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 : Terms.Blob) =
16 module IDX = Index.Index(B)
17 module Unif = FoUnif.Founif(B)
18 module Subst = FoSubst (*.Subst(B)*)
19 module Order = Orderings.Orderings(B)
20 module Utils = FoUtils.Utils(B)
23 exception Success of B.t Terms.bag * int * B.t Terms.unit_clause
26 () (* 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 rec aux pos ctx = function
36 | Terms.Leaf _ as t -> f t pos ctx
39 match f t pos ctx with
42 let rec first pre post = function
45 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
46 match aux (List.length pre :: pos) newctx t with
49 if post = [] then None (* tl is also empty *)
50 else first (pre @ [t]) (List.tl post) tl
52 first [] (List.tl l) l
57 let all_positions pos ctx t f =
58 let rec aux pos ctx = function
59 | Terms.Leaf _ as t -> f t pos ctx
64 (fun (acc,pre,post) t -> (* Invariant: pre @ [t] @ post = l *)
65 let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in
66 let acc = aux (List.length pre :: pos) newctx t @ acc in
67 if post = [] then acc, l, []
68 else acc, pre @ [t], List.tl post)
69 (f t pos ctx, [], List.tl l) l
77 let rec aux acc = function
79 | Terms.Var i -> if (List.mem i acc) then acc else i::acc
80 | Terms.Node l -> List.fold_left aux acc l
84 let build_clause bag filter rule t subst vl id id2 pos dir =
85 let proof = Terms.Step(rule,id,id2,dir,pos,subst) in
86 let t = Subst.apply_subst subst t in
90 | Terms.Node [ Terms.Leaf eq ; ty; l; r ] when B.eq B.eqP eq ->
91 let o = Order.compare_terms l r in
92 Terms.Equation (l, r, ty, o)
93 | t -> Terms.Predicate t
96 Utils.add_to_bag bag (0, literal, vars_of_term t, proof)
100 ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None)
104 (* ============ simplification ================= *)
106 let demod table varlist subterm pos context =
107 let cands = IDX.DT.retrieve_generalizations table subterm in
109 (fun (dir, (id,lit,vl,_)) ->
111 | Terms.Predicate _ -> assert false
112 | Terms.Equation (l,r,_,o) ->
113 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
116 Unif.unification (varlist@vl) varlist subterm side
118 if o = Terms.Incomparable then
119 let side = Subst.apply_subst subst side in
120 let newside = Subst.apply_subst subst newside in
121 let o = Order.compare_terms newside side in
122 (* Riazanov, pp. 45 (ii) *)
124 Some (context newside, subst, varlist, id, pos, dir)
126 ((*prerr_endline ("Filtering: " ^
127 Pp.pp_foterm side ^ " =(< || =)" ^
128 Pp.pp_foterm newside ^ " coming from " ^
129 Pp.pp_unit_clause uc );*)None)
131 Some (context newside, subst, varlist, id, pos, dir)
132 with FoUnif.UnificationFailure _ -> None)
133 (IDX.ClauseSet.elements cands)
136 (* XXX: possible optimization, if the literal has a "side" already
137 * in normal form we should not traverse it again *)
138 let demodulate_once bag (id, literal, vl, pr) table =
139 (* debug ("Demodulating : " ^ (Pp.pp_unit_clause (id, literal, vl, pr)));*)
141 | Terms.Predicate t -> assert false
142 | Terms.Equation (l,r,ty,_) ->
143 match first_position [2]
144 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) l
147 | Some (newt, subst, varlist, id2, pos, dir) ->
148 build_clause bag (fun _ -> true) Terms.Demodulation
149 newt subst varlist id id2 pos dir
152 [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) r
156 | Some (newt, subst, varlist, id2, pos, dir) ->
157 build_clause bag (fun _ -> true) Terms.Demodulation
158 newt subst varlist id id2 pos dir
161 let rec demodulate bag clause table =
162 match demodulate_once bag clause table with
163 | None -> bag, clause
164 | Some (bag, clause) -> demodulate bag clause table
168 let is_identity_clause = function
169 | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
170 | _, Terms.Predicate _, _, _ -> assert false
174 let build_new_clause bag maxvar filter rule t subst vl id id2 pos dir =
175 let maxvar, vl, relocsubst = Utils.relocate maxvar vl in
176 let subst = Subst.concat relocsubst subst in
177 match build_clause bag filter rule t subst vl id id2 pos dir with
178 | Some (bag, c) -> Some ((bag, maxvar), c)
183 let fold_build_new_clause bag maxvar id rule filter res =
184 let (bag, maxvar), res =
185 HExtlib.filter_map_acc
186 (fun (bag, maxvar) (t,subst,vl,id2,pos,dir) ->
187 build_new_clause bag maxvar filter rule t subst vl id id2 pos dir)
193 let is_subsumed ~unify bag maxvar (id, lit, vl, _) table =
195 | Terms.Predicate _ -> assert false
196 | Terms.Equation (l,r,ty,_) ->
197 let retrieve = if unify then IDX.DT.retrieve_unifiables
198 else IDX.DT.retrieve_generalizations in
199 let lcands = retrieve table l in
200 let rcands = retrieve table r in
202 let id, dir, l, r, vl =
204 | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl
207 let reverse = (dir = Terms.Left2Right) = b in
208 let l, r, proof_rewrite_dir = if reverse then l,r,Terms.Left2Right
209 else r,l, Terms.Right2Left in
210 (id,proof_rewrite_dir,Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl)
212 let cands1 = List.map (f true) (IDX.ClauseSet.elements lcands) in
213 let cands2 = List.map (f false) (IDX.ClauseSet.elements rcands) in
214 let t = Terms.Node [ Terms.Leaf B.eqP; ty; l; r ] in
215 let locked_vars = if unify then [] else vl in
216 let rec aux = function
218 | (id2,dir,c,vl1)::tl ->
220 let subst,vl1 = Unif.unification (vl@vl1) locked_vars c t in
221 let id_t = Terms.Node [ Terms.Leaf B.eqP; ty; r; r ] in
222 build_new_clause bag maxvar (fun _ -> true)
223 Terms.Superposition id_t subst [] id id2 [2] dir
224 with FoUnif.UnificationFailure _ -> aux tl
226 aux (cands1 @ cands2)
229 (* demodulate and check for subsumption *)
230 let simplify table maxvar bag clause =
231 let bag, clause = demodulate bag clause table in
232 if is_identity_clause clause then None
234 match is_subsumed ~unify:false bag maxvar clause table with
235 | None -> Some (bag, clause)
239 let one_pass_simplification new_clause (alist,atable) bag maxvar =
240 match simplify atable maxvar bag new_clause with
241 | None -> None (* new_clause has been discarded *)
242 | Some (bag, clause) ->
243 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
244 let bag, alist, atable =
246 (fun (bag, alist, atable as acc) c ->
247 match simplify ctable maxvar bag c with
248 |None -> acc (* an active clause as been discarded *)
250 bag, c :: alist, IDX.index_unit_clause atable c)
251 (bag,[],IDX.DT.empty) alist
253 Some (clause, bag, (alist,atable))
256 let simplification_step ~new_cl cl (alist,atable) bag maxvar new_clause =
258 if new_cl then atable else
259 IDX.index_unit_clause atable cl
261 (* Simplification of new_clause with : *
262 * - actives and cl if new_clause is not cl *
263 * - only actives otherwise *)
264 match simplify atable1 maxvar bag new_clause with
265 | None -> (Some cl, None) (* new_clause has been discarded *)
266 | Some (bag, clause) ->
267 (* Simplification of each active clause with clause *
268 * which is the simplified form of new_clause *)
269 let ctable = IDX.index_unit_clause IDX.DT.empty clause in
270 let bag, newa, alist, atable =
272 (fun (bag, newa, alist, atable as acc) c ->
273 match simplify ctable maxvar bag c with
274 |None -> acc (* an active clause as been discarded *)
277 bag, newa, c :: alist,
278 IDX.index_unit_clause atable c
280 bag, c1 :: newa, alist, atable)
281 (bag,[],[],IDX.DT.empty) alist
284 (Some cl, Some (clause, (alist,atable), newa, bag))
286 (* if new_clause is not cl, we simplify cl with clause *)
287 match simplify ctable maxvar bag cl with
289 (* cl has been discarded *)
290 (None, Some (clause, (alist,atable), newa, bag))
292 (Some cl1, Some (clause, (alist,atable), newa, bag))
295 let keep_simplified cl (alist,atable) bag maxvar =
296 let rec keep_simplified_aux ~new_cl cl (alist,atable) bag newc =
298 match simplification_step ~new_cl cl (alist,atable) bag maxvar cl with
299 | (None, _) -> assert false
300 | (Some _, None) -> None
301 | (Some _, Some (clause, (alist,atable), newa, bag)) ->
302 keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable)
306 | [] -> Some (cl, bag, (alist,atable))
308 match simplification_step ~new_cl cl
309 (alist,atable) bag maxvar hd with
310 | (None,None) -> assert false
312 keep_simplified_aux ~new_cl cl (alist,atable) bag tl
313 | (None, Some _) -> None
314 | (Some cl1, Some (clause, (alist,atable), newa, bag)) ->
316 (clause::alist, IDX.index_unit_clause atable clause)
318 keep_simplified_aux ~new_cl:(cl!=cl1) cl1 (alist,atable)
321 keep_simplified_aux ~new_cl:true cl (alist,atable) bag []
324 (* this is like simplify but raises Success *)
325 let simplify_goal maxvar table bag clause =
326 let bag, clause = demodulate bag clause table in
327 if (is_identity_clause clause)
328 then raise (Success (bag, maxvar, clause))
329 else match is_subsumed ~unify:true bag maxvar clause table with
330 | None -> bag, clause
331 | Some ((bag,maxvar),c) ->
332 debug "Goal subsumed";
333 raise (Success (bag,maxvar,c))
336 (* =================== inference ===================== *)
338 (* this is OK for both the sup_left and sup_right inference steps *)
339 let superposition table varlist subterm pos context =
340 let cands = IDX.DT.retrieve_unifiables table subterm in
342 (fun (dir, (id,lit,vl,_ (*as uc*))) ->
344 | Terms.Predicate _ -> assert false
345 | Terms.Equation (l,r,_,o) ->
346 let side, newside = if dir=Terms.Left2Right then l,r else r,l in
349 Unif.unification (varlist@vl) [] subterm side
351 if o = Terms.Incomparable then
352 let side = Subst.apply_subst subst side in
353 let newside = Subst.apply_subst subst newside in
354 let o = Order.compare_terms side newside in
355 (* XXX: check Riazanov p. 33 (iii) *)
356 if o <> Terms.Lt && o <> Terms.Eq then
357 Some (context newside, subst, varlist, id, pos, dir)
359 ((*prerr_endline ("Filtering: " ^
360 Pp.pp_foterm side ^ " =(< || =)" ^
361 Pp.pp_foterm newside ^ " coming from " ^
362 Pp.pp_unit_clause uc );*)None)
364 Some (context newside, subst, varlist, id, pos, dir)
365 with FoUnif.UnificationFailure _ -> None)
366 (IDX.ClauseSet.elements cands)
369 (* Superposes selected equation with equalities in table *)
370 let superposition_with_table bag maxvar (id,selected,vl,_) table =
372 | Terms.Predicate _ -> assert false
373 | Terms.Equation (l,r,ty,Terms.Lt) ->
374 fold_build_new_clause bag maxvar id Terms.Superposition
377 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
378 r (superposition table vl))
379 | Terms.Equation (l,r,ty,Terms.Gt) ->
380 fold_build_new_clause bag maxvar id Terms.Superposition
383 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
384 l (superposition table vl))
385 | Terms.Equation (l,r,ty,Terms.Incomparable) ->
386 fold_build_new_clause bag maxvar id Terms.Superposition
387 (function (* Riazanov: p.33 condition (iv) *)
388 | Terms.Node [Terms.Leaf eq; ty; l; r ] when B.eq B.eqP eq ->
389 Order.compare_terms l r <> Terms.Eq
392 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
393 r (superposition table vl)) @
395 (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
396 l (superposition table vl)))
400 (* the current equation is normal w.r.t. demodulation with atable
401 * (and is not the identity) *)
402 let infer_right bag maxvar current (alist,atable) =
403 (* We demodulate actives clause with current until all *
404 * active clauses are reduced w.r.t each other *)
405 (* let bag, (alist,atable) = keep_simplified (alist,atable) bag [current] in *)
406 let ctable = IDX.index_unit_clause IDX.DT.empty current in
407 (* let bag, (alist, atable) =
409 HExtlib.filter_map_acc (simplify ctable) bag alist
411 bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist)
413 debug "Simplified active clauses with fact";
414 (* We superpose active clauses with current *)
415 let bag, maxvar, new_clauses =
417 (fun (bag, maxvar, acc) active ->
418 let bag, maxvar, newc =
419 superposition_with_table bag maxvar active ctable
421 bag, maxvar, newc @ acc)
422 (bag, maxvar, []) alist
424 debug "First superpositions";
425 (* We add current to active clauses so that it can be *
426 * superposed with itself *)
428 current :: alist, IDX.index_unit_clause atable current
431 let fresh_current, maxvar = Utils.fresh_unit_clause maxvar current in
432 (* We need to put fresh_current into the bag so that all *
433 * variables clauses refer to are known. *)
434 let bag, fresh_current = Utils.add_to_bag bag fresh_current in
435 (* We superpose current with active clauses *)
436 let bag, maxvar, additional_new_clauses =
437 superposition_with_table bag maxvar fresh_current atable
439 debug "Another superposition";
440 let new_clauses = new_clauses @ additional_new_clauses in
441 let bag, new_clauses =
442 HExtlib.filter_map_acc (simplify atable maxvar) bag new_clauses
444 debug "Demodulated new clauses";
445 bag, maxvar, (alist, atable), new_clauses
448 let infer_left bag maxvar goal (_alist, atable) =
449 (* We superpose the goal with active clauses *)
450 let bag, maxvar, new_goals =
451 superposition_with_table bag maxvar goal atable
453 debug "Superposed goal with active clauses";
454 (* We demodulate the new goals with active clauses *)
458 let bag, g = demodulate bag g atable in
462 debug "Demodulated goal with active clauses";
463 bag, maxvar, List.rev new_goals