE: uncomment these two lines to stop execution at each iteration
1357 auto_status := elems;
1360 let elems = filter_prune_hint elems in
1362 | (m, s, size, don, todo, fl)::orlist when !hint <> None ->
1364 | Some i when condition_for_hint i todo ->
1365 aux tables maxm flags cache orlist
1368 aux tables maxm flags cache elems)
1370 (* complete failure *)
1371 Gaveup (tables, cache, maxm)
1372 | (m, s, _, _, [],_)::orlist ->
1373 (* complete success *)
1374 Proved (m, s, orlist, tables, cache, maxm)
1375 | (m, s, size, don, (D (_,_,T))::todo, fl)::orlist
1376 when not flags.AutoTypes.do_types ->
1377 (* skip since not Prop, don't even check if closed by side-effect *)
1378 aux tables maxm flags cache ((m, s, size, don, todo, fl)::orlist)
1379 | (m, s, size, don, (S(g, key, c,minsize) as op)::todo, fl)::orlist ->
1380 (* partial success, cache g and go on *)
1381 let cache, orlist, fl, sibling_pruned =
1382 add_to_cache_and_del_from_orlist_if_green_cut
1383 g s m cache key todo orlist fl context size minsize
1385 debug_print (lazy (AutoCache.cache_print context cache));
1386 let fl = remove_s_from_fl g fl in
1387 let don = if sibling_pruned then don else op::don in
1388 aux tables maxm flags cache ((m, s, size, don, todo, fl)::orlist)
1389 | (m, s, size, don, todo, fl)::orlist
1390 when List.length(prop_only (d_goals todo)) > flags.maxwidth ->
1391 debug_print (lazy ("FAIL: WIDTH"));
1392 (* too many goals in and generated by last th *)
1393 let cache = close_failures fl cache in
1394 aux tables maxm flags cache orlist
1395 | (m, s, size, don, todo, fl)::orlist when size > flags.maxsize ->
1397 (lazy ("FAIL: SIZE: "^string_of_int size ^
1398 " > " ^ string_of_int flags.maxsize ));
1399 (* we already have a too large proof term *)
1400 let cache = close_failures fl cache in
1401 aux tables maxm flags cache orlist
1402 | _ when Unix.gettimeofday () > flags.timeout ->
1404 debug_print (lazy ("FAIL: TIMEOUT"));
1405 Gaveup (tables, cache, maxm)
1406 | (m, s, size, don, (D (gno,depth,_ as g))::todo, fl)::orlist as status ->
1408 match calculate_goal_ty g s m with
1410 (* closed by side effect *)
1411 debug_print (lazy ("SUCCESS: SIDE EFFECT: " ^ string_of_int gno));
1412 aux tables maxm flags cache ((m,s,size,don,todo, fl)::orlist)
1413 | Some (canonical_ctx, gty) ->
1415 Utils.weight_of_term ~consider_metas:false ~count_metas_occurrences:true gty
1417 if gsize > flags.maxgoalsizefactor then
1418 (debug_print (lazy ("FAIL: SIZE: goal: "^string_of_int gsize));
1419 aux tables maxm flags cache orlist)
1420 else if prunable_for_size flags s m todo then
1421 (debug_print (lazy ("POTO at depth: "^(string_of_int depth)));
1422 aux tables maxm flags cache orlist)
1424 (* still to be proved *)
1425 (debug_print (lazy ("EXAMINE: "^CicPp.ppterm gty));
1426 match cache_examine cache gty with
1427 | Failed_in d when d >= depth ->
1429 debug_print (lazy ("FAIL: DEPTH (cache): "^string_of_int gno));
1430 let cache = close_failures fl cache in
1431 aux tables maxm flags cache orlist
1432 | UnderInspection ->
1434 debug_print (lazy ("FAIL: LOOP: " ^ string_of_int gno));
1435 let cache = close_failures fl cache in
1436 aux tables maxm flags cache orlist
1438 debug_print (lazy ("SUCCESS: CACHE HIT: " ^ string_of_int gno));
1439 let s, m = put_in_subst s m g canonical_ctx t gty in
1440 aux tables maxm flags cache ((m, s, size, don,todo, fl)::orlist)
1442 | Failed_in _ when depth > 0 ->
1443 ( (* more depth or is the first time we see the goal *)
1444 if prunable m s gty todo then
1446 "FAIL: LOOP: one father is equal"));
1447 aux tables maxm flags cache orlist)
1449 let cache = cache_add_underinspection cache gty depth in
1450 auto_status := status;
1453 (lazy ("INSPECTING: " ^
1454 string_of_int gno ^ "("^ string_of_int size ^ "): "^
1456 (* elems are possible computations for proving gty *)
1457 let elems, tables, cache, maxm, flags =
1458 equational_and_applicative_case
1459 universe flags m s g gty tables cache maxm context
1462 (* this goal has failed *)
1463 let cache = close_failures ((g,gty)::fl) cache in
1464 aux tables maxm flags cache orlist
1466 (* elems = (cand,m,s,gl) *)
1467 let size_gl l = List.length
1468 (List.filter (function (_,_,P) -> true | _ -> false) l)
1471 let inj_gl gl = List.map (fun g -> D g) gl in
1472 let rec map = function
1473 | [] -> assert false
1474 | (cand,m,s,gl)::[] ->
1475 (* in the last one we add the failure *)
1477 inj_gl gl @ (S(g,gty,cand,size+1))::todo
1479 (* we are the last in OR, we fail on g and
1480 * also on all failures implied by g *)
1481 (m,s, size + size_gl gl, don, todo, (g,gty)::fl)
1483 | (cand,m,s,gl)::tl ->
1484 (* we add the S step after gl and before todo *)
1486 inj_gl gl @ (S(g,gty,cand,size+1))::todo
1488 (* since we are not the last in OR, we do not
1490 (m,s, size + size_gl gl, don, todo, []) :: map tl
1494 aux tables maxm flags cache elems)
1497 debug_print (lazy ("FAIL: DEPTH: " ^ string_of_int gno));
1498 let cache = close_failures fl cache in
1499 aux tables maxm flags cache orlist)
1501 (aux tables maxm flags cache elems : auto_result)
1506 auto_all_solutions maxm tables universe cache context metasenv gl flags
1508 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
1511 (fun (x,s) -> D (x,flags.maxdepth,s)) goals
1513 let elems = [metasenv,[],1,[],goals,[]] in
1514 let rec aux tables maxm solutions cache elems flags =
1515 match auto_main tables maxm context flags universe cache elems with
1516 | Gaveup (tables,cache,maxm) ->
1517 solutions,cache,maxm
1518 | Proved (metasenv,subst,others,tables,cache,maxm) ->
1519 if Unix.gettimeofday () > flags.timeout then
1520 ((subst,metasenv)::solutions), cache, maxm
1522 aux tables maxm ((subst,metasenv)::solutions) cache others flags
1524 let rc = aux tables maxm [] cache elems flags in
1526 | [],cache,maxm -> [],cache,maxm
1527 | solutions,cache,maxm ->
1530 (fun (subst,newmetasenv) ->
1532 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv ~newmetasenv
1534 if opened = [] then Some subst else None)
1537 solutions,cache,maxm
1540 (* }}} ****************** AUTO ***************)
1542 let auto flags metasenv tables universe cache context metasenv gl =
1543 let initial_time = Unix.gettimeofday() in
1544 let goals = order_new_goals metasenv [] gl CicPp.ppterm in
1545 let goals = List.map (fun (x,s) -> D(x,flags.maxdepth,s)) goals in
1546 let elems = [metasenv,[],1,[],goals,[]] in
1547 match auto_main tables 0 context flags universe cache elems with
1548 | Proved (metasenv,subst,_, tables,cache,_) ->
1550 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
1551 Some (subst,metasenv), cache
1552 | Gaveup (tables,cache,maxm) ->
1554 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time)));
1558 let applyS_tac ~dbd ~term ~params ~universe =
1559 ProofEngineTypes.mk_tactic
1563 apply_smart ~dbd ~term ~subst:[] ~params ~universe status
1567 | CicUnification.UnificationFailure msg
1568 | CicTypeChecker.TypeCheckerFailure msg ->
1569 raise (ProofEngineTypes.Fail msg))
1571 let auto_tac ~(dbd:HSql.dbd) ~params:(univ,params) ~universe (proof, goal) =
1572 let _,metasenv,_subst,_,_, _ = proof in
1573 let _,context,goalty = CicUtil.lookup_meta goal metasenv in
1574 let universe = universe_of_params metasenv context universe univ in
1575 let flags = flags_of_params params () in
1576 let use_library = flags.use_library in
1577 let tables,cache,newmeta =
1578 init_cache_and_tables ~dbd use_library flags.use_only_paramod true
1579 false universe (proof, goal) in
1580 let tables,cache,newmeta =
1581 if flags.close_more then
1583 tables newmeta context (proof, goal)
1584 auto_all_solutions universe cache
1585 else tables,cache,newmeta in
1586 let initial_time = Unix.gettimeofday() in
1587 let (_,oldmetasenv,_subst,_,_, _) = proof in
1590 metasenv,[],1,[],[D (goal,flags.maxdepth,P)],[]
1592 match auto_main tables newmeta context flags universe cache [elem] with
1593 | Proved (metasenv,subst,_, tables,cache,_) ->
1595 ("TIME:"^string_of_float(Unix.gettimeofday()-.initial_time));*)
1596 let proof,metasenv =
1597 ProofEngineHelpers.subst_meta_and_metasenv_in_proof
1598 proof goal subst metasenv
1601 ProofEngineHelpers.compare_metasenvs ~oldmetasenv
1602 ~newmetasenv:metasenv
1605 | Gaveup (tables,cache,maxm) ->
1608 string_of_float(Unix.gettimeofday()-.initial_time)));
1609 raise (ProofEngineTypes.Fail (lazy "Auto gave up"))
1612 let auto_tac ~dbd ~params ~universe =
1613 ProofEngineTypes.mk_tactic (auto_tac ~params ~dbd ~universe);;
1615 let eq_of_goal = function
1616 | Cic.Appl [Cic.MutInd(uri,0,_);_;_;_] when LibraryObjects.is_eq_URI uri ->
1618 | _ -> raise (ProofEngineTypes.Fail (lazy ("The goal is not an equality ")))
1621 (* performs steps of rewrite with the universe, obtaining if possible
1623 let solve_rewrite_tac ~universe ~params:(univ,params) (proof,goal as status)=
1624 let _,metasenv,_subst,_,_,_ = proof in
1625 let _,context,ty = CicUtil.lookup_meta goal metasenv in
1626 let steps = int_of_string (string params "steps" "1") in
1627 let universe = universe_of_params metasenv context universe univ in
1628 let eq_uri = eq_of_goal ty in
1629 let (active,passive,bag), cache, maxm =
1630 (* we take the whole universe (no signature filtering) *)
1631 init_cache_and_tables false true false true universe (proof,goal)
1633 let initgoal = [], metasenv, ty in
1635 let equalities = (Saturation.list_of_passive passive) in
1636 (* we demodulate using both actives passives *)
1637 List.fold_left (fun tbl eq -> Indexing.index tbl eq) (snd active) equalities
1639 let env = metasenv,context,CicUniv.empty_ugraph in
1640 match Indexing.solve_demodulating bag env table initgoal steps with
1641 | Some (proof, metasenv, newty) ->
1644 | Cic.Appl[Cic.MutInd _;eq_ty;left;_] ->
1645 Equality.Exact (Equality.refl_proof eq_uri eq_ty left)
1649 Equality.build_goal_proof
1650 bag eq_uri proof refl newty [] context metasenv
1652 ProofEngineTypes.apply_tactic
1653 (PrimitiveTactics.apply_tac ~term:proofterm) status
1656 (ProofEngineTypes.Fail (lazy
1657 ("Unable to solve with " ^ string_of_int steps ^ " demodulations")))
1659 let solve_rewrite_tac ~params ~universe () =
1660 ProofEngineTypes.mk_tactic (solve_rewrite_tac ~universe ~params)
1664 let demodulate_tac ~dbd ~universe ~params:(univ, params) (proof,goal)=
1665 let curi,metasenv,_subst,pbo,pty, attrs = proof in
1666 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
1667 let universe = universe_of_params metasenv context universe univ in
1668 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
1669 let initgoal = [], metasenv, ty in
1670 let eq_uri = eq_of_goal ty in
1671 let (active,passive,bag), cache, maxm =
1672 init_cache_and_tables
1673 ~dbd false true true false universe (proof,goal)
1675 let equalities = (Saturation.list_of_passive passive) in
1676 (* we demodulate using both actives passives *)
1679 (fun tbl eq -> Indexing.index tbl eq)
1680 (snd active) equalities
1682 let changed,(newproof,newmetasenv, newty) =
1683 Indexing.demodulation_goal bag
1684 (metasenv,context,CicUniv.empty_ugraph) table initgoal
1688 let opengoal = Equality.Exact (Cic.Meta(maxm,irl)) in
1690 Equality.build_goal_proof bag
1691 eq_uri newproof opengoal ty [] context metasenv
1693 let extended_metasenv = (maxm,context,newty)::metasenv in
1694 let extended_status =
1695 (curi,extended_metasenv,_subst,pbo,pty, attrs),goal in
1696 let (status,newgoals) =
1697 ProofEngineTypes.apply_tactic
1698 (PrimitiveTactics.apply_tac ~term:proofterm)
1700 (status,maxm::newgoals)
1702 else (* if newty = ty then *)
1703 raise (ProofEngineTypes.Fail (lazy "no progress"))
1704 (*else ProofEngineTypes.apply_tactic
1705 (ReductionTactics.simpl_tac
1706 ~pattern:(ProofEngineTypes.conclusion_pattern None)) initialstatus*)
1709 let demodulate_tac ~dbd ~params ~universe =
1710 ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~params ~universe);;
1712 let pp_proofterm = Equality.pp_proofterm;;
1714 let revision = "$Revision$";;
1715 let size_and_depth context metasenv t = 100, 100