X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_paramodulation%2Fsuperposition.ml;h=d823c5a533bd8c5bab86d63b5ba98da5b9d34af4;hb=bd3680d6b90f6c8bdda4eb4a915a86a0e806de63;hp=4015d4b6d4a37444ce4b0f2ec6bda3473fce8cbb;hpb=96c91e470f670018df67c9cbff62fa06e3b57c5e;p=helm.git diff --git a/helm/software/components/ng_paramodulation/superposition.ml b/helm/software/components/ng_paramodulation/superposition.ml index 4015d4b6d..d823c5a53 100644 --- a/helm/software/components/ng_paramodulation/superposition.ml +++ b/helm/software/components/ng_paramodulation/superposition.ml @@ -15,13 +15,17 @@ module Superposition (B : Terms.Blob) = struct module IDX = Index.Index(B) module Unif = FoUnif.Founif(B) - module Subst = FoSubst.Subst(B) + module Subst = FoSubst (*.Subst(B)*) module Order = Orderings.Orderings(B) module Utils = FoUtils.Utils(B) module Pp = Pp.Pp(B) exception Success of B.t Terms.bag * int * B.t Terms.unit_clause + let debug s = + () (* prerr_endline s *) + ;; + let rec list_first f = function | [] -> None | x::tl -> match f x with Some _ as x -> x | _ -> list_first f tl @@ -68,6 +72,14 @@ module Superposition (B : Terms.Blob) = in aux pos ctx t ;; + + let vars_of_term t = + let rec aux acc = function + | Terms.Leaf _ -> acc + | Terms.Var i -> if (List.mem i acc) then acc else i::acc + | Terms.Node l -> List.fold_left aux acc l + in aux [] t + ;; let build_clause bag filter rule t subst vl id id2 pos dir = let proof = Terms.Step(rule,id,id2,dir,pos,subst) in @@ -81,7 +93,7 @@ module Superposition (B : Terms.Blob) = | t -> Terms.Predicate t in let bag, uc = - Utils.add_to_bag bag (0, literal, vl, proof) + Utils.add_to_bag bag (0, literal, vars_of_term t, proof) in Some (bag, uc) else @@ -106,7 +118,7 @@ module Superposition (B : Terms.Blob) = if o = Terms.Incomparable then let side = Subst.apply_subst subst side in let newside = Subst.apply_subst subst newside in - let o = Order.compare_terms side newside in + let o = Order.compare_terms newside side in (* Riazanov, pp. 45 (ii) *) if o = Terms.Lt then Some (context newside, subst, varlist, id, pos, dir) @@ -123,7 +135,8 @@ module Superposition (B : Terms.Blob) = (* XXX: possible optimization, if the literal has a "side" already * in normal form we should not traverse it again *) - let demodulate_once bag (id, literal, vl, _) table = + let demodulate_once bag (id, literal, vl, pr) table = + (* debug ("Demodulating : " ^ (Pp.pp_unit_clause (id, literal, vl, pr)));*) let t = match literal with | Terms.Predicate t -> t @@ -149,45 +162,166 @@ module Superposition (B : Terms.Blob) = | _ -> false ;; - let is_subsumed (id, lit, vl, _) table = + let build_new_clause bag maxvar filter rule t subst vl id id2 pos dir = + let maxvar, vl, relocsubst = Utils.relocate maxvar vl in + let subst = Subst.concat relocsubst subst in + match build_clause bag filter rule t subst vl id id2 pos dir with + | Some (bag, c) -> Some ((bag, maxvar), c) + | None -> None + ;; + + + let fold_build_new_clause bag maxvar id rule filter res = + let (bag, maxvar), res = + HExtlib.filter_map_acc + (fun (bag, maxvar) (t,subst,vl,id2,pos,dir) -> + build_new_clause bag maxvar filter rule t subst vl id id2 pos dir) + (bag, maxvar) res + in + bag, maxvar, res + ;; + + let is_subsumed ~unify bag maxvar (id, lit, vl, _) table = match lit with | Terms.Predicate _ -> assert false | Terms.Equation (l,r,ty,_) -> - let lcands = IDX.DT.retrieve_generalizations table l in - let rcands = IDX.DT.retrieve_generalizations table l in + let retrieve = if unify then IDX.DT.retrieve_unifiables + else IDX.DT.retrieve_generalizations in + let lcands = retrieve table l in + let rcands = retrieve table r in let f b c = - let dir, l, r, vl = + let id, dir, l, r, vl = match c with - | (d, (_,Terms.Equation (l,r,ty,_),vl,_))-> d, l, r, vl + | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl |_ -> assert false in - let l, r = if (dir = Terms.Left2Right) = b then l,r else r,l in - Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl + let reverse = (dir = Terms.Left2Right) = b in + let l, r, proof_rewrite_dir = if reverse then l,r,Terms.Left2Right + else r,l, Terms.Right2Left in + (id,proof_rewrite_dir,Terms.Node [ Terms.Leaf B.eqP; ty; l; r ], vl) in let cands1 = List.map (f true) (IDX.ClauseSet.elements lcands) in let cands2 = List.map (f false) (IDX.ClauseSet.elements rcands) in let t = Terms.Node [ Terms.Leaf B.eqP; ty; l; r ] in - List.exists - (fun (c, vl1) -> - try ignore(Unif.unification (vl@vl1) vl c t); true - with FoUnif.UnificationFailure _ -> false) - (cands1 @ cands2) + let locked_vars = if unify then [] else vl in + let rec aux = function + | [] -> None + | (id2,dir,c,vl1)::tl -> + try + let subst,vl1 = Unif.unification (vl@vl1) locked_vars c t in + let id_t = Terms.Node [ Terms.Leaf B.eqP; ty; r; r ] in + build_new_clause bag maxvar (fun _ -> true) + Terms.Superposition id_t subst [] id id2 [2] dir + with FoUnif.UnificationFailure _ -> aux tl + in + aux (cands1 @ cands2) ;; (* demodulate and check for subsumption *) - let forward_simplify table bag clause = + let simplify table maxvar bag clause = let bag, clause = demodulate bag clause table in if is_identity_clause clause then None else - if is_subsumed clause table then None - else Some (bag, clause) + match is_subsumed ~unify:false bag maxvar clause table with + | None -> Some (bag, clause) + | Some _ -> None ;; - (* this is like forward_simplify but raises Success *) - let backward_simplify maxvar table bag clause = + let one_pass_simplification new_clause (alist,atable) bag maxvar = + match simplify atable maxvar bag new_clause with + | None -> None (* new_clause has been discarded *) + | Some (bag, clause) -> + let ctable = IDX.index_unit_clause IDX.DT.empty clause in + let bag, alist, atable = + List.fold_left + (fun (bag, alist, atable as acc) c -> + match simplify ctable maxvar bag c with + |None -> acc (* an active clause as been discarded *) + |Some (bag, c1) -> + bag, c :: alist, IDX.index_unit_clause atable c) + (bag,[],IDX.DT.empty) alist + in + Some (clause, bag, (alist,atable)) + ;; + + let simplification_step ~new_cl cl (alist,atable) bag maxvar new_clause = + let atable1 = + if new_cl then atable else + IDX.index_unit_clause atable cl + in + (* Simplification of new_clause with : * + * - actives and cl if new_clause is not cl * + * - only actives otherwise *) + match simplify atable1 maxvar bag new_clause with + | None -> (Some cl, None) (* new_clause has been discarded *) + | Some (bag, clause) -> + (* Simplification of each active clause with clause * + * which is the simplified form of new_clause *) + let ctable = IDX.index_unit_clause IDX.DT.empty clause in + let bag, newa, alist, atable = + List.fold_left + (fun (bag, newa, alist, atable as acc) c -> + match simplify ctable maxvar bag c with + |None -> acc (* an active clause as been discarded *) + |Some (bag, c1) -> + if (c1 == c) then + bag, newa, c :: alist, + IDX.index_unit_clause atable c + else + bag, c1 :: newa, alist, atable) + (bag,[],[],IDX.DT.empty) alist + in + if new_cl then + (Some cl, Some (clause, (alist,atable), newa, bag)) + else + (* if new_clause is not cl, we simplify cl with clause *) + match simplify ctable maxvar bag cl with + | None -> + (* cl has been discarded *) + (None, Some (clause, (alist,atable), newa, bag)) + | Some (bag,cl1) -> + (Some cl1, Some (clause, (alist,atable), newa, bag)) + ;; + + let keep_simplified cl (alist,atable) bag maxvar = + let rec keep_simplified_aux ~new_cl cl (alist,atable) bag newc = + if new_cl then + match simplification_step ~new_cl cl (alist,atable) bag maxvar cl with + | (None, _) -> assert false + | (Some _, None) -> None + | (Some _, Some (clause, (alist,atable), newa, bag)) -> + keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable) + bag (newa@newc) + else + match newc with + | [] -> Some (cl, bag, (alist,atable)) + | hd::tl -> + match simplification_step ~new_cl cl + (alist,atable) bag maxvar hd with + | (None,None) -> assert false + | (Some _,None) -> + keep_simplified_aux ~new_cl cl (alist,atable) bag tl + | (None, Some _) -> None + | (Some cl1, Some (clause, (alist,atable), newa, bag)) -> + let alist,atable = + (clause::alist, IDX.index_unit_clause atable clause) + in + keep_simplified_aux ~new_cl:(cl!=cl1) cl1 (alist,atable) + bag (newa@tl) + in + keep_simplified_aux ~new_cl:true cl (alist,atable) bag [] + ;; + + (* this is like simplify but raises Success *) + let simplify_goal maxvar table bag clause = let bag, clause = demodulate bag clause table in - if is_identity_clause clause then raise (Success (bag, maxvar, clause)) - else bag, clause + if (is_identity_clause clause) + then raise (Success (bag, maxvar, clause)) + else match is_subsumed ~unify:true bag maxvar clause table with + | None -> bag, clause + | Some ((bag,maxvar),c) -> + debug "Goal subsumed"; + raise (Success (bag,maxvar,c)) ;; (* =================== inference ===================== *) @@ -223,25 +357,7 @@ module Superposition (B : Terms.Blob) = (IDX.ClauseSet.elements cands) ;; - let build_new_clause bag maxvar filter rule t subst vl id id2 pos dir = - let maxvar, vl, relocsubst = Utils.relocate maxvar vl in - let subst = Subst.concat relocsubst subst in - match build_clause bag filter rule t subst vl id id2 pos dir with - | Some (bag, c) -> Some ((bag, maxvar), c) - | None -> None - ;; - - - let fold_build_new_clause bag maxvar id rule filter res = - let (bag, maxvar), res = - HExtlib.filter_map_acc - (fun (bag, maxvar) (t,subst,vl,id2,pos,dir) -> - build_new_clause bag maxvar filter rule t subst vl id id2 pos dir) - (bag, maxvar) res - in - bag, maxvar, res - ;; - + (* Superposes selected equation with equalities in table *) let superposition_with_table bag maxvar (id,selected,vl,_) table = match selected with | Terms.Predicate _ -> assert false @@ -250,7 +366,7 @@ module Superposition (B : Terms.Blob) = (fun _ -> true) (all_positions [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) - r (superposition table vl)) + r (superposition table vl)) | Terms.Equation (l,r,ty,Terms.Gt) -> fold_build_new_clause bag maxvar id Terms.Superposition (fun _ -> true) @@ -275,13 +391,18 @@ module Superposition (B : Terms.Blob) = (* the current equation is normal w.r.t. demodulation with atable * (and is not the identity) *) let infer_right bag maxvar current (alist,atable) = + (* We demodulate actives clause with current until all * + * active clauses are reduced w.r.t each other *) + (* let bag, (alist,atable) = keep_simplified (alist,atable) bag [current] in *) let ctable = IDX.index_unit_clause IDX.DT.empty current in - let bag, (alist, atable) = + (* let bag, (alist, atable) = let bag, alist = - HExtlib.filter_map_acc (forward_simplify ctable) bag alist + HExtlib.filter_map_acc (simplify ctable) bag alist in bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist) - in + in*) + debug "Simplified active clauses with fact"; + (* We superpose active clauses with current *) let bag, maxvar, new_clauses = List.fold_left (fun (bag, maxvar, acc) active -> @@ -291,24 +412,36 @@ module Superposition (B : Terms.Blob) = bag, maxvar, newc @ acc) (bag, maxvar, []) alist in + debug "First superpositions"; + (* We add current to active clauses so that it can be * + * superposed with itself *) let alist, atable = current :: alist, IDX.index_unit_clause atable current in + debug "Indexed"; let fresh_current, maxvar = Utils.fresh_unit_clause maxvar current in + (* We need to put fresh_current into the bag so that all * + * variables clauses refer to are known. *) + let bag, fresh_current = Utils.add_to_bag bag fresh_current in + (* We superpose current with active clauses *) let bag, maxvar, additional_new_clauses = superposition_with_table bag maxvar fresh_current atable in + debug "Another superposition"; let new_clauses = new_clauses @ additional_new_clauses in let bag, new_clauses = - HExtlib.filter_map_acc (forward_simplify atable) bag new_clauses + HExtlib.filter_map_acc (simplify atable maxvar) bag new_clauses in + debug "Demodulated new clauses"; bag, maxvar, (alist, atable), new_clauses ;; let infer_left bag maxvar goal (_alist, atable) = + (* We superpose the goal with active clauses *) let bag, maxvar, new_goals = superposition_with_table bag maxvar goal atable in + (* We demodulate the goal with active clauses *) let bag, new_goals = List.fold_left (fun (bag, acc) g -> @@ -320,6 +453,3 @@ module Superposition (B : Terms.Blob) = ;; end - - -