2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
12 (* $Id: index.mli 9822 2009-06-03 15:37:06Z tassi $ *)
14 module Superposition (B : Orderings.Blob) =
16 module IDX = Index.Index(B)
17 module Unif = FoUnif.Founif(B)
18 module Subst = FoSubst
20 module Utils = FoUtils.Utils(B)
23 exception Success of B.t Terms.bag * int * B.t Terms.unit_clause
25 (* let debug s = prerr_endline s;; *)
29 let rec list_first f = function
31 | x::tl -> match f x with Some _ as x -> x | _ -> list_first f tl
34 let first_position pos ctx t f =
35 let inject_pos pos ctx = function
37 | Some (a,b,c,d) -> Some(ctx a,b,c,d,pos)
39 let rec aux pos ctx = function
40 | Terms.Leaf _ as t -> inject_pos pos ctx (f t)
44 | Some _ as x -> inject_pos pos ctx x
46 let rec first pre post = function
49 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
50 match aux (List.length pre :: pos) newctx t with
53 if post = [] then None (* tl is also empty *)
54 else first (pre @ [t]) (List.tl post) tl
56 first [] (List.tl l) l
61 let all_positions pos ctx t f =
62 let rec aux pos ctx = function
63 | Terms.Leaf _ as t -> f t pos ctx
68 (fun (acc,pre,post) t -> (* Invariant: pre @ [t] @ post = l *)
69 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
70 let acc = aux (List.length pre :: pos) newctx t @ acc in
71 if post = [] then acc, l, []
72 else acc, pre @ [t], List.tl post)
73 (f t pos ctx, [], List.tl l) l
80 let parallel_positions bag pos ctx id t f =
81 let rec aux bag pos ctx id = function
82 | Terms.Leaf _ as t -> f bag t pos ctx id
83 | Terms.Var _ as t -> bag,t,id
84 | Terms.Node (hd::l) as t->
85 let bag,t,id1 = f bag t pos ctx id in
89 (fun (bag,pre,post,id) t ->
90 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
91 let newpos = (List.length pre)::pos in
92 let bag,newt,id = aux bag newpos newctx id t in
93 if post = [] then bag, pre@[newt], [], id
94 else bag, pre @ [newt], List.tl post, id)
95 (bag, [hd], List.tl l, id) l
99 (* else aux bag pos ctx id1 t *)
105 let visit bag pos ctx id t f =
106 let rec aux bag pos ctx id subst = function
107 | Terms.Leaf _ as t ->
108 let bag,subst,t,id = f bag t pos ctx id
109 in assert (subst=[]); bag,t,id
110 | Terms.Var i as t ->
111 let t= Subst.apply_subst subst t in
113 | Terms.Node (hd::l) ->
116 (fun (bag,pre,post,id) t ->
117 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
118 let newpos = (List.length pre)::pos in
119 let bag,newt,id = aux bag newpos newctx id subst t in
120 if post = [] then bag, pre@[newt], [], id
121 else bag, pre @ [newt], List.tl post, id)
122 (bag, [hd], List.map (Subst.apply_subst subst) (List.tl l), id) l
124 let bag,subst,t,id1 = f bag (Terms.Node l) pos ctx id
126 if id1 = id then (assert (subst=[]); bag,t,id)
127 else aux bag pos ctx id1 subst t
130 aux bag pos ctx id [] t
133 let build_clause bag filter rule t subst id id2 pos dir =
134 let proof = Terms.Step(rule,id,id2,dir,pos,subst) in
135 let t = Subst.apply_subst subst t in
139 | Terms.Node [ Terms.Leaf eq ; ty; l; r ] when B.eq B.eqP eq ->
140 let o = Order.compare_terms l r in
141 Terms.Equation (l, r, ty, o)
142 | t -> Terms.Predicate t
145 Terms.add_to_bag (0, literal, Terms.vars_of_term t, proof) bag
149 ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None)
151 let prof_build_clause = HExtlib.profile ~enable "build_clause";;
152 let build_clause bag filter rule t subst id id2 pos x =
153 prof_build_clause.HExtlib.profile (build_clause bag filter rule t subst id id2 pos) x
157 (* ============ simplification ================= *)
158 let prof_demod_u = HExtlib.profile ~enable "demod.unify";;
159 let prof_demod_r = HExtlib.profile ~enable "demod.retrieve_generalizations";;
160 let prof_demod_o = HExtlib.profile ~enable "demod.compare_terms";;
161 let prof_demod_s = HExtlib.profile ~enable "demod.apply_subst";;
163 let demod table varlist subterm =
165 prof_demod_r.HExtlib.profile
166 (IDX.DT.retrieve_generalizations table) subterm
169 (fun (dir, (id,lit,vl,_)) ->
171 | Terms.Predicate _ -> assert false
172 | Terms.Equation (l,r,_,o) ->
173 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
176 prof_demod_u.HExtlib.profile
177 (Unif.unification (* (varlist@vl) *) varlist subterm) side
180 prof_demod_s.HExtlib.profile
181 (Subst.apply_subst subst) side
184 prof_demod_s.HExtlib.profile
185 (Subst.apply_subst subst) newside
187 if o = Terms.Incomparable || o = Terms.Invertible then
189 prof_demod_o.HExtlib.profile
190 (Order.compare_terms newside) side in
191 (* Riazanov, pp. 45 (ii) *)
193 Some (newside, subst, id, dir)
195 ((*prerr_endline ("Filtering: " ^
196 Pp.pp_foterm side ^ " =(< || =)" ^
197 Pp.pp_foterm newside ^ " coming from " ^
198 Pp.pp_unit_clause uc );*)None)
200 Some (newside, subst, id, dir)
201 with FoUnif.UnificationFailure _ -> None)
202 (IDX.ClauseSet.elements cands)
204 let prof_demod = HExtlib.profile ~enable "demod";;
205 let demod table varlist x =
206 prof_demod.HExtlib.profile (demod table varlist) x
209 let mydemod table varlist subterm =
211 prof_demod_r.HExtlib.profile
212 (IDX.DT.retrieve_generalizations table) subterm
215 (fun (dir, (id,lit,vl,_)) ->
217 | Terms.Predicate _ -> assert false
218 | Terms.Equation (l,r,_,o) ->
219 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
222 prof_demod_u.HExtlib.profile
223 (Unif.unification (* (varlist@vl) *) varlist subterm) side
226 prof_demod_s.HExtlib.profile
227 (Subst.apply_subst subst) side
230 prof_demod_s.HExtlib.profile
231 (Subst.apply_subst subst) newside
233 if o = Terms.Incomparable || o = Terms.Invertible then
235 prof_demod_o.HExtlib.profile
236 (Order.compare_terms inewside) iside in
237 (* Riazanov, pp. 45 (ii) *)
239 Some (newside, subst, id, dir)
241 ((*prerr_endline ("Filtering: " ^
242 Pp.pp_foterm side ^ " =(< || =)" ^
243 Pp.pp_foterm newside ^ " coming from " ^
244 Pp.pp_unit_clause uc );*)None)
246 Some (newside, subst, id, dir)
247 with FoUnif.UnificationFailure _ -> None)
248 (IDX.ClauseSet.elements cands)
251 let ctx_demod table vl bag t pos ctx id =
252 match mydemod table vl t with
253 | None -> (bag,[],t,id)
254 | Some (newside, subst, id2, dir) ->
255 let inewside = Subst.apply_subst subst newside in
256 match build_clause bag (fun _ -> true)
257 Terms.Demodulation (ctx inewside) subst id id2 pos dir
259 | None -> assert false
260 | Some (bag,(id,_,_,_)) ->
261 (bag,subst,newside,id)
264 let rec demodulate ~jump_to_right bag (id, literal, vl, pr) table =
266 | Terms.Predicate t -> assert false
267 | Terms.Equation (l,r,ty,_) ->
270 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) id l
275 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) id1 r
278 let cl,_,_ = Terms.get_from_bag id2 bag in
283 let demodulate_once_old ~jump_to_right bag (id, literal, vl, pr) table =
285 | Terms.Predicate t -> assert false
286 | Terms.Equation (l,r,ty,_) ->
287 let left_position = if jump_to_right then None else
289 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) l
292 match left_position with
293 | Some (newt, subst, id2, dir, pos) ->
295 match build_clause bag (fun _ -> true) Terms.Demodulation
296 newt subst id id2 pos dir
298 | None -> assert false
299 | Some x -> Some (x,false)
303 [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) r
307 | Some (newt, subst, id2, dir, pos) ->
308 match build_clause bag (fun _ -> true)
309 Terms.Demodulation newt subst id id2 pos dir
311 | None -> assert false
312 | Some x -> Some (x,true)
315 let parallel_demod table vl bag t pos ctx id =
316 match demod table vl t with
318 | Some (newside, subst, id2, dir) ->
319 match build_clause bag (fun _ -> true)
320 Terms.Demodulation (ctx newside) subst id id2 pos dir
322 | None -> assert false
323 | Some (bag,(id,_,_,_)) ->
327 let demodulate_once ~jump_to_right bag (id, literal, vl, pr) table =
329 | Terms.Predicate t -> assert false
330 | Terms.Equation (l,r,ty,_) ->
331 let bag,l,id1 = if jump_to_right then (bag,l,id) else
332 parallel_positions bag [2]
333 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) id l
334 (parallel_demod table vl)
336 let jump_to_right = id1 = id in
338 parallel_positions bag [3]
339 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) id1 r
340 (parallel_demod table vl)
342 if id = id2 then None
344 let cl,_,_ = Terms.get_from_bag id2 bag in
345 Some ((bag,cl),jump_to_right)
348 let rec demodulate_old ~jump_to_right bag clause table =
349 match demodulate_once ~jump_to_right bag clause table with
350 | None -> bag, clause
351 | Some ((bag, clause),r) -> demodulate ~jump_to_right:r
355 let rec demodulate_old ~jump_to_right bag clause table =
356 match demodulate_once_old ~jump_to_right bag clause table with
357 | None -> bag, clause
358 | Some ((bag, clause),r) -> demodulate_old ~jump_to_right:r
363 let are_alpha_eq cl1 cl2 =
364 let get_term (_,lit,_,_) =
366 | Terms.Predicate _ -> assert false
367 | Terms.Equation (l,r,ty,_) ->
368 Terms.Node [Terms.Leaf B.eqP; ty; l ; r]
370 try ignore(Unif.alpha_eq (get_term cl1) (get_term cl2)) ; true
371 with FoUnif.UnificationFailure _ -> false
374 let demodulate bag clause table =
375 demodulate ~jump_to_right:false bag clause table
378 let (bag1,c1), (bag2,c2) =
379 demodulate ~jump_to_right:false bag clause table,
380 demodulate_old ~jump_to_right:false bag clause table
382 if are_alpha_eq c1 c2 then bag1,c1
385 prerr_endline (Pp.pp_unit_clause clause);
386 prerr_endline (Pp.pp_unit_clause c1);
387 prerr_endline (Pp.pp_unit_clause c2);
388 prerr_endline "Bag1 :";
389 prerr_endline (Pp.pp_bag bag1);
390 prerr_endline "Bag2 :";
391 prerr_endline (Pp.pp_bag bag2);
396 let prof_demodulate = HExtlib.profile ~enable "demodulate";;
397 let demodulate bag clause x =
398 prof_demodulate.HExtlib.profile (demodulate bag clause) x
402 let is_identity_clause ~unify = function
403 | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
404 | _, Terms.Equation (l,r,_,_), vl, proof when unify ->
405 (try ignore(Unif.unification (* vl *) [] l r); true
406 with FoUnif.UnificationFailure _ -> false)
407 | _, Terms.Equation (_,_,_,_), _, _ -> false
408 | _, Terms.Predicate _, _, _ -> assert false
411 let build_new_clause bag maxvar filter rule t subst id id2 pos dir =
412 let maxvar, _vl, subst = Utils.relocate maxvar (Terms.vars_of_term
413 (Subst.apply_subst subst t)) subst in
414 match build_clause bag filter rule t subst id id2 pos dir with
415 | Some (bag, c) -> Some ((bag, maxvar), c)
418 let prof_build_new_clause = HExtlib.profile ~enable "build_new_clause";;
419 let build_new_clause bag maxvar filter rule t subst id id2 pos x =
420 prof_build_new_clause.HExtlib.profile (build_new_clause bag maxvar filter
421 rule t subst id id2 pos) x
424 let fold_build_new_clause bag maxvar id rule filter res =
425 let (bag, maxvar), res =
426 HExtlib.filter_map_acc
427 (fun (bag, maxvar) (t,subst,id2,pos,dir) ->
428 build_new_clause bag maxvar filter rule t subst id id2 pos dir)
435 let rewrite_eq ~unify l r ty vl table =
436 let retrieve = if unify then IDX.DT.retrieve_unifiables
437 else IDX.DT.retrieve_generalizations in
438 let lcands = retrieve table l in
439 let rcands = retrieve table r in
441 let id, dir, l, r, vl =
443 | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl
446 let reverse = (dir = Terms.Left2Right) = b in
447 let l, r, proof_rewrite_dir = if reverse then l,r,Terms.Left2Right
448 else r,l, Terms.Right2Left in
449 (id,proof_rewrite_dir,Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl)
451 let cands1 = List.map (f true) (IDX.ClauseSet.elements lcands) in
452 let cands2 = List.map (f false) (IDX.ClauseSet.elements rcands) in
453 let t = Terms.Node [ Terms.Leaf B.eqP; ty; l; r ] in
454 let locked_vars = if unify then [] else vl in
455 let rec aux = function
457 | (id2,dir,c,vl1)::tl ->
459 let subst = Unif.unification (* (vl@vl1) *) locked_vars c t in
460 Some (id2, dir, subst)
461 with FoUnif.UnificationFailure _ -> aux tl
463 aux (cands1 @ cands2)
466 let is_subsumed ~unify bag maxvar (id, lit, vl, _) table =
468 | Terms.Predicate _ -> assert false
469 | Terms.Equation (l,r,ty,_) ->
470 match rewrite_eq ~unify l r ty vl table with
472 | Some (id2, dir, subst) ->
473 let id_t = Terms.Node [ Terms.Leaf B.eqP; ty; r; r ] in
474 build_new_clause bag maxvar (fun _ -> true)
475 Terms.Superposition id_t subst id id2 [2] dir
477 let prof_is_subsumed = HExtlib.profile ~enable "is_subsumed";;
478 let is_subsumed ~unify bag maxvar c x =
479 prof_is_subsumed.HExtlib.profile (is_subsumed ~unify bag maxvar c) x
481 (* id refers to a clause proving contextl l = contextr r *)
483 let rec deep_eq ~unify l r ty pos contextl contextr table acc =
486 | Some(bag,maxvar,(id,lit,vl,p),subst) ->
487 let l = Subst.apply_subst subst l in
488 let r = Subst.apply_subst subst r in
490 let subst1 = Unif.unification (* vl *) [] l r in
492 match lit with Terms.Predicate _ -> assert false
493 | Terms.Equation (l,r,ty,o) ->
494 Terms.Equation (FoSubst.apply_subst subst1 l,
495 FoSubst.apply_subst subst1 r, ty, o)
497 Some(bag,maxvar,(id,lit,vl,p),Subst.concat subst1 subst)
498 with FoUnif.UnificationFailure _ ->
499 match rewrite_eq ~unify l r ty vl table with
500 | Some (id2, dir, subst1) ->
501 let newsubst = Subst.concat subst1 subst in
503 FoSubst.apply_subst newsubst
504 (Terms.Node[Terms.Leaf B.eqP;ty;contextl r;contextr r])
507 build_new_clause bag maxvar (fun _ -> true)
508 Terms.Superposition id_t
509 subst1 id id2 (pos@[2]) dir
511 | Some ((bag, maxvar), c) ->
512 Some(bag,maxvar,c,newsubst)
513 | None -> assert false)
516 | Terms.Node (a::la), Terms.Node (b::lb) when
517 a = b && List.length la = List.length lb ->
520 (fun (acc,pre,postl,postr) a b ->
522 fun x -> contextl(Terms.Node (pre@(x::postl))) in
524 fun x -> contextr(Terms.Node (pre@(x::postr))) in
525 let newpos = List.length pre::pos in
527 if l = [] then [] else List.tl l in
528 (deep_eq ~unify a b ty
529 newpos newcl newcr table acc,pre@[b],
530 footail postl, footail postr))
531 (acc,[a],List.tl la,List.tl lb) la lb
535 let prof_deep_eq = HExtlib.profile ~enable "deep_eq";;
536 let deep_eq ~unify l r ty pos contextl contextr table x =
537 prof_deep_eq.HExtlib.profile (deep_eq ~unify l r ty pos contextl contextr table) x
540 let rec orphan_murder bag acc i =
541 match Terms.get_from_bag i bag with
542 | (_,_,_,Terms.Exact _),discarded,_ -> (discarded,acc)
543 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),true,_ -> (true,acc)
544 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),false,_ ->
545 if (List.mem i acc) then (false,acc)
546 else match orphan_murder bag acc i1 with
547 | (true,acc) -> (true,acc)
549 let (res,acc) = orphan_murder bag acc i2 in
550 if res then res,acc else res,i::acc
553 let orphan_murder bag actives cl =
554 let (id,_,_,_) = cl in
555 let actives = List.map (fun (i,_,_,_) -> i) actives in
556 let (res,_) = orphan_murder bag actives id in
557 if res then debug "Orphan murdered"; res
559 let prof_orphan_murder = HExtlib.profile ~enable "orphan_murder";;
560 let orphan_murder bag actives x =
561 prof_orphan_murder.HExtlib.profile (orphan_murder bag actives) x
564 (* demodulate and check for subsumption *)
565 let simplify table maxvar bag clause =
566 if is_identity_clause ~unify:false clause then bag,None
567 (* else if orphan_murder bag actives clause then bag,None *)
568 else let bag, clause = demodulate bag clause table in
569 if is_identity_clause ~unify:false clause then bag,None
571 match is_subsumed ~unify:false bag maxvar clause table with
572 | None -> bag, Some clause
573 | Some _ -> bag, None
576 let simplify table maxvar bag clause =
577 match simplify table maxvar bag clause with
579 let (id,_,_,_) = clause in
580 let (_,_,iter) = Terms.get_from_bag id bag in
581 Terms.replace_in_bag (clause,true,iter) bag, None
582 | bag, Some clause -> bag, Some clause
583 (*let (id,_,_,_) = clause in
584 if orphan_murder bag clause then
585 Terms.M.add id (clause,true) bag, Some clause
586 else bag, Some clause*)
588 let prof_simplify = HExtlib.profile ~enable "simplify";;
589 let simplify table maxvar bag x =
590 prof_simplify.HExtlib.profile (simplify table maxvar bag ) x
593 let one_pass_simplification new_clause (alist,atable) bag maxvar =
594 match simplify atable maxvar bag new_clause with
595 | bag,None -> bag,None (* new_clause has been discarded *)
596 | bag,(Some clause) ->
597 let ctable = IDX.index_unit_clause maxvar IDX.DT.empty clause in
598 let bag, alist, atable =
600 (fun (bag, alist, atable) c ->
601 match simplify ctable maxvar bag c with
602 |bag,None -> (bag,alist,atable)
603 (* an active clause as been discarded *)
605 bag, c :: alist, IDX.index_unit_clause maxvar atable c)
606 (bag,[],IDX.DT.empty) alist
608 bag, Some (clause, (alist,atable))
610 let prof_one_pass_simplification = HExtlib.profile ~enable "one_pass_simplification";;
611 let one_pass_simplification new_clause t bag x =
612 prof_one_pass_simplification.HExtlib.profile (one_pass_simplification new_clause t bag ) x
615 let simplification_step ~new_cl cl (alist,atable) bag maxvar new_clause =
617 if new_cl then atable else
618 IDX.index_unit_clause maxvar atable cl
620 (* Simplification of new_clause with : *
621 * - actives and cl if new_clause is not cl *
622 * - only actives otherwise *)
624 simplify atable1 maxvar bag new_clause with
625 | bag,None -> bag,(Some cl, None) (* new_clause has been discarded *)
627 (* Simplification of each active clause with clause *
628 * which is the simplified form of new_clause *)
629 let ctable = IDX.index_unit_clause maxvar IDX.DT.empty clause in
630 let bag, newa, alist, atable =
632 (fun (bag, newa, alist, atable) c ->
633 match simplify ctable maxvar bag c with
634 |bag,None -> (bag, newa, alist, atable)
635 (* an active clause as been discarded *)
638 bag, newa, c :: alist,
639 IDX.index_unit_clause maxvar atable c
641 bag, c1 :: newa, alist, atable)
642 (bag,[],[],IDX.DT.empty) alist
645 bag, (Some cl, Some (clause, (alist,atable), newa))
647 (* if new_clause is not cl, we simplify cl with clause *)
648 match simplify ctable maxvar bag cl with
650 (* cl has been discarded *)
651 bag,(None, Some (clause, (alist,atable), newa))
653 bag,(Some cl1, Some (clause, (alist,atable), newa))
655 let prof_simplification_step = HExtlib.profile ~enable "simplification_step";;
656 let simplification_step ~new_cl cl (alist,atable) bag maxvar x =
657 prof_simplification_step.HExtlib.profile (simplification_step ~new_cl cl (alist,atable) bag maxvar) x
660 let keep_simplified cl (alist,atable) bag maxvar =
661 let rec keep_simplified_aux ~new_cl cl (alist,atable) bag newc =
663 match simplification_step ~new_cl cl (alist,atable) bag maxvar cl with
664 | _,(None, _) -> assert false
665 | bag,(Some _, None) -> bag,None
666 | bag,(Some _, Some (clause, (alist,atable), newa)) ->
667 keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable)
671 | [] -> bag, Some (cl, (alist,atable))
673 match simplification_step ~new_cl cl
674 (alist,atable) bag maxvar hd with
675 | _,(None,None) -> assert false
676 | bag,(Some _,None) ->
677 keep_simplified_aux ~new_cl cl (alist,atable) bag tl
678 | bag,(None, Some _) -> bag,None
679 | bag,(Some cl1, Some (clause, (alist,atable), newa)) ->
681 (clause::alist, IDX.index_unit_clause maxvar atable clause)
683 keep_simplified_aux ~new_cl:(cl!=cl1) cl1 (alist,atable)
686 keep_simplified_aux ~new_cl:true cl (alist,atable) bag []
688 let prof_keep_simplified = HExtlib.profile ~enable "keep_simplified";;
689 let keep_simplified cl t bag x =
690 prof_keep_simplified.HExtlib.profile (keep_simplified cl t bag) x
693 (* this is like simplify but raises Success *)
694 let simplify_goal ~no_demod maxvar table bag g_actives clause =
696 if no_demod then bag, clause else demodulate bag clause table
698 if List.exists (are_alpha_eq clause) g_actives then None else
699 if (is_identity_clause ~unify:true clause)
700 then raise (Success (bag, maxvar, clause))
702 let (id,lit,vl,_) = clause in
703 if vl = [] then Some (bag,clause)
707 | Terms.Equation(l,r,ty,_) -> l,r,ty
710 match deep_eq ~unify:true l r ty [] (fun x -> x) (fun x -> x)
711 table (Some(bag,maxvar,clause,Subst.id_subst)) with
712 | None -> Some (bag,clause)
713 | Some (bag,maxvar,cl,subst) ->
714 prerr_endline "Goal subsumed";
715 raise (Success (bag,maxvar,cl))
717 else match is_subsumed ~unify:true bag maxvar clause table with
718 | None -> Some (bag, clause)
719 | Some ((bag,maxvar),c) ->
720 prerr_endline "Goal subsumed";
721 raise (Success (bag,maxvar,c))
725 let prof_simplify_goal = HExtlib.profile ~enable "simplify_goal";;
726 let simplify_goal ~no_demod maxvar table bag g_actives x =
727 prof_simplify_goal.HExtlib.profile ( simplify_goal ~no_demod maxvar table bag g_actives) x
730 (* =================== inference ===================== *)
732 (* this is OK for both the sup_left and sup_right inference steps *)
733 let superposition table varlist subterm pos context =
734 let cands = IDX.DT.retrieve_unifiables table subterm in
736 (fun (dir, (id,lit,vl,_ (*as uc*))) ->
738 | Terms.Predicate _ -> assert false
739 | Terms.Equation (l,r,_,o) ->
740 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
743 Unif.unification (* (varlist@vl)*) [] subterm side
745 if o = Terms.Incomparable || o = Terms.Invertible then
746 let side = Subst.apply_subst subst side in
747 let newside = Subst.apply_subst subst newside in
748 let o = Order.compare_terms side newside in
749 (* XXX: check Riazanov p. 33 (iii) *)
750 if o <> Terms.Lt && o <> Terms.Eq then
751 Some (context newside, subst, id, pos, dir)
753 ((*prerr_endline ("Filtering: " ^
754 Pp.pp_foterm side ^ " =(< || =)" ^
755 Pp.pp_foterm newside);*)None)
757 Some (context newside, subst, id, pos, dir)
758 with FoUnif.UnificationFailure _ -> None)
759 (IDX.ClauseSet.elements cands)
762 (* Superposes selected equation with equalities in table *)
763 let superposition_with_table bag maxvar (id,selected,vl,_) table =
765 | Terms.Predicate _ -> assert false
766 | Terms.Equation (l,r,ty,Terms.Lt) ->
767 fold_build_new_clause bag maxvar id Terms.Superposition
770 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
771 r (superposition table vl))
772 | Terms.Equation (l,r,ty,Terms.Invertible)
773 | Terms.Equation (l,r,ty,Terms.Gt) ->
774 fold_build_new_clause bag maxvar id Terms.Superposition
777 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
778 l (superposition table vl))
779 | Terms.Equation (l,r,ty,Terms.Incomparable) ->
780 let filtering avoid subst = (* Riazanov: p.33 condition (iv) *)
781 let l = Subst.apply_subst subst l in
782 let r = Subst.apply_subst subst r in
783 let o = Order.compare_terms l r in
784 o <> avoid && o <> Terms.Eq
786 let bag, maxvar,r_terms =
787 fold_build_new_clause bag maxvar id Terms.Superposition
790 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
791 r (superposition table vl))
793 let bag, maxvar, l_terms =
794 fold_build_new_clause bag maxvar id Terms.Superposition
797 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
798 l (superposition table vl))
800 bag, maxvar, r_terms @ l_terms
804 (* the current equation is normal w.r.t. demodulation with atable
805 * (and is not the identity) *)
806 let infer_right bag maxvar current (alist,atable) =
807 (* We demodulate actives clause with current until all *
808 * active clauses are reduced w.r.t each other *)
809 (* let bag, (alist,atable) = keep_simplified (alist,atable) bag [current] in *)
810 let ctable = IDX.index_unit_clause maxvar IDX.DT.empty current in
811 (* let bag, (alist, atable) =
813 HExtlib.filter_map_acc (simplify ctable) bag alist
815 bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist)
817 debug "Simplified active clauses with fact";
818 (* We superpose active clauses with current *)
819 let bag, maxvar, new_clauses =
821 (fun (bag, maxvar, acc) active ->
822 let bag, maxvar, newc =
823 superposition_with_table bag maxvar active ctable
825 bag, maxvar, newc @ acc)
826 (bag, maxvar, []) alist
828 debug "First superpositions";
829 (* We add current to active clauses so that it can be *
830 * superposed with itself *)
832 current :: alist, IDX.index_unit_clause maxvar atable current
835 let fresh_current, maxvar = Utils.fresh_unit_clause maxvar current in
836 (* We need to put fresh_current into the bag so that all *
837 * variables clauses refer to are known. *)
838 let bag, fresh_current = Terms.add_to_bag fresh_current bag in
839 (* We superpose current with active clauses *)
840 let bag, maxvar, additional_new_clauses =
841 superposition_with_table bag maxvar fresh_current atable
843 debug "Another superposition";
844 let new_clauses = new_clauses @ additional_new_clauses in
845 debug (lazy (Printf.sprintf "Demodulating %d clauses"
846 (List.length new_clauses)));
847 let bag, new_clauses =
848 HExtlib.filter_map_monad (simplify atable maxvar) bag new_clauses
850 debug "Demodulated new clauses";
851 bag, maxvar, (alist, atable), new_clauses
854 let prof_ir = HExtlib.profile ~enable "infer_right";;
855 let infer_right bag maxvar current t =
856 prof_ir.HExtlib.profile (infer_right bag maxvar current) t
859 let infer_left bag maxvar goal (_alist, atable) =
860 (* We superpose the goal with active clauses *)
861 if (match goal with (_,_,[],_) -> true | _ -> false) then bag, maxvar, []
863 let bag, maxvar, new_goals =
864 superposition_with_table bag maxvar goal atable
866 debug "Superposed goal with active clauses";
867 (* We simplify the new goals with active clauses *)
871 match simplify_goal ~no_demod:false maxvar atable bag [] g with
872 | None -> assert false
873 | Some (bag,g) -> bag,g::acc)
876 debug "Simplified new goals with active clauses";
877 bag, maxvar, List.rev new_goals
880 let prof_il = HExtlib.profile ~enable "infer_left";;
881 let infer_left bag maxvar goal t =
882 prof_il.HExtlib.profile (infer_left bag maxvar goal) t