X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_paramodulation%2Fsuperposition.ml;h=8070b4b5db69a2334ccc1e536009ae38895136ea;hb=a232a59672817abd3d6ec07db0b20d8b3fe5ad3b;hp=64cc35bd4e3a41e8331bb0ec071bbb9e5f30826f;hpb=637114791874df9ebc4e0f0936513c71886a913f;p=helm.git diff --git a/helm/software/components/ng_paramodulation/superposition.ml b/helm/software/components/ng_paramodulation/superposition.ml index 64cc35bd4..8070b4b5d 100644 --- a/helm/software/components/ng_paramodulation/superposition.ml +++ b/helm/software/components/ng_paramodulation/superposition.ml @@ -15,10 +15,44 @@ 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 debug _ = ();; + + let rec list_first f = function + | [] -> None + | x::tl -> match f x with Some _ as x -> x | _ -> list_first f tl + ;; + + let first_position pos ctx t f = + let rec aux pos ctx = function + | Terms.Leaf _ as t -> f t pos ctx + | Terms.Var _ -> None + | Terms.Node l as t-> + match f t pos ctx with + | Some _ as x -> x + | None -> + let rec first pre post = function + | [] -> None + | t :: tl -> + let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in + match aux (List.length pre :: pos) newctx t with + | Some _ as x -> x + | None -> + if post = [] then None (* tl is also empty *) + else first (pre @ [t]) (List.tl post) tl + in + first [] (List.tl l) l + in + aux pos ctx t + ;; + let all_positions pos ctx t f = let rec aux pos ctx = function | Terms.Leaf _ as t -> f t pos ctx @@ -38,96 +72,539 @@ module Superposition (B : Terms.Blob) = aux pos ctx t ;; - let superposition_right table varlist subterm pos context = - let cands = IDX.DT.retrieve_unifiables table subterm in - HExtlib.filter_map + 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 + let t = Subst.apply_subst subst t in + if filter t then + let literal = + match t with + | Terms.Node [ Terms.Leaf eq ; ty; l; r ] when B.eq B.eqP eq -> + let o = Order.compare_terms l r in + Terms.Equation (l, r, ty, o) + | t -> Terms.Predicate t + in + let bag, uc = + Utils.add_to_bag bag (0, literal, vars_of_term t, proof) + in + Some (bag, uc) + else + ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None) + ;; + + + (* ============ simplification ================= *) + + let demod table varlist subterm pos context = + let cands = IDX.DT.retrieve_generalizations table subterm in + list_first (fun (dir, (id,lit,vl,_)) -> match lit with | Terms.Predicate _ -> assert false | Terms.Equation (l,r,_,o) -> - assert(o <> Terms.Eq); let side, newside = if dir=Terms.Left2Right then l,r else r,l in try let subst, varlist = - Unif.unification (varlist@vl) [] subterm side + Unif.unification (varlist@vl) varlist subterm side in 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 - (* XXX: check Riazanov p. 33 (iii) *) - if o <> Terms.Lt && o <> Terms.Eq then + 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) else - None + ((*prerr_endline ("Filtering: " ^ + Pp.pp_foterm side ^ " =(< || =)" ^ + Pp.pp_foterm newside ^ " coming from " ^ + Pp.pp_unit_clause uc );*)None) else Some (context newside, subst, varlist, id, pos, dir) with FoUnif.UnificationFailure _ -> None) (IDX.ClauseSet.elements cands) ;; - let build_new_clause bag maxvar filter t subst vl id id2 pos dir = + let demodulate_once ~jump_to_right bag (id, literal, vl, pr) table = + (* debug ("Demodulating : " ^ (Pp.pp_unit_clause (id, literal, vl, pr)));*) + match literal with + | Terms.Predicate t -> assert false + | Terms.Equation (l,r,ty,_) -> + let left_position = if jump_to_right then None else + first_position [2] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) l + (demod table vl) + in + match left_position with + | Some (newt, subst, varlist, id2, pos, dir) -> + begin + match build_clause bag (fun _ -> true) Terms.Demodulation + newt subst varlist id id2 pos dir + with + | None -> assert false + | Some x -> Some (x,false) + end + | None -> + match first_position + [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) r + (demod table vl) + with + | None -> None + | Some (newt, subst, varlist, id2, pos, dir) -> + match build_clause bag (fun _ -> true) + Terms.Demodulation newt subst varlist id id2 pos dir + with + | None -> assert false + | Some x -> Some (x,true) + ;; + + let rec demodulate ~jump_to_right bag clause table = + match demodulate_once ~jump_to_right bag clause table with + | None -> bag, clause + | Some ((bag, clause),r) -> demodulate ~jump_to_right:r + bag clause table + ;; + + let demodulate bag clause table = demodulate ~jump_to_right:false + bag clause table + ;; + + (* move away *) + let is_identity_clause ~unify = function + | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true + | _, Terms.Equation (l,r,_,_), vl, proof when unify -> + (try ignore(Unif.unification vl [] l r); true + with FoUnif.UnificationFailure _ -> false) + | _, Terms.Equation (_,_,_,_), _, _ -> false + | _, Terms.Predicate _, _, _ -> assert false + ;; + + 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 - let proof = Terms.Step(Terms.SuperpositionRight,id,id2,dir,pos,subst) in - let t = Subst.apply_subst subst t in - if filter t then - let literal = - match t with - | Terms.Node [ Terms.Leaf eq ; ty; l; r ] when B.eq B.eqP eq -> - let o = Order.compare_terms l r in - Terms.Equation (l, r, ty, o) - | t -> Terms.Predicate t - in - let bag, uc = - Utils.add_to_bag bag (0, literal, vl, proof) - in - Some (bag, maxvar, uc) + 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 rewrite_eq ~unify l r ty vl table = + 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 id, dir, l, r, vl = + match c with + | (d, (id,Terms.Equation (l,r,ty,_),vl,_))-> id, d, l, r, vl + |_ -> assert false + in + 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 + 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 + Some (id2, dir, subst) + with FoUnif.UnificationFailure _ -> aux tl + in + aux (cands1 @ cands2) + ;; + + let is_subsumed ~unify bag maxvar (id, lit, vl, _) table = + match lit with + | Terms.Predicate _ -> assert false + | Terms.Equation (l,r,ty,_) -> + match rewrite_eq ~unify l r ty vl table with + | None -> None + | Some (id2, dir, subst) -> + 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 + ;; + (* id refers to a clause proving contextl l = contextr r *) + + let rec deep_eq ~unify l r ty pos contextl contextr table acc = + match acc with + | None -> None + | Some(bag,maxvar,(id,lit,vl,p),subst) -> + let l = Subst.apply_subst subst l in + let r = Subst.apply_subst subst r in + try + let subst1,vl1 = Unif.unification vl [] l r in + let lit = + match lit with Terms.Predicate _ -> assert false + | Terms.Equation (l,r,ty,o) -> + Terms.Equation (FoSubst.apply_subst subst1 l, + FoSubst.apply_subst subst1 r, ty, o) + in + Some(bag,maxvar,(id,lit,vl1,p),Subst.concat subst1 subst) + with FoUnif.UnificationFailure _ -> + match rewrite_eq ~unify l r ty vl table with + | Some (id2, dir, subst1) -> + let newsubst = Subst.concat subst1 subst in + let id_t = + FoSubst.apply_subst newsubst + (Terms.Node[Terms.Leaf B.eqP;ty;contextl r;contextr r]) + in + (match + build_new_clause bag maxvar (fun _ -> true) + Terms.Superposition id_t + subst1 [] id id2 (pos@[2]) dir + with + | Some ((bag, maxvar), c) -> + Some(bag,maxvar,c,newsubst) + | None -> assert false) + | None -> + match l,r with + | Terms.Node (a::la), Terms.Node (b::lb) when + a = b && List.length la = List.length lb -> + let acc,_,_,_ = + List.fold_left2 + (fun (acc,pre,postl,postr) a b -> + let newcl = + fun x -> contextl(Terms.Node (pre@(x::postl))) in + let newcr = + fun x -> contextr(Terms.Node (pre@(x::postr))) in + let newpos = List.length pre::pos in + let footail l = + if l = [] then [] else List.tl l in + (deep_eq ~unify a b ty + newpos newcl newcr table acc,pre@[b], + footail postl, footail postr)) + (acc,[a],List.tl la,List.tl lb) la lb + in acc + | _,_ -> None + ;; + + let rec orphan_murder bag acc i = + match Terms.M.find i bag with + | (_,_,_,Terms.Exact _),discarded -> (discarded,acc) + | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),true -> (true,acc) + | (_,_,_,Terms.Step (_,i1,i2,_,_,_)),false -> + if (List.mem i acc) then (false,acc) + else match orphan_murder bag acc i1 with + | (true,acc) -> (true,acc) + | (false,acc) -> + let (res,acc) = orphan_murder bag acc i2 in + if res then res,acc else res,i::acc + ;; + + let orphan_murder bag actives cl = + let (id,_,_,_) = cl in + let actives = List.map (fun (i,_,_,_) -> i) actives in + let (res,_) = orphan_murder bag actives id in + if res then debug "Orphan murdered"; res + ;; + + (* demodulate and check for subsumption *) + let simplify table maxvar bag clause = + if is_identity_clause ~unify:false clause then bag,None + (* else if orphan_murder bag actives clause then bag,None *) + else let bag, clause = demodulate bag clause table in + if is_identity_clause ~unify:false clause then bag,None else - None + match is_subsumed ~unify:false bag maxvar clause table with + | None -> bag, Some clause + | Some _ -> bag, None ;; - let fold_build_new_clause bag maxvar id filter res = - let maxvar, bag, new_clauses = - List.fold_left - (fun (maxvar, bag, acc) (t,subst,vl,id2,pos,dir) -> - match build_new_clause bag maxvar filter t subst vl id id2 pos dir - with Some (bag, maxvar, uc) -> maxvar, bag, uc::acc - | None -> maxvar, bag, acc) - (maxvar, bag, []) res + let simplify table maxvar bag clause = + match simplify table maxvar bag clause with + | bag, None -> let (id,_,_,_) = clause in + Terms.M.add id (clause,true) bag, None + | bag, Some clause -> bag, Some clause + (*let (id,_,_,_) = clause in + if orphan_murder bag clause then + Terms.M.add id (clause,true) bag, Some clause + else bag, Some clause*) + ;; + + let one_pass_simplification new_clause (alist,atable) bag maxvar = + match simplify atable maxvar bag new_clause with + | bag,None -> bag,None (* new_clause has been discarded *) + | bag,(Some clause) -> + let ctable = IDX.index_unit_clause IDX.DT.empty clause in + let bag, alist, atable = + List.fold_left + (fun (bag, alist, atable) c -> + match simplify ctable maxvar bag c with + |bag,None -> (bag,alist,atable) + (* an active clause as been discarded *) + |bag,Some c1 -> + bag, c :: alist, IDX.index_unit_clause atable c) + (bag,[],IDX.DT.empty) alist + in + bag, Some (clause, (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 + | bag,None -> bag,(Some cl, None) (* new_clause has been discarded *) + | bag,Some 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) c -> + match simplify ctable maxvar bag c with + |bag,None -> (bag, newa, alist, atable) + (* an active clause as been discarded *) + |bag,Some 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 + bag, (Some cl, Some (clause, (alist,atable), newa)) + else + (* if new_clause is not cl, we simplify cl with clause *) + match simplify ctable maxvar bag cl with + | bag,None -> + (* cl has been discarded *) + bag,(None, Some (clause, (alist,atable), newa)) + | bag,Some cl1 -> + bag,(Some cl1, Some (clause, (alist,atable), newa)) + ;; + + 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 + | bag,(Some _, None) -> bag,None + | bag,(Some _, Some (clause, (alist,atable), newa)) -> + keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable) + bag (newa@newc) + else + match newc with + | [] -> bag, Some (cl, (alist,atable)) + | hd::tl -> + match simplification_step ~new_cl cl + (alist,atable) bag maxvar hd with + | _,(None,None) -> assert false + | bag,(Some _,None) -> + keep_simplified_aux ~new_cl cl (alist,atable) bag tl + | bag,(None, Some _) -> bag,None + | bag,(Some cl1, Some (clause, (alist,atable), newa)) -> + 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 - bag, maxvar, new_clauses + keep_simplified_aux ~new_cl:true cl (alist,atable) bag [] + ;; + + let are_alpha_eq cl1 cl2 = + let get_term (_,lit,_,_) = + match lit with + | Terms.Predicate _ -> assert false + | Terms.Equation (l,r,ty,_) -> + Terms.Node [Terms.Leaf B.eqP; ty; l ; r] + in + try ignore(Unif.alpha_eq (get_term cl1) (get_term cl2)) ; true + with FoUnif.UnificationFailure _ -> false +;; + + (* this is like simplify but raises Success *) + let simplify_goal ~no_demod maxvar table bag g_actives clause = + let bag, clause = + if no_demod then bag, clause else demodulate bag clause table + in + if List.exists (are_alpha_eq clause) g_actives then None else + if (is_identity_clause ~unify:true clause) + then raise (Success (bag, maxvar, clause)) + else + let (id,lit,vl,_) = clause in + let l,r,ty = + match lit with + | Terms.Equation(l,r,ty,_) -> l,r,ty + | _ -> assert false + in + match deep_eq ~unify:true l r ty [] (fun x -> x) (fun x -> x) + table (Some(bag,maxvar,clause,Subst.id_subst)) with + | None -> Some (bag,clause) + | Some (bag,maxvar,cl,subst) -> + prerr_endline "Goal subsumed"; + raise (Success (bag,maxvar,cl)) +(* + else match is_subsumed ~unify:true bag maxvar clause table with + | None -> Some (bag, clause) + | Some ((bag,maxvar),c) -> + prerr_endline "Goal subsumed"; + raise (Success (bag,maxvar,c)) +*) + ;; + + (* =================== inference ===================== *) + + (* this is OK for both the sup_left and sup_right inference steps *) + let superposition table varlist subterm pos context = + let cands = IDX.DT.retrieve_unifiables table subterm in + HExtlib.filter_map + (fun (dir, (id,lit,vl,_ (*as uc*))) -> + match lit with + | Terms.Predicate _ -> assert false + | Terms.Equation (l,r,_,o) -> + let side, newside = if dir=Terms.Left2Right then l,r else r,l in + try + let subst, varlist = + Unif.unification (varlist@vl) [] subterm side + in + 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 + (* XXX: check Riazanov p. 33 (iii) *) + if o <> Terms.Lt && o <> Terms.Eq then + Some (context newside, subst, varlist, id, pos, dir) + else + ((*prerr_endline ("Filtering: " ^ + Pp.pp_foterm side ^ " =(< || =)" ^ + Pp.pp_foterm newside ^ " coming from " ^ + Pp.pp_unit_clause uc );*)None) + else + Some (context newside, subst, varlist, id, pos, dir) + with FoUnif.UnificationFailure _ -> None) + (IDX.ClauseSet.elements cands) ;; - let superposition_right_with_table bag maxvar (id,selected,vl,_) table = + (* Superposes selected equation with equalities in table *) + let superposition_with_table bag maxvar (id,selected,vl,_) table = match selected with | Terms.Predicate _ -> assert false | Terms.Equation (l,r,ty,Terms.Lt) -> - fold_build_new_clause bag maxvar id (fun _ -> true) + fold_build_new_clause bag maxvar id Terms.Superposition + (fun _ -> true) (all_positions [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) - r (superposition_right table vl)) + r (superposition table vl)) | Terms.Equation (l,r,ty,Terms.Gt) -> - fold_build_new_clause bag maxvar id (fun _ -> true) + fold_build_new_clause bag maxvar id Terms.Superposition + (fun _ -> true) (all_positions [2] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) - l (superposition_right table vl)) + l (superposition table vl)) | Terms.Equation (l,r,ty,Terms.Incomparable) -> - fold_build_new_clause bag maxvar id + fold_build_new_clause bag maxvar id Terms.Superposition (function (* Riazanov: p.33 condition (iv) *) | Terms.Node [Terms.Leaf eq; ty; l; r ] when B.eq B.eqP eq -> Order.compare_terms l r <> Terms.Eq | _ -> assert false) ((all_positions [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) - r (superposition_right table vl)) @ + r (superposition table vl)) @ (all_positions [2] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) - l (superposition_right table vl))) + l (superposition table vl))) | _ -> assert false ;; - - end + (* 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 = + HExtlib.filter_map_acc (simplify ctable) bag alist + in + bag, (alist, List.fold_left IDX.index_unit_clause IDX.DT.empty alist) + 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 -> + let bag, maxvar, newc = + superposition_with_table bag maxvar active ctable + in + 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 + debug (Printf.sprintf "Demodulating %d clauses" + (List.length new_clauses)); + let bag, new_clauses = + HExtlib.filter_map_monad (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 + debug "Superposed goal with active clauses"; + (* We simplify the new goals with active clauses *) + let bag, new_goals = + List.fold_left + (fun (bag, acc) g -> + match simplify_goal ~no_demod:false maxvar atable bag [] g with + | None -> assert false + | Some (bag,g) -> bag,g::acc) + (bag, []) new_goals + in + debug "Simplified new goals with active clauses"; + bag, maxvar, List.rev new_goals + ;; + end