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)
26 * B.t Terms.unit_clause
27 * B.t Terms.substitution
29 let print s = prerr_endline (Lazy.force s);;
33 let rec list_first f = function
35 | x::tl -> match f x with Some _ as x -> x | _ -> list_first f tl
38 let first_position pos ctx t f =
39 let inject_pos pos ctx = function
41 | Some (a,b,c,d) -> Some(ctx a,b,c,d,pos)
43 let rec aux pos ctx = function
44 | Terms.Leaf _ as t -> inject_pos pos ctx (f t)
48 | Some _ as x -> inject_pos pos ctx x
50 let rec first pre post = function
53 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
54 match aux (List.length pre :: pos) newctx t with
57 if post = [] then None (* tl is also empty *)
58 else first (pre @ [t]) (List.tl post) tl
60 first [] (List.tl l) l
65 let all_positions pos ctx t f =
66 let rec aux pos ctx = function
67 | Terms.Leaf _ as t -> f t pos ctx
72 (fun (acc,pre,post) t -> (* Invariant: pre @ [t] @ post = l *)
73 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
74 let acc = aux (List.length pre :: pos) newctx t @ acc in
75 if post = [] then acc, l, []
76 else acc, pre @ [t], List.tl post)
77 (f t pos ctx, [], List.tl l) l
84 let parallel_positions bag pos ctx id t f =
85 let rec aux bag pos ctx id = function
86 | Terms.Leaf _ as t -> f bag t pos ctx id
87 | Terms.Var _ as t -> bag,t,id
88 | Terms.Node (hd::l) as t->
89 let bag,t,id1 = f bag t pos ctx id in
93 (fun (bag,pre,post,id) t ->
94 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
95 let newpos = (List.length pre)::pos in
96 let bag,newt,id = aux bag newpos newctx id t in
97 if post = [] then bag, pre@[newt], [], id
98 else bag, pre @ [newt], List.tl post, id)
99 (bag, [hd], List.tl l, id) l
101 bag, Terms.Node l, id
103 (* else aux bag pos ctx id1 t *)
109 let visit bag pos ctx id t f =
110 let rec aux bag pos ctx id subst = function
111 | Terms.Leaf _ as t ->
112 let bag,subst,t,id = f bag t pos ctx id in
113 assert (subst=[]); bag,t,id
114 | Terms.Var i as t ->
115 let t= Subst.apply_subst subst t in
117 | Terms.Node (hd::l) ->
120 (fun (bag,pre,post,id) t ->
121 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
122 let newpos = (List.length pre)::pos in
123 let bag,newt,id = aux bag newpos newctx id subst t in
124 if post = [] then bag, pre@[newt], [], id
125 else bag, pre @ [newt], List.tl post, id)
126 (bag, [hd], List.map (Subst.apply_subst subst) (List.tl l), id) l
128 let bag,subst,t,id1 = f bag (Terms.Node l) pos ctx id
130 if id1 = id then (assert (subst=[]); bag,t,id)
131 else aux bag pos ctx id1 subst t
134 aux bag pos ctx id [] t
137 let build_clause bag filter rule t subst id id2 pos dir =
138 let proof = Terms.Step(rule,id,id2,dir,pos,subst) in
139 let t = Subst.apply_subst subst t in
143 | Terms.Node [ Terms.Leaf eq ; ty; l; r ] when B.eq B.eqP eq ->
144 let o = Order.compare_terms l r in
145 (* CSC: to avoid equations of the form ? -> T that
146 can always be applied and that lead to type-checking errors *)
148 Terms.Var _,_,Terms.Gt
149 | _,Terms.Var _,Terms.Lt -> assert false
150 | Terms.Var _,_,(Terms.Incomparable | Terms.Invertible) ->
151 Terms.Equation (l, r, ty, Terms.Lt)
152 | _, Terms.Var _,(Terms.Incomparable | Terms.Invertible) ->
153 Terms.Equation (l, r, ty, Terms.Gt)
154 | _ -> Terms.Equation (l, r, ty, o))
155 | t -> Terms.Predicate t
158 Terms.add_to_bag (0, literal, Terms.vars_of_term t, proof) bag
162 ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None)
164 let prof_build_clause = HExtlib.profile ~enable "build_clause";;
165 let build_clause bag filter rule t subst id id2 pos x =
166 prof_build_clause.HExtlib.profile (build_clause bag filter rule t subst id id2 pos) x
170 (* ============ simplification ================= *)
171 let prof_demod_u = HExtlib.profile ~enable "demod.unify";;
172 let prof_demod_r = HExtlib.profile ~enable "demod.retrieve_generalizations";;
173 let prof_demod_o = HExtlib.profile ~enable "demod.compare_terms";;
174 let prof_demod_s = HExtlib.profile ~enable "demod.apply_subst";;
176 let demod table varlist subterm =
178 prof_demod_r.HExtlib.profile
179 (IDX.DT.retrieve_generalizations table) subterm
182 (fun (dir, (id,lit,vl,_)) ->
184 | Terms.Predicate _ -> assert false
185 | Terms.Equation (l,r,_,o) ->
186 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
189 prof_demod_u.HExtlib.profile
190 (Unif.unification (* (varlist@vl) *) varlist subterm) side
193 prof_demod_s.HExtlib.profile
194 (Subst.apply_subst subst) side
197 prof_demod_s.HExtlib.profile
198 (Subst.apply_subst subst) newside
200 if o = Terms.Incomparable || o = Terms.Invertible then
202 prof_demod_o.HExtlib.profile
203 (Order.compare_terms newside) side in
204 (* Riazanov, pp. 45 (ii) *)
206 Some (newside, subst, id, dir)
208 ((*prerr_endline ("Filtering: " ^
209 Pp.pp_foterm side ^ " =(< || =)" ^
210 Pp.pp_foterm newside ^ " coming from " ^
211 Pp.pp_unit_clause uc );*)None)
213 Some (newside, subst, id, dir)
214 with FoUnif.UnificationFailure _ -> None)
215 (IDX.ClauseSet.elements cands)
217 let prof_demod = HExtlib.profile ~enable "demod";;
218 let demod table varlist x =
219 prof_demod.HExtlib.profile (demod table varlist) x
222 let mydemod table varlist subterm =
224 prof_demod_r.HExtlib.profile
225 (IDX.DT.retrieve_generalizations table) subterm
228 (fun (dir, ((id,lit,vl,_) as c)) ->
229 debug (lazy("candidate: "
230 ^ Pp.pp_unit_clause c));
232 | Terms.Predicate _ -> assert false
233 | Terms.Equation (l,r,_,o) ->
234 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
237 prof_demod_u.HExtlib.profile
238 (Unif.unification (* (varlist@vl) *) varlist subterm) side
241 prof_demod_s.HExtlib.profile
242 (Subst.apply_subst subst) side
245 prof_demod_s.HExtlib.profile
246 (Subst.apply_subst subst) newside
248 if o = Terms.Incomparable || o = Terms.Invertible then
250 prof_demod_o.HExtlib.profile
251 (Order.compare_terms inewside) iside in
252 (* Riazanov, pp. 45 (ii) *)
254 Some (newside, subst, id, dir)
256 ((*prerr_endline ("Filtering: " ^
257 Pp.pp_foterm side ^ " =(< || =)" ^
258 Pp.pp_foterm newside ^ " coming from " ^
259 Pp.pp_unit_clause uc );*)
260 debug (lazy "not applied");None)
262 Some (newside, subst, id, dir)
263 with FoUnif.UnificationFailure _ ->
264 debug (lazy "not applied"); None)
265 (IDX.ClauseSet.elements cands)
268 let ctx_demod table vl bag t pos ctx id =
269 match mydemod table vl t with
270 | None -> (bag,[],t,id)
271 | Some (newside, subst, id2, dir) ->
272 let inewside = Subst.apply_subst subst newside in
273 match build_clause bag (fun _ -> true)
274 Terms.Demodulation (ctx inewside) subst id id2 pos dir
276 | None -> assert false
277 | Some (bag,(id,_,_,_)) ->
278 (bag,subst,newside,id)
281 let rec demodulate bag (id, literal, vl, pr) table =
282 debug (lazy ("demodulate " ^ (string_of_int id)));
284 | Terms.Predicate t -> (* assert false *)
286 visit bag [] (fun x -> x) id t (ctx_demod table vl)
288 let cl,_,_ = Terms.get_from_bag id1 bag in
290 | Terms.Equation (l,r,ty,_) ->
293 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) id l
298 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) id1 r
301 let cl,_,_ = Terms.get_from_bag id2 bag in
305 let parallel_demod table vl bag t pos ctx id =
306 match demod table vl t with
308 | Some (newside, subst, id2, dir) ->
309 match build_clause bag (fun _ -> true)
310 Terms.Demodulation (ctx newside) subst id id2 pos dir
312 | None -> assert false
313 | Some (bag,(id,_,_,_)) ->
317 let are_alpha_eq cl1 cl2 =
318 let get_term (_,lit,_,_) =
320 | Terms.Predicate _ -> assert false
321 | Terms.Equation (l,r,ty,_) ->
322 Terms.Node [Terms.Leaf B.eqP; ty; l ; r]
324 try ignore(Unif.alpha_eq (get_term cl1) (get_term cl2)) ; true
325 with FoUnif.UnificationFailure _ -> false
328 let prof_demodulate = HExtlib.profile ~enable "demodulate";;
329 let demodulate bag clause x =
330 prof_demodulate.HExtlib.profile (demodulate bag clause) x
334 let is_identity_clause = function
335 | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
336 | _, Terms.Equation (_,_,_,_), _, _ -> false
337 | _, Terms.Predicate _, _, _ -> assert false
340 let is_identity_goal = function
341 | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> Some []
342 | _, Terms.Equation (l,r,_,_), vl, proof ->
343 (try Some (Unif.unification (* vl *) [] l r)
344 with FoUnif.UnificationFailure _ -> None)
345 | _, Terms.Predicate _, _, _ -> assert false
348 let build_new_clause_reloc bag maxvar filter rule t subst id id2 pos dir =
349 let maxvar, _vl, subst = Utils.relocate maxvar (Terms.vars_of_term
350 (Subst.apply_subst subst t)) subst in
351 match build_clause bag filter rule t subst id id2 pos dir with
352 | Some (bag, c) -> Some ((bag, maxvar), c), subst
356 let build_new_clause bag maxvar filter rule t subst id id2 pos dir =
357 fst (build_new_clause_reloc bag maxvar filter rule t
358 subst id id2 pos dir)
361 let prof_build_new_clause = HExtlib.profile ~enable "build_new_clause";;
362 let build_new_clause bag maxvar filter rule t subst id id2 pos x =
363 prof_build_new_clause.HExtlib.profile (build_new_clause bag maxvar filter
364 rule t subst id id2 pos) x
367 let fold_build_new_clause bag maxvar id rule filter res =
368 let (bag, maxvar), res =
369 HExtlib.filter_map_acc
370 (fun (bag, maxvar) (t,subst,id2,pos,dir) ->
371 build_new_clause bag maxvar filter rule t subst id id2 pos dir)
377 (* rewrite_eq check if in table there an equation matching l=r;
378 used in subsumption and deep_eq. In deep_eq, we need to match
379 several times times w.r.t. the same table, hence we should refresh
380 the retrieved clauses, to avoid clashes of variables *)
382 let rewrite_eq ~refresh ~unify maxvar l r ty vl table =
383 let retrieve = if unify then IDX.DT.retrieve_unifiables
384 else IDX.DT.retrieve_generalizations in
385 let lcands = retrieve table l in
386 let rcands = retrieve table r in
388 let id, dir, l, r, vl =
390 | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl
393 let reverse = (dir = Terms.Left2Right) = b in
394 let l, r, proof_rewrite_dir = if reverse then l,r,Terms.Left2Right
395 else r,l, Terms.Right2Left in
396 (id,proof_rewrite_dir,Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl)
398 let cands1 = List.map (f true) (IDX.ClauseSet.elements lcands) in
399 let cands2 = List.map (f false) (IDX.ClauseSet.elements rcands) in
400 let t = Terms.Node [ Terms.Leaf B.eqP; ty; l; r ] in
401 let locked_vars = if unify then [] else vl in
402 let rec aux = function
404 | (id2,dir,c,vl1)::tl ->
406 let c,maxvar = if refresh then
407 let maxvar,_,r = Utils.relocate maxvar vl1 [] in
408 Subst.apply_subst r c,maxvar
410 let subst = Unif.unification (* (vl@vl1) *) locked_vars c t in
411 Some (id2, dir, subst, maxvar)
412 with FoUnif.UnificationFailure _ -> aux tl
414 aux (cands1 @ cands2)
417 let is_subsumed ~unify bag maxvar (id, lit, vl, _) table =
419 | Terms.Predicate _ -> assert false
420 | Terms.Equation (l,r,ty,_) ->
421 match rewrite_eq ~refresh:false ~unify maxvar l r ty vl table with
423 | Some (id2, dir, subst, maxvar) ->
424 let id_t = Terms.Node [ Terms.Leaf B.eqP; ty; r; r ] in
425 build_new_clause bag maxvar (fun _ -> true)
426 Terms.Superposition id_t subst id id2 [2] dir
428 let prof_is_subsumed = HExtlib.profile ~enable "is_subsumed";;
429 let is_subsumed ~unify bag maxvar c x =
430 prof_is_subsumed.HExtlib.profile (is_subsumed ~unify bag maxvar c) x
432 (* id refers to a clause proving contextl l = contextr r *)
434 let rec deep_eq ~unify l r ty pos contextl contextr table acc =
435 (* let _ = prerr_endline ("pos = " ^ String.concat ","
436 (List.map string_of_int pos)) in *)
439 | Some(bag,maxvar,(id,lit,vl,p),subst) ->
440 (* prerr_endline ("input subst = "^Pp.pp_substitution subst); *)
441 (* prerr_endline ("l prima =" ^ Pp.pp_foterm l); *)
442 (* prerr_endline ("r prima =" ^ Pp.pp_foterm r); *)
443 let l = Subst.apply_subst subst l in
444 let r = Subst.apply_subst subst r in
445 (* prerr_endline ("l dopo =" ^ Pp.pp_foterm l); *)
446 (* prerr_endline ("r dopo =" ^ Pp.pp_foterm r); *)
448 let subst1 = Unif.unification (* vl *) [] l r in
450 match lit with Terms.Predicate _ -> assert false
451 | Terms.Equation (l,r,ty,o) ->
452 let l = Subst.apply_subst subst1 l in
453 let r = Subst.apply_subst subst1 r in
454 Terms.Equation (l, r, ty, o)
456 Some(bag,maxvar,(id,lit,vl,p),Subst.concat subst1 subst)
457 with FoUnif.UnificationFailure _ ->
458 match rewrite_eq ~refresh:true ~unify maxvar l r ty vl table with
459 | Some (id2, dir, subst1, maxvar) ->
460 (* prerr_endline ("subst1 = "^Pp.pp_substitution subst1);
461 prerr_endline ("old subst = "^Pp.pp_substitution subst); *)
462 let newsubst = Subst.concat subst1 subst in
464 FoSubst.apply_subst newsubst
465 (Terms.Node[Terms.Leaf B.eqP;ty;contextl r;contextr r])
468 build_new_clause_reloc bag maxvar (fun _ -> true)
469 Terms.Superposition id_t
470 subst1 id id2 (pos@[2]) dir
472 | Some ((bag, maxvar), c), r ->
473 (* prerr_endline ("creo "^ Pp.pp_unit_clause c); *)
474 (* prerr_endline ("r = "^Pp.pp_substitution r); *)
475 let newsubst = Subst.flat
476 (Subst.concat r subst) in
477 Some(bag,maxvar,c,newsubst)
478 | None, _ -> assert false)
481 | Terms.Node (a::la), Terms.Node (b::lb) when
482 a = b && List.length la = List.length lb ->
485 (fun (acc,pre,postl,postr) a b ->
487 fun x -> contextl(Terms.Node (pre@(x::postl))) in
489 fun x -> contextr(Terms.Node (pre@(x::postr))) in
490 let newpos = List.length pre::pos in
492 if l = [] then [] else List.tl l in
493 (deep_eq ~unify a b ty
494 newpos newcl newcr table acc,pre@[b],
495 footail postl, footail postr))
496 (acc,[a],List.tl la,List.tl lb) la lb
501 let prof_deep_eq = HExtlib.profile ~enable "deep_eq";;
502 let deep_eq ~unify l r ty pos contextl contextr table x =
503 prof_deep_eq.HExtlib.profile (deep_eq ~unify l r ty pos contextl contextr table) x
506 let rec orphan_murder bag acc i =
507 match Terms.get_from_bag i bag with
508 | (_,_,_,Terms.Exact _),discarded,_ -> (discarded,acc)
509 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),true,_ -> (true,acc)
510 | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),false,_ ->
511 if (List.mem i acc) then (false,acc)
512 else match orphan_murder bag acc i1 with
513 | (true,acc) -> (true,acc)
515 let (res,acc) = orphan_murder bag acc i2 in
516 if res then res,acc else res,i::acc
519 let orphan_murder bag actives cl =
520 let (id,_,_,_) = cl in
521 let actives = List.map (fun (i,_,_,_) -> i) actives in
522 let (res,_) = orphan_murder bag actives id in
523 if res then debug (lazy "Orphan murdered"); res
525 let prof_orphan_murder = HExtlib.profile ~enable "orphan_murder";;
526 let orphan_murder bag actives x =
527 prof_orphan_murder.HExtlib.profile (orphan_murder bag actives) x
530 (* demodulate and check for subsumption *)
531 let simplify table maxvar bag clause =
532 debug (lazy "simplify...");
533 if is_identity_clause clause then bag,None
534 (* else if orphan_murder bag actives clause then bag,None *)
535 else let bag, clause = demodulate bag clause table in
536 if is_identity_clause clause then bag,None
538 match is_subsumed ~unify:false bag maxvar clause table with
539 | None -> bag, Some clause
540 | Some _ -> bag, None
543 let simplify table maxvar bag clause =
544 match simplify table maxvar bag clause with
546 let (id,_,_,_) = clause in
547 let (_,_,iter) = Terms.get_from_bag id bag in
548 Terms.replace_in_bag (clause,true,iter) bag, None
549 | bag, Some clause -> bag, Some clause
550 (*let (id,_,_,_) = clause in
551 if orphan_murder bag clause then
552 Terms.M.add id (clause,true) bag, Some clause
553 else bag, Some clause*)
555 let prof_simplify = HExtlib.profile ~enable "simplify";;
556 let simplify table maxvar bag x =
557 prof_simplify.HExtlib.profile (simplify table maxvar bag ) x
560 let one_pass_simplification new_clause (alist,atable) bag maxvar =
561 match simplify atable maxvar bag new_clause with
562 | bag,None -> bag,None (* new_clause has been discarded *)
563 | bag,(Some clause) ->
564 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
565 let bag, alist, atable =
567 (fun (bag, alist, atable) c ->
568 match simplify ctable maxvar bag c with
569 |bag,None -> (bag,alist,atable)
570 (* an active clause as been discarded *)
572 bag, c :: alist, IDX.index_unit_clause atable c)
573 (bag,[],IDX.DT.empty) alist
575 bag, Some (clause, (alist,atable))
577 let prof_one_pass_simplification = HExtlib.profile ~enable "one_pass_simplification";;
578 let one_pass_simplification new_clause t bag x =
579 prof_one_pass_simplification.HExtlib.profile (one_pass_simplification new_clause t bag ) x
582 let simplification_step ~new_cl cl (alist,atable) bag maxvar new_clause =
584 if new_cl then atable else
585 IDX.index_unit_clause atable cl
587 (* Simplification of new_clause with : *
588 * - actives and cl if new_clause is not cl *
589 * - only actives otherwise *)
591 simplify atable1 maxvar bag new_clause with
592 | bag,None -> bag,(Some cl, None) (* new_clause has been discarded *)
594 (* Simplification of each active clause with clause *
595 * which is the simplified form of new_clause *)
596 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
597 let bag, newa, alist, atable =
599 (fun (bag, newa, alist, atable) c ->
600 match simplify ctable maxvar bag c with
601 |bag,None -> (bag, newa, alist, atable)
602 (* an active clause as been discarded *)
605 bag, newa, c :: alist,
606 IDX.index_unit_clause atable c
608 bag, c1 :: newa, alist, atable)
609 (bag,[],[],IDX.DT.empty) alist
612 bag, (Some cl, Some (clause, (alist,atable), newa))
614 (* if new_clause is not cl, we simplify cl with clause *)
615 match simplify ctable maxvar bag cl with
617 (* cl has been discarded *)
618 bag,(None, Some (clause, (alist,atable), newa))
620 bag,(Some cl1, Some (clause, (alist,atable), newa))
622 let prof_simplification_step = HExtlib.profile ~enable "simplification_step";;
623 let simplification_step ~new_cl cl (alist,atable) bag maxvar x =
624 prof_simplification_step.HExtlib.profile (simplification_step ~new_cl cl (alist,atable) bag maxvar) x
627 let keep_simplified cl (alist,atable) bag maxvar =
628 let rec keep_simplified_aux ~new_cl cl (alist,atable) bag newc =
630 match simplification_step ~new_cl cl (alist,atable) bag maxvar cl with
631 | _,(None, _) -> assert false
632 | bag,(Some _, None) -> bag,None
633 | bag,(Some _, Some (clause, (alist,atable), newa)) ->
634 keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable)
638 | [] -> bag, Some (cl, (alist,atable))
640 match simplification_step ~new_cl cl
641 (alist,atable) bag maxvar hd with
642 | _,(None,None) -> assert false
643 | bag,(Some _,None) ->
644 keep_simplified_aux ~new_cl cl (alist,atable) bag tl
645 | bag,(None, Some _) -> bag,None
646 | bag,(Some cl1, Some (clause, (alist,atable), newa)) ->
648 (clause::alist, IDX.index_unit_clause atable clause)
650 keep_simplified_aux ~new_cl:(cl!=cl1) cl1 (alist,atable)
653 keep_simplified_aux ~new_cl:true cl (alist,atable) bag []
655 let prof_keep_simplified = HExtlib.profile ~enable "keep_simplified";;
656 let keep_simplified cl t bag x =
657 prof_keep_simplified.HExtlib.profile (keep_simplified cl t bag) x
660 (* this is like simplify but raises Success *)
661 let simplify_goal ~no_demod maxvar table bag g_actives clause =
663 if no_demod then bag, clause else demodulate bag clause table
665 let _ = debug(lazy ("demodulated goal : "
666 ^ Pp.pp_unit_clause clause))
668 if List.exists (are_alpha_eq clause) g_actives then None
669 else match (is_identity_goal clause) with
670 | Some subst -> raise (Success (bag,maxvar,clause,subst))
672 let (id,lit,vl,_) = clause in
673 (* this optimization makes sense only if we demodulated, since in
674 that case the clause should have been turned into an identity *)
675 if (vl = [] && not(no_demod))
676 then Some (bag,clause)
680 | Terms.Equation(l,r,ty,_) -> l,r,ty
683 match deep_eq ~unify:true l r ty [] (fun x -> x) (fun x -> x)
684 table (Some(bag,maxvar,clause,Subst.id_subst)) with
685 | None -> Some (bag,clause)
686 | Some (bag,maxvar,cl,subst) ->
687 debug (lazy "Goal subsumed");
688 debug (lazy ("subst in superpos: " ^ Pp.pp_substitution subst));
689 raise (Success (bag,maxvar,cl,subst))
691 match is_subsumed ~unify:true bag maxvar clause table with
692 | None -> Some (bag, clause)
693 | Some ((bag,maxvar),c) ->
694 debug (lazy "Goal subsumed");
695 raise (Success (bag,maxvar,c))
699 let prof_simplify_goal = HExtlib.profile ~enable "simplify_goal";;
700 let simplify_goal ~no_demod maxvar table bag g_actives x =
701 prof_simplify_goal.HExtlib.profile ( simplify_goal ~no_demod maxvar table bag g_actives) x
704 (* =================== inference ===================== *)
706 (* this is OK for both the sup_left and sup_right inference steps *)
707 let superposition table varlist subterm pos context =
708 let cands = IDX.DT.retrieve_unifiables table subterm in
710 (fun (dir, (id,lit,vl,_ (*as uc*))) ->
712 | Terms.Predicate _ -> assert false
713 | Terms.Equation (l,r,_,o) ->
714 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
717 Unif.unification (* (varlist@vl)*) [] subterm side
719 if o = Terms.Incomparable || o = Terms.Invertible then
720 let side = Subst.apply_subst subst side in
721 let newside = Subst.apply_subst subst newside in
722 let o = Order.compare_terms side newside in
723 (* XXX: check Riazanov p. 33 (iii) *)
724 if o <> Terms.Lt && o <> Terms.Eq then
725 Some (context newside, subst, id, pos, dir)
727 ((*prerr_endline ("Filtering: " ^
728 Pp.pp_foterm side ^ " =(< || =)" ^
729 Pp.pp_foterm newside);*)None)
731 Some (context newside, subst, id, pos, dir)
732 with FoUnif.UnificationFailure _ -> None)
733 (IDX.ClauseSet.elements cands)
736 (* Superposes selected equation with equalities in table *)
737 let superposition_with_table bag maxvar (id,selected,vl,_) table =
739 | Terms.Predicate _ -> assert false
740 | Terms.Equation (l,r,ty,Terms.Lt) ->
741 fold_build_new_clause bag maxvar id Terms.Superposition
744 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
745 r (superposition table vl))
746 | Terms.Equation (l,r,ty,Terms.Invertible)
747 | Terms.Equation (l,r,ty,Terms.Gt) ->
748 fold_build_new_clause bag maxvar id Terms.Superposition
751 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
752 l (superposition table vl))
753 | Terms.Equation (l,r,ty,Terms.Incomparable) ->
754 let filtering avoid subst = (* Riazanov: p.33 condition (iv) *)
755 let l = Subst.apply_subst subst l in
756 let r = Subst.apply_subst subst r in
757 let o = Order.compare_terms l r in
758 o <> avoid && o <> Terms.Eq
760 let bag, maxvar,r_terms =
761 fold_build_new_clause bag maxvar id Terms.Superposition
764 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
765 r (superposition table vl))
767 let bag, maxvar, l_terms =
768 fold_build_new_clause bag maxvar id Terms.Superposition
771 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
772 l (superposition table vl))
774 bag, maxvar, r_terms @ l_terms
778 (* the current equation is normal w.r.t. demodulation with atable
779 * (and is not the identity) *)
780 let infer_right bag maxvar current (alist,atable) =
781 (* We demodulate actives clause with current until all *
782 * active clauses are reduced w.r.t each other *)
783 (* let bag, (alist,atable) = keep_simplified (alist,atable) bag [current] in *)
784 let ctable = IDX.index_unit_clause IDX.DT.empty current in
785 (* let bag, (alist, atable) =
787 HExtlib.filter_map_acc (simplify ctable) bag alist
789 bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist)
791 debug (lazy "Simplified active clauses with fact");
792 (* We superpose active clauses with current *)
793 let bag, maxvar, new_clauses =
795 (fun (bag, maxvar, acc) active ->
796 let bag, maxvar, newc =
797 superposition_with_table bag maxvar active ctable
799 bag, maxvar, newc @ acc)
800 (bag, maxvar, []) alist
804 ("New clauses :" ^ (String.concat ";\n"
805 (List.map Pp.pp_unit_clause new_clauses))));
806 debug (lazy "First superpositions");
807 (* We add current to active clauses so that it can be *
808 * superposed with itself *)
810 current :: alist, IDX.index_unit_clause atable current
812 debug (lazy "Indexed");
813 let fresh_current, maxvar = Utils.fresh_unit_clause maxvar current in
814 (* We need to put fresh_current into the bag so that all *
815 * variables clauses refer to are known. *)
816 let bag, fresh_current = Terms.add_to_bag fresh_current bag in
817 (* We superpose current with active clauses *)
818 let bag, maxvar, additional_new_clauses =
819 superposition_with_table bag maxvar fresh_current atable
821 debug (lazy "Another superposition");
822 let new_clauses = new_clauses @ additional_new_clauses in
823 (* debug (lazy (Printf.sprintf "Demodulating %d clauses"
824 (List.length new_clauses))); *)
825 let bag, new_clauses =
826 HExtlib.filter_map_monad (simplify atable maxvar) bag new_clauses
828 debug (lazy "Demodulated new clauses");
829 bag, maxvar, (alist, atable), new_clauses
832 let prof_ir = HExtlib.profile ~enable "infer_right";;
833 let infer_right bag maxvar current t =
834 prof_ir.HExtlib.profile (infer_right bag maxvar current) t
837 let infer_left bag maxvar goal (_alist, atable) =
838 (* We superpose the goal with active clauses *)
839 if (match goal with (_,_,[],_) -> true | _ -> false) then bag, maxvar, []
841 let bag, maxvar, new_goals =
842 superposition_with_table bag maxvar goal atable
844 debug(lazy "Superposed goal with active clauses");
845 (* We simplify the new goals with active clauses *)
849 match simplify_goal ~no_demod:false maxvar atable bag [] g with
850 | None -> assert false
851 | Some (bag,g) -> bag,g::acc)
854 debug (lazy "Simplified new goals with active clauses");
855 bag, maxvar, List.rev new_goals
858 let prof_il = HExtlib.profile ~enable "infer_left";;
859 let infer_left bag maxvar goal t =
860 prof_il.HExtlib.profile (infer_left bag maxvar goal) t