X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fcomponents%2Fng_paramodulation%2Fsuperposition.ml;fp=matitaB%2Fcomponents%2Fng_paramodulation%2Fsuperposition.ml;h=42cf063b64f08b3e352693d7a30bebff78025e95;hb=cacbe3c6493ddce76c4c13379ade271d8dd172e8;hp=0000000000000000000000000000000000000000;hpb=f04a064bb34aabaf91dc0c48e3b08b37ecd7b0a2;p=helm.git diff --git a/matitaB/components/ng_paramodulation/superposition.ml b/matitaB/components/ng_paramodulation/superposition.ml new file mode 100644 index 000000000..42cf063b6 --- /dev/null +++ b/matitaB/components/ng_paramodulation/superposition.ml @@ -0,0 +1,836 @@ +(* + ||M|| This file is part of HELM, an Hypertextual, Electronic + ||A|| Library of Mathematics, developed at the Computer Science + ||T|| Department, University of Bologna, Italy. + ||I|| + ||T|| HELM is free software; you can redistribute it and/or + ||A|| modify it under the terms of the GNU General Public License + \ / version 2 or (at your option) any later version. + \ / This software is distributed as is, NO WARRANTY. + V_______________________________________________________________ *) + +(* $Id: index.mli 9822 2009-06-03 15:37:06Z tassi $ *) + +module Superposition (B : Orderings.Blob) = + struct + module IDX = Index.Index(B) + module Unif = FoUnif.Founif(B) + module Subst = FoSubst + module Order = B + module Utils = FoUtils.Utils(B) + module Pp = Pp.Pp(B) + + exception Success of + B.t Terms.bag + * int + * B.t Terms.unit_clause + * B.t Terms.substitution + + let print s = prerr_endline (Lazy.force s);; + let debug _ = ();; + let enable = true;; + + 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 inject_pos pos ctx = function + | None -> None + | Some (a,b,c,d) -> Some(ctx a,b,c,d,pos) + in + let rec aux pos ctx = function + | Terms.Leaf _ as t -> inject_pos pos ctx (f t) + | Terms.Var _ -> None + | Terms.Node l as t-> + match f t with + | Some _ as x -> inject_pos pos ctx 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 + | Terms.Var _ -> [] + | Terms.Node l as t-> + let acc, _, _ = + List.fold_left + (fun (acc,pre,post) t -> (* Invariant: pre @ [t] @ post = l *) + let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in + let acc = aux (List.length pre :: pos) newctx t @ acc in + if post = [] then acc, l, [] + else acc, pre @ [t], List.tl post) + (f t pos ctx, [], List.tl l) l + in + acc + in + aux pos ctx t + ;; + + let parallel_positions bag pos ctx id t f = + let rec aux bag pos ctx id = function + | Terms.Leaf _ as t -> f bag t pos ctx id + | Terms.Var _ as t -> bag,t,id + | Terms.Node (hd::l) as t-> + let bag,t,id1 = f bag t pos ctx id in + if id = id1 then + let bag, l, _, id = + List.fold_left + (fun (bag,pre,post,id) t -> + let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in + let newpos = (List.length pre)::pos in + let bag,newt,id = aux bag newpos newctx id t in + if post = [] then bag, pre@[newt], [], id + else bag, pre @ [newt], List.tl post, id) + (bag, [hd], List.tl l, id) l + in + bag, Terms.Node l, id + else bag,t,id1 + (* else aux bag pos ctx id1 t *) + | _ -> assert false + in + aux bag pos ctx id t + ;; + + let visit bag pos ctx id t f = + let rec aux bag pos ctx id subst = function + | Terms.Leaf _ as t -> + let bag,subst,t,id = f bag t pos ctx id + in assert (subst=[]); bag,t,id + | Terms.Var i as t -> + let t= Subst.apply_subst subst t in + bag,t,id + | Terms.Node (hd::l) -> + let bag, l, _, id = + List.fold_left + (fun (bag,pre,post,id) t -> + let newctx = fun x -> ctx (Terms.Node (pre@[x]@post)) in + let newpos = (List.length pre)::pos in + let bag,newt,id = aux bag newpos newctx id subst t in + if post = [] then bag, pre@[newt], [], id + else bag, pre @ [newt], List.tl post, id) + (bag, [hd], List.map (Subst.apply_subst subst) (List.tl l), id) l + in + let bag,subst,t,id1 = f bag (Terms.Node l) pos ctx id + in + if id1 = id then (assert (subst=[]); bag,t,id) + else aux bag pos ctx id1 subst t + | _ -> assert false + in + aux bag pos ctx id [] t + ;; + + let build_clause bag filter rule t subst 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 subst 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 = + Terms.add_to_bag (0, literal, Terms.vars_of_term t, proof) bag + in + Some (bag, uc) + else + ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None) + ;; + let prof_build_clause = HExtlib.profile ~enable "build_clause";; + let build_clause bag filter rule t subst id id2 pos x = + prof_build_clause.HExtlib.profile (build_clause bag filter rule t subst id id2 pos) x + ;; + + + (* ============ simplification ================= *) + let prof_demod_u = HExtlib.profile ~enable "demod.unify";; + let prof_demod_r = HExtlib.profile ~enable "demod.retrieve_generalizations";; + let prof_demod_o = HExtlib.profile ~enable "demod.compare_terms";; + let prof_demod_s = HExtlib.profile ~enable "demod.apply_subst";; + + let demod table varlist subterm = + let cands = + prof_demod_r.HExtlib.profile + (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) -> + let side, newside = if dir=Terms.Left2Right then l,r else r,l in + try + let subst = + prof_demod_u.HExtlib.profile + (Unif.unification (* (varlist@vl) *) varlist subterm) side + in + let side = + prof_demod_s.HExtlib.profile + (Subst.apply_subst subst) side + in + let newside = + prof_demod_s.HExtlib.profile + (Subst.apply_subst subst) newside + in + if o = Terms.Incomparable || o = Terms.Invertible then + let o = + prof_demod_o.HExtlib.profile + (Order.compare_terms newside) side in + (* Riazanov, pp. 45 (ii) *) + if o = Terms.Lt then + Some (newside, subst, id, dir) + else + ((*prerr_endline ("Filtering: " ^ + Pp.pp_foterm side ^ " =(< || =)" ^ + Pp.pp_foterm newside ^ " coming from " ^ + Pp.pp_unit_clause uc );*)None) + else + Some (newside, subst, id, dir) + with FoUnif.UnificationFailure _ -> None) + (IDX.ClauseSet.elements cands) + ;; + let prof_demod = HExtlib.profile ~enable "demod";; + let demod table varlist x = + prof_demod.HExtlib.profile (demod table varlist) x + ;; + + let mydemod table varlist subterm = + let cands = + prof_demod_r.HExtlib.profile + (IDX.DT.retrieve_generalizations table) subterm + in + list_first + (fun (dir, ((id,lit,vl,_) as c)) -> + debug (lazy("candidate: " + ^ Pp.pp_unit_clause c)); + 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 = + prof_demod_u.HExtlib.profile + (Unif.unification (* (varlist@vl) *) varlist subterm) side + in + let iside = + prof_demod_s.HExtlib.profile + (Subst.apply_subst subst) side + in + let inewside = + prof_demod_s.HExtlib.profile + (Subst.apply_subst subst) newside + in + if o = Terms.Incomparable || o = Terms.Invertible then + let o = + prof_demod_o.HExtlib.profile + (Order.compare_terms inewside) iside in + (* Riazanov, pp. 45 (ii) *) + if o = Terms.Lt then + Some (newside, subst, id, dir) + else + ((*prerr_endline ("Filtering: " ^ + Pp.pp_foterm side ^ " =(< || =)" ^ + Pp.pp_foterm newside ^ " coming from " ^ + Pp.pp_unit_clause uc );*) + debug (lazy "not applied");None) + else + Some (newside, subst, id, dir) + with FoUnif.UnificationFailure _ -> + debug (lazy "not applied"); None) + (IDX.ClauseSet.elements cands) + ;; + + let ctx_demod table vl bag t pos ctx id = + match mydemod table vl t with + | None -> (bag,[],t,id) + | Some (newside, subst, id2, dir) -> + let inewside = Subst.apply_subst subst newside in + match build_clause bag (fun _ -> true) + Terms.Demodulation (ctx inewside) subst id id2 pos dir + with + | None -> assert false + | Some (bag,(id,_,_,_)) -> + (bag,subst,newside,id) + ;; + + let rec demodulate bag (id, literal, vl, pr) table = + debug (lazy ("demodulate " ^ (string_of_int id))); + match literal with + | Terms.Predicate t -> (* assert false *) + let bag,_,id1 = + visit bag [] (fun x -> x) id t (ctx_demod table vl) + in + let cl,_,_ = Terms.get_from_bag id1 bag in + bag,cl + | Terms.Equation (l,r,ty,_) -> + let bag,l,id1 = + visit bag [2] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) id l + (ctx_demod table vl) + in + let bag,_,id2 = + visit bag [3] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) id1 r + (ctx_demod table vl) + in + let cl,_,_ = Terms.get_from_bag id2 bag in + bag,cl + ;; + + let parallel_demod table vl bag t pos ctx id = + match demod table vl t with + | None -> (bag,t,id) + | Some (newside, subst, id2, dir) -> + match build_clause bag (fun _ -> true) + Terms.Demodulation (ctx newside) subst id id2 pos dir + with + | None -> assert false + | Some (bag,(id,_,_,_)) -> + (bag,newside,id) + ;; + + 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 + ;; + + let prof_demodulate = HExtlib.profile ~enable "demodulate";; + let demodulate bag clause x = + prof_demodulate.HExtlib.profile (demodulate bag clause) x + ;; + + (* move away *) + let is_identity_clause = function + | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true + | _, Terms.Equation (_,_,_,_), _, _ -> false + | _, Terms.Predicate _, _, _ -> assert false + ;; + + let is_identity_goal = function + | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> Some [] + | _, Terms.Equation (l,r,_,_), vl, proof -> + (try Some (Unif.unification (* vl *) [] l r) + with FoUnif.UnificationFailure _ -> None) + | _, Terms.Predicate _, _, _ -> assert false + ;; + + let build_new_clause_reloc bag maxvar filter rule t subst id id2 pos dir = + let maxvar, _vl, subst = Utils.relocate maxvar (Terms.vars_of_term + (Subst.apply_subst subst t)) subst in + match build_clause bag filter rule t subst id id2 pos dir with + | Some (bag, c) -> Some ((bag, maxvar), c), subst + | None -> None,subst + ;; + + let build_new_clause bag maxvar filter rule t subst id id2 pos dir = + fst (build_new_clause_reloc bag maxvar filter rule t + subst id id2 pos dir) + ;; + + let prof_build_new_clause = HExtlib.profile ~enable "build_new_clause";; + let build_new_clause bag maxvar filter rule t subst id id2 pos x = + prof_build_new_clause.HExtlib.profile (build_new_clause bag maxvar filter + rule t subst id id2 pos) x + ;; + + let fold_build_new_clause bag maxvar id rule filter res = + let (bag, maxvar), res = + HExtlib.filter_map_acc + (fun (bag, maxvar) (t,subst,id2,pos,dir) -> + build_new_clause bag maxvar filter rule t subst 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 = 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 + ;; + let prof_is_subsumed = HExtlib.profile ~enable "is_subsumed";; + let is_subsumed ~unify bag maxvar c x = + prof_is_subsumed.HExtlib.profile (is_subsumed ~unify bag maxvar c) x + ;; + (* 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) -> + (* prerr_endline ("input subst = "^Pp.pp_substitution subst); *) + let l = Subst.apply_subst subst l in + let r = Subst.apply_subst subst r in + try + let subst1 = 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,vl,p),Subst.concat subst1 subst) + with FoUnif.UnificationFailure _ -> + match rewrite_eq ~unify l r ty vl table with + | Some (id2, dir, subst1) -> + (* prerr_endline ("subst1 = "^Pp.pp_substitution subst1); + prerr_endline ("old subst = "^Pp.pp_substitution subst);*) + 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_reloc bag maxvar (fun _ -> true) + Terms.Superposition id_t + subst1 id id2 (pos@[2]) dir + with + | Some ((bag, maxvar), c), r -> + (* prerr_endline ("r = "^Pp.pp_substitution r); *) + let newsubst = Subst.flat + (Subst.concat r subst) in + 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 prof_deep_eq = HExtlib.profile ~enable "deep_eq";; + let deep_eq ~unify l r ty pos contextl contextr table x = + prof_deep_eq.HExtlib.profile (deep_eq ~unify l r ty pos contextl contextr table) x + ;; + + let rec orphan_murder bag acc i = + match Terms.get_from_bag 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 (lazy "Orphan murdered"); res + ;; + let prof_orphan_murder = HExtlib.profile ~enable "orphan_murder";; + let orphan_murder bag actives x = + prof_orphan_murder.HExtlib.profile (orphan_murder bag actives) x + ;; + + (* demodulate and check for subsumption *) + let simplify table maxvar bag clause = + debug (lazy "simplify..."); + if is_identity_clause 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 clause then bag,None + else + match is_subsumed ~unify:false bag maxvar clause table with + | None -> bag, Some clause + | Some _ -> bag, None + ;; + + let simplify table maxvar bag clause = + match simplify table maxvar bag clause with + | bag, None -> + let (id,_,_,_) = clause in + let (_,_,iter) = Terms.get_from_bag id bag in + Terms.replace_in_bag (clause,true,iter) 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 prof_simplify = HExtlib.profile ~enable "simplify";; + let simplify table maxvar bag x = + prof_simplify.HExtlib.profile (simplify table maxvar bag ) x + ;; + + 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 prof_one_pass_simplification = HExtlib.profile ~enable "one_pass_simplification";; + let one_pass_simplification new_clause t bag x = + prof_one_pass_simplification.HExtlib.profile (one_pass_simplification new_clause t bag ) x + ;; + + 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 prof_simplification_step = HExtlib.profile ~enable "simplification_step";; + let simplification_step ~new_cl cl (alist,atable) bag maxvar x = + prof_simplification_step.HExtlib.profile (simplification_step ~new_cl cl (alist,atable) bag maxvar) x + ;; + + 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 + keep_simplified_aux ~new_cl:true cl (alist,atable) bag [] + ;; + let prof_keep_simplified = HExtlib.profile ~enable "keep_simplified";; + let keep_simplified cl t bag x = + prof_keep_simplified.HExtlib.profile (keep_simplified cl t bag) x + ;; + + (* 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 + let _ = debug (lazy ("demodulated goal : " + ^ Pp.pp_unit_clause clause)) + in + if List.exists (are_alpha_eq clause) g_actives then None + else match (is_identity_goal clause) with + | Some subst -> raise (Success (bag,maxvar,clause,subst)) + | None -> + let (id,lit,vl,_) = clause in + (* this optimization makes sense only if we demodulated, since in + that case the clause should have been turned into an identity *) + if (vl = [] && not(no_demod)) + then Some (bag,clause) + else + 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) -> + debug (lazy "Goal subsumed"); + raise (Success (bag,maxvar,cl,subst)) +(* + 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)) +*) + ;; + + let prof_simplify_goal = HExtlib.profile ~enable "simplify_goal";; + let simplify_goal ~no_demod maxvar table bag g_actives x = + prof_simplify_goal.HExtlib.profile ( simplify_goal ~no_demod maxvar table bag g_actives) x + ;; + + (* =================== 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 = + Unif.unification (* (varlist@vl)*) [] subterm side + in + if o = Terms.Incomparable || o = Terms.Invertible 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, id, pos, dir) + else + ((*prerr_endline ("Filtering: " ^ + Pp.pp_foterm side ^ " =(< || =)" ^ + Pp.pp_foterm newside);*)None) + else + Some (context newside, subst, id, pos, dir) + with FoUnif.UnificationFailure _ -> None) + (IDX.ClauseSet.elements cands) + ;; + + (* 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 Terms.Superposition + (fun _ -> true) + (all_positions [3] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) + r (superposition table vl)) + | Terms.Equation (l,r,ty,Terms.Invertible) + | Terms.Equation (l,r,ty,Terms.Gt) -> + 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 table vl)) + | Terms.Equation (l,r,ty,Terms.Incomparable) -> + let filtering avoid subst = (* Riazanov: p.33 condition (iv) *) + let l = Subst.apply_subst subst l in + let r = Subst.apply_subst subst r in + let o = Order.compare_terms l r in + o <> avoid && o <> Terms.Eq + in + let bag, maxvar,r_terms = + fold_build_new_clause bag maxvar id Terms.Superposition + (filtering Terms.Gt) + (all_positions [3] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) + r (superposition table vl)) + in + let bag, maxvar, l_terms = + fold_build_new_clause bag maxvar id Terms.Superposition + (filtering Terms.Lt) + (all_positions [2] + (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) + l (superposition table vl)) + in + bag, maxvar, r_terms @ l_terms + | _ -> assert false + ;; + + (* 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 (lazy "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 + (lazy + ("New clauses :" ^ (String.concat ";\n" + (List.map Pp.pp_unit_clause new_clauses)))); + debug (lazy "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 (lazy "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 = Terms.add_to_bag fresh_current bag in + (* We superpose current with active clauses *) + let bag, maxvar, additional_new_clauses = + superposition_with_table bag maxvar fresh_current atable + in + debug (lazy "Another superposition"); + let new_clauses = new_clauses @ additional_new_clauses in + (* debug (lazy (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 (lazy "Demodulated new clauses"); + bag, maxvar, (alist, atable), new_clauses + ;; + + let prof_ir = HExtlib.profile ~enable "infer_right";; + let infer_right bag maxvar current t = + prof_ir.HExtlib.profile (infer_right bag maxvar current) t + ;; + + let infer_left bag maxvar goal (_alist, atable) = + (* We superpose the goal with active clauses *) + if (match goal with (_,_,[],_) -> true | _ -> false) then bag, maxvar, [] + else + let bag, maxvar, new_goals = + superposition_with_table bag maxvar goal atable + in + debug(lazy "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 (lazy "Simplified new goals with active clauses"); + bag, maxvar, List.rev new_goals + ;; + + let prof_il = HExtlib.profile ~enable "infer_left";; + let infer_left bag maxvar goal t = + prof_il.HExtlib.profile (infer_left bag maxvar goal) t + ;; + + end