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 (Lazy.force 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,_) as c)) ->
216 debug (lazy("candidate: "
217 ^ Pp.pp_unit_clause c));
219 | Terms.Predicate _ -> assert false
220 | Terms.Equation (l,r,_,o) ->
221 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
224 prof_demod_u.HExtlib.profile
225 (Unif.unification (* (varlist@vl) *) varlist subterm) side
228 prof_demod_s.HExtlib.profile
229 (Subst.apply_subst subst) side
232 prof_demod_s.HExtlib.profile
233 (Subst.apply_subst subst) newside
235 if o = Terms.Incomparable || o = Terms.Invertible then
237 prof_demod_o.HExtlib.profile
238 (Order.compare_terms inewside) iside in
239 (* Riazanov, pp. 45 (ii) *)
241 Some (newside, subst, id, dir)
243 ((*prerr_endline ("Filtering: " ^
244 Pp.pp_foterm side ^ " =(< || =)" ^
245 Pp.pp_foterm newside ^ " coming from " ^
246 Pp.pp_unit_clause uc );*)None)
248 Some (newside, subst, id, dir)
249 with FoUnif.UnificationFailure _ -> None)
250 (IDX.ClauseSet.elements cands)
253 let ctx_demod table vl bag t pos ctx id =
254 match mydemod table vl t with
255 | None -> (bag,[],t,id)
256 | Some (newside, subst, id2, dir) ->
257 let inewside = Subst.apply_subst subst newside in
258 match build_clause bag (fun _ -> true)
259 Terms.Demodulation (ctx inewside) subst id id2 pos dir
261 | None -> assert false
262 | Some (bag,(id,_,_,_)) ->
263 (bag,subst,newside,id)
266 let rec demodulate bag (id, literal, vl, pr) table =
267 debug (lazy "demodulate...");
269 | Terms.Predicate t -> assert false
270 | Terms.Equation (l,r,ty,_) ->
273 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) id l
278 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) id1 r
281 let cl,_,_ = Terms.get_from_bag id2 bag in
285 let parallel_demod table vl bag t pos ctx id =
286 match demod table vl t with
288 | Some (newside, subst, id2, dir) ->
289 match build_clause bag (fun _ -> true)
290 Terms.Demodulation (ctx newside) subst id id2 pos dir
292 | None -> assert false
293 | Some (bag,(id,_,_,_)) ->
297 let are_alpha_eq cl1 cl2 =
298 let get_term (_,lit,_,_) =
300 | Terms.Predicate _ -> assert false
301 | Terms.Equation (l,r,ty,_) ->
302 Terms.Node [Terms.Leaf B.eqP; ty; l ; r]
304 try ignore(Unif.alpha_eq (get_term cl1) (get_term cl2)) ; true
305 with FoUnif.UnificationFailure _ -> false
308 let prof_demodulate = HExtlib.profile ~enable "demodulate";;
309 let demodulate bag clause x =
310 prof_demodulate.HExtlib.profile (demodulate bag clause) x
314 let is_identity_clause ~unify = function
315 | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
316 | _, Terms.Equation (l,r,_,_), vl, proof when unify ->
317 (try ignore(Unif.unification (* vl *) [] l r); true
318 with FoUnif.UnificationFailure _ -> false)
319 | _, Terms.Equation (_,_,_,_), _, _ -> false
320 | _, Terms.Predicate _, _, _ -> assert false
323 let build_new_clause bag maxvar filter rule t subst id id2 pos dir =
324 let maxvar, _vl, subst = Utils.relocate maxvar (Terms.vars_of_term
325 (Subst.apply_subst subst t)) subst in
326 match build_clause bag filter rule t subst id id2 pos dir with
327 | Some (bag, c) -> Some ((bag, maxvar), c)
330 let prof_build_new_clause = HExtlib.profile ~enable "build_new_clause";;
331 let build_new_clause bag maxvar filter rule t subst id id2 pos x =
332 prof_build_new_clause.HExtlib.profile (build_new_clause bag maxvar filter
333 rule t subst id id2 pos) x
336 let fold_build_new_clause bag maxvar id rule filter res =
337 let (bag, maxvar), res =
338 HExtlib.filter_map_acc
339 (fun (bag, maxvar) (t,subst,id2,pos,dir) ->
340 build_new_clause bag maxvar filter rule t subst id id2 pos dir)
346 let rewrite_eq ~unify l r ty vl table =
347 let retrieve = if unify then IDX.DT.retrieve_unifiables
348 else IDX.DT.retrieve_generalizations in
349 let lcands = retrieve table l in
350 let rcands = retrieve table r in
352 let id, dir, l, r, vl =
354 | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl
357 let reverse = (dir = Terms.Left2Right) = b in
358 let l, r, proof_rewrite_dir = if reverse then l,r,Terms.Left2Right
359 else r,l, Terms.Right2Left in
360 (id,proof_rewrite_dir,Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl)
362 let cands1 = List.map (f true) (IDX.ClauseSet.elements lcands) in
363 let cands2 = List.map (f false) (IDX.ClauseSet.elements rcands) in
364 let t = Terms.Node [ Terms.Leaf B.eqP; ty; l; r ] in
365 let locked_vars = if unify then [] else vl in
366 let rec aux = function
368 | (id2,dir,c,vl1)::tl ->
370 let subst = Unif.unification (* (vl@vl1) *) locked_vars c t in
371 Some (id2, dir, subst)
372 with FoUnif.UnificationFailure _ -> aux tl
374 aux (cands1 @ cands2)
377 let is_subsumed ~unify bag maxvar (id, lit, vl, _) table =
379 | Terms.Predicate _ -> assert false
380 | Terms.Equation (l,r,ty,_) ->
381 match rewrite_eq ~unify l r ty vl table with
383 | Some (id2, dir, subst) ->
384 let id_t = Terms.Node [ Terms.Leaf B.eqP; ty; r; r ] in
385 build_new_clause bag maxvar (fun _ -> true)
386 Terms.Superposition id_t subst id id2 [2] dir
388 let prof_is_subsumed = HExtlib.profile ~enable "is_subsumed";;
389 let is_subsumed ~unify bag maxvar c x =
390 prof_is_subsumed.HExtlib.profile (is_subsumed ~unify bag maxvar c) x
392 (* id refers to a clause proving contextl l = contextr r *)
394 let rec deep_eq ~unify l r ty pos contextl contextr table acc =
397 | Some(bag,maxvar,(id,lit,vl,p),subst) ->
398 let l = Subst.apply_subst subst l in
399 let r = Subst.apply_subst subst r in
401 let subst1 = Unif.unification (* vl *) [] l r in
403 match lit with Terms.Predicate _ -> assert false
404 | Terms.Equation (l,r,ty,o) ->
405 Terms.Equation (FoSubst.apply_subst subst1 l,
406 FoSubst.apply_subst subst1 r, ty, o)
408 Some(bag,maxvar,(id,lit,vl,p),Subst.concat subst1 subst)
409 with FoUnif.UnificationFailure _ ->
410 match rewrite_eq ~unify l r ty vl table with
411 | Some (id2, dir, subst1) ->
412 let newsubst = Subst.concat subst1 subst in
414 FoSubst.apply_subst newsubst
415 (Terms.Node[Terms.Leaf B.eqP;ty;contextl r;contextr r])
418 build_new_clause bag maxvar (fun _ -> true)
419 Terms.Superposition id_t
420 subst1 id id2 (pos@[2]) dir
422 | Some ((bag, maxvar), c) ->
423 Some(bag,maxvar,c,newsubst)
424 | None -> assert false)
427 | Terms.Node (a::la), Terms.Node (b::lb) when
428 a = b && List.length la = List.length lb ->
431 (fun (acc,pre,postl,postr) a b ->
433 fun x -> contextl(Terms.Node (pre@(x::postl))) in
435 fun x -> contextr(Terms.Node (pre@(x::postr))) in
436 let newpos = List.length pre::pos in
438 if l = [] then [] else List.tl l in
439 (deep_eq ~unify a b ty
440 newpos newcl newcr table acc,pre@[b],
441 footail postl, footail postr))
442 (acc,[a],List.tl la,List.tl lb) la lb
446 let prof_deep_eq = HExtlib.profile ~enable "deep_eq";;
447 let deep_eq ~unify l r ty pos contextl contextr table x =
448 prof_deep_eq.HExtlib.profile (deep_eq ~unify l r ty pos contextl contextr table) x
451 let rec orphan_murder bag acc i =
452 match Terms.get_from_bag i bag with
453 | (_,_,_,Terms.Exact _),discarded,_ -> (discarded,acc)
454 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),true,_ -> (true,acc)
455 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),false,_ ->
456 if (List.mem i acc) then (false,acc)
457 else match orphan_murder bag acc i1 with
458 | (true,acc) -> (true,acc)
460 let (res,acc) = orphan_murder bag acc i2 in
461 if res then res,acc else res,i::acc
464 let orphan_murder bag actives cl =
465 let (id,_,_,_) = cl in
466 let actives = List.map (fun (i,_,_,_) -> i) actives in
467 let (res,_) = orphan_murder bag actives id in
468 if res then debug (lazy "Orphan murdered"); res
470 let prof_orphan_murder = HExtlib.profile ~enable "orphan_murder";;
471 let orphan_murder bag actives x =
472 prof_orphan_murder.HExtlib.profile (orphan_murder bag actives) x
475 (* demodulate and check for subsumption *)
476 let simplify table maxvar bag clause =
477 debug (lazy "simplify...");
478 if is_identity_clause ~unify:false clause then bag,None
479 (* else if orphan_murder bag actives clause then bag,None *)
480 else let bag, clause = demodulate bag clause table in
481 if is_identity_clause ~unify:false clause then bag,None
483 match is_subsumed ~unify:false bag maxvar clause table with
484 | None -> bag, Some clause
485 | Some _ -> bag, None
488 let simplify table maxvar bag clause =
489 match simplify table maxvar bag clause with
491 let (id,_,_,_) = clause in
492 let (_,_,iter) = Terms.get_from_bag id bag in
493 Terms.replace_in_bag (clause,true,iter) bag, None
494 | bag, Some clause -> bag, Some clause
495 (*let (id,_,_,_) = clause in
496 if orphan_murder bag clause then
497 Terms.M.add id (clause,true) bag, Some clause
498 else bag, Some clause*)
500 let prof_simplify = HExtlib.profile ~enable "simplify";;
501 let simplify table maxvar bag x =
502 prof_simplify.HExtlib.profile (simplify table maxvar bag ) x
505 let one_pass_simplification new_clause (alist,atable) bag maxvar =
506 match simplify atable maxvar bag new_clause with
507 | bag,None -> bag,None (* new_clause has been discarded *)
508 | bag,(Some clause) ->
509 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
510 let bag, alist, atable =
512 (fun (bag, alist, atable) c ->
513 match simplify ctable maxvar bag c with
514 |bag,None -> (bag,alist,atable)
515 (* an active clause as been discarded *)
517 bag, c :: alist, IDX.index_unit_clause atable c)
518 (bag,[],IDX.DT.empty) alist
520 bag, Some (clause, (alist,atable))
522 let prof_one_pass_simplification = HExtlib.profile ~enable "one_pass_simplification";;
523 let one_pass_simplification new_clause t bag x =
524 prof_one_pass_simplification.HExtlib.profile (one_pass_simplification new_clause t bag ) x
527 let simplification_step ~new_cl cl (alist,atable) bag maxvar new_clause =
529 if new_cl then atable else
530 IDX.index_unit_clause atable cl
532 (* Simplification of new_clause with : *
533 * - actives and cl if new_clause is not cl *
534 * - only actives otherwise *)
536 simplify atable1 maxvar bag new_clause with
537 | bag,None -> bag,(Some cl, None) (* new_clause has been discarded *)
539 (* Simplification of each active clause with clause *
540 * which is the simplified form of new_clause *)
541 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
542 let bag, newa, alist, atable =
544 (fun (bag, newa, alist, atable) c ->
545 match simplify ctable maxvar bag c with
546 |bag,None -> (bag, newa, alist, atable)
547 (* an active clause as been discarded *)
550 bag, newa, c :: alist,
551 IDX.index_unit_clause atable c
553 bag, c1 :: newa, alist, atable)
554 (bag,[],[],IDX.DT.empty) alist
557 bag, (Some cl, Some (clause, (alist,atable), newa))
559 (* if new_clause is not cl, we simplify cl with clause *)
560 match simplify ctable maxvar bag cl with
562 (* cl has been discarded *)
563 bag,(None, Some (clause, (alist,atable), newa))
565 bag,(Some cl1, Some (clause, (alist,atable), newa))
567 let prof_simplification_step = HExtlib.profile ~enable "simplification_step";;
568 let simplification_step ~new_cl cl (alist,atable) bag maxvar x =
569 prof_simplification_step.HExtlib.profile (simplification_step ~new_cl cl (alist,atable) bag maxvar) x
572 let keep_simplified cl (alist,atable) bag maxvar =
573 let rec keep_simplified_aux ~new_cl cl (alist,atable) bag newc =
575 match simplification_step ~new_cl cl (alist,atable) bag maxvar cl with
576 | _,(None, _) -> assert false
577 | bag,(Some _, None) -> bag,None
578 | bag,(Some _, Some (clause, (alist,atable), newa)) ->
579 keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable)
583 | [] -> bag, Some (cl, (alist,atable))
585 match simplification_step ~new_cl cl
586 (alist,atable) bag maxvar hd with
587 | _,(None,None) -> assert false
588 | bag,(Some _,None) ->
589 keep_simplified_aux ~new_cl cl (alist,atable) bag tl
590 | bag,(None, Some _) -> bag,None
591 | bag,(Some cl1, Some (clause, (alist,atable), newa)) ->
593 (clause::alist, IDX.index_unit_clause atable clause)
595 keep_simplified_aux ~new_cl:(cl!=cl1) cl1 (alist,atable)
598 keep_simplified_aux ~new_cl:true cl (alist,atable) bag []
600 let prof_keep_simplified = HExtlib.profile ~enable "keep_simplified";;
601 let keep_simplified cl t bag x =
602 prof_keep_simplified.HExtlib.profile (keep_simplified cl t bag) x
605 (* this is like simplify but raises Success *)
606 let simplify_goal ~no_demod maxvar table bag g_actives clause =
608 if no_demod then bag, clause else demodulate bag clause table
610 if List.exists (are_alpha_eq clause) g_actives then None
611 else if (is_identity_clause ~unify:true clause)
612 then raise (Success (bag, maxvar, clause))
614 let (id,lit,vl,_) = clause in
615 (* this optimization makes sense only if we demodulated, since in
616 that case the clause should have been turned into an identity *)
617 if (vl = [] && not(no_demod))
618 then Some (bag,clause)
622 | Terms.Equation(l,r,ty,_) -> l,r,ty
625 match deep_eq ~unify:true l r ty [] (fun x -> x) (fun x -> x)
626 table (Some(bag,maxvar,clause,Subst.id_subst)) with
627 | None -> Some (bag,clause)
628 | Some (bag,maxvar,cl,subst) ->
629 debug (lazy "Goal subsumed");
630 raise (Success (bag,maxvar,cl))
632 match is_subsumed ~unify:true bag maxvar clause table with
633 | None -> Some (bag, clause)
634 | Some ((bag,maxvar),c) ->
635 prerr_endline "Goal subsumed";
636 raise (Success (bag,maxvar,c))
640 let prof_simplify_goal = HExtlib.profile ~enable "simplify_goal";;
641 let simplify_goal ~no_demod maxvar table bag g_actives x =
642 prof_simplify_goal.HExtlib.profile ( simplify_goal ~no_demod maxvar table bag g_actives) x
645 (* =================== inference ===================== *)
647 (* this is OK for both the sup_left and sup_right inference steps *)
648 let superposition table varlist subterm pos context =
649 let cands = IDX.DT.retrieve_unifiables table subterm in
651 (fun (dir, (id,lit,vl,_ (*as uc*))) ->
653 | Terms.Predicate _ -> assert false
654 | Terms.Equation (l,r,_,o) ->
655 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
658 Unif.unification (* (varlist@vl)*) [] subterm side
660 if o = Terms.Incomparable || o = Terms.Invertible then
661 let side = Subst.apply_subst subst side in
662 let newside = Subst.apply_subst subst newside in
663 let o = Order.compare_terms side newside in
664 (* XXX: check Riazanov p. 33 (iii) *)
665 if o <> Terms.Lt && o <> Terms.Eq then
666 Some (context newside, subst, id, pos, dir)
668 ((*prerr_endline ("Filtering: " ^
669 Pp.pp_foterm side ^ " =(< || =)" ^
670 Pp.pp_foterm newside);*)None)
672 Some (context newside, subst, id, pos, dir)
673 with FoUnif.UnificationFailure _ -> None)
674 (IDX.ClauseSet.elements cands)
677 (* Superposes selected equation with equalities in table *)
678 let superposition_with_table bag maxvar (id,selected,vl,_) table =
680 | Terms.Predicate _ -> assert false
681 | Terms.Equation (l,r,ty,Terms.Lt) ->
682 fold_build_new_clause bag maxvar id Terms.Superposition
685 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
686 r (superposition table vl))
687 | Terms.Equation (l,r,ty,Terms.Invertible)
688 | Terms.Equation (l,r,ty,Terms.Gt) ->
689 fold_build_new_clause bag maxvar id Terms.Superposition
692 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
693 l (superposition table vl))
694 | Terms.Equation (l,r,ty,Terms.Incomparable) ->
695 let filtering avoid subst = (* Riazanov: p.33 condition (iv) *)
696 let l = Subst.apply_subst subst l in
697 let r = Subst.apply_subst subst r in
698 let o = Order.compare_terms l r in
699 o <> avoid && o <> Terms.Eq
701 let bag, maxvar,r_terms =
702 fold_build_new_clause bag maxvar id Terms.Superposition
705 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
706 r (superposition table vl))
708 let bag, maxvar, l_terms =
709 fold_build_new_clause bag maxvar id Terms.Superposition
712 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
713 l (superposition table vl))
715 bag, maxvar, r_terms @ l_terms
719 (* the current equation is normal w.r.t. demodulation with atable
720 * (and is not the identity) *)
721 let infer_right bag maxvar current (alist,atable) =
722 (* We demodulate actives clause with current until all *
723 * active clauses are reduced w.r.t each other *)
724 (* let bag, (alist,atable) = keep_simplified (alist,atable) bag [current] in *)
725 let ctable = IDX.index_unit_clause IDX.DT.empty current in
726 (* let bag, (alist, atable) =
728 HExtlib.filter_map_acc (simplify ctable) bag alist
730 bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist)
732 debug (lazy "Simplified active clauses with fact");
733 (* We superpose active clauses with current *)
734 let bag, maxvar, new_clauses =
736 (fun (bag, maxvar, acc) active ->
737 let bag, maxvar, newc =
738 superposition_with_table bag maxvar active ctable
740 bag, maxvar, newc @ acc)
741 (bag, maxvar, []) alist
743 debug (lazy "First superpositions");
744 (* We add current to active clauses so that it can be *
745 * superposed with itself *)
747 current :: alist, IDX.index_unit_clause atable current
749 debug (lazy "Indexed");
750 let fresh_current, maxvar = Utils.fresh_unit_clause maxvar current in
751 (* We need to put fresh_current into the bag so that all *
752 * variables clauses refer to are known. *)
753 let bag, fresh_current = Terms.add_to_bag fresh_current bag in
754 (* We superpose current with active clauses *)
755 let bag, maxvar, additional_new_clauses =
756 superposition_with_table bag maxvar fresh_current atable
758 debug (lazy "Another superposition");
759 let new_clauses = new_clauses @ additional_new_clauses in
760 (* debug (lazy (Printf.sprintf "Demodulating %d clauses"
761 (List.length new_clauses))); *)
762 let bag, new_clauses =
763 HExtlib.filter_map_monad (simplify atable maxvar) bag new_clauses
765 debug (lazy "Demodulated new clauses");
766 bag, maxvar, (alist, atable), new_clauses
769 let prof_ir = HExtlib.profile ~enable "infer_right";;
770 let infer_right bag maxvar current t =
771 prof_ir.HExtlib.profile (infer_right bag maxvar current) t
774 let infer_left bag maxvar goal (_alist, atable) =
775 (* We superpose the goal with active clauses *)
776 if (match goal with (_,_,[],_) -> true | _ -> false) then bag, maxvar, []
778 let bag, maxvar, new_goals =
779 superposition_with_table bag maxvar goal atable
781 debug(lazy "Superposed goal with active clauses");
782 (* We simplify the new goals with active clauses *)
786 match simplify_goal ~no_demod:false maxvar atable bag [] g with
787 | None -> assert false
788 | Some (bag,g) -> bag,g::acc)
791 debug (lazy "Simplified new goals with active clauses");
792 bag, maxvar, List.rev new_goals
795 let prof_il = HExtlib.profile ~enable "infer_left";;
796 let infer_left bag maxvar goal t =
797 prof_il.HExtlib.profile (infer_left bag maxvar goal) t