(* ||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 (* CSC: to avoid equations of the form ? -> T that can always be applied and that lead to type-checking errors *) (match l,r,o with (* (Terms.Var _ | Terms.Node (Terms.Var _ ::_)),_,Terms.Gt | _,(Terms.Var _ | Terms.Node (Terms.Var _ ::_)),Terms.Lt -> assert false *) | (Terms.Var _ | Terms.Node (Terms.Var _ ::_)),_,(Terms.Incomparable | Terms.Invertible) -> Terms.Equation (l, r, ty, Terms.Lt) | _, (Terms.Var _ | Terms.Node (Terms.Var _ ::_)),(Terms.Incomparable | Terms.Invertible) -> Terms.Equation (l, r, ty, Terms.Gt) | _ -> 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 ;; (* rewrite_eq check if in table there an equation matching l=r; used in subsumption and deep_eq. In deep_eq, we need to match several times times w.r.t. the same table, hence we should refresh the retrieved clauses, to avoid clashes of variables *) let rewrite_eq ~refresh ~unify maxvar 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 c,maxvar = if refresh then let maxvar,_,r = Utils.relocate maxvar vl1 [] in Subst.apply_subst r c,maxvar else c,maxvar in let subst = Unif.unification (* (vl@vl1) *) locked_vars c t in Some (id2, dir, subst, maxvar) 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 ~refresh:false ~unify maxvar l r ty vl table with | None -> None | Some (id2, dir, subst, maxvar) -> 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 = (* let _ = prerr_endline ("pos = " ^ String.concat "," (List.map string_of_int pos)) in *) match acc with | None -> None | Some(bag,maxvar,(id,lit,vl,p),subst) -> (* prerr_endline ("input subst = "^Pp.pp_substitution subst); *) (* prerr_endline ("l prima =" ^ Pp.pp_foterm l); *) (* prerr_endline ("r prima =" ^ Pp.pp_foterm r); *) let l = Subst.apply_subst subst l in let r = Subst.apply_subst subst r in (* prerr_endline ("l dopo =" ^ Pp.pp_foterm l); *) (* prerr_endline ("r dopo =" ^ Pp.pp_foterm r); *) try let subst1 = Unif.unification (* vl *) [] l r in let lit = match lit with Terms.Predicate _ -> assert false | Terms.Equation (l,r,ty,o) -> let l = Subst.apply_subst subst1 l in let r = Subst.apply_subst subst1 r in Terms.Equation (l, r, ty, o) in Some(bag,maxvar,(id,lit,vl,p),Subst.concat subst1 subst) with FoUnif.UnificationFailure _ -> match rewrite_eq ~refresh:true ~unify maxvar l r ty vl table with | Some (id2, dir, subst1, maxvar) -> (* 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 ("creo "^ Pp.pp_unit_clause c); *) (* 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"); debug (lazy ("subst in superpos: " ^ Pp.pp_substitution subst)); raise (Success (bag,maxvar,cl,subst)) (* match is_subsumed ~unify:true bag maxvar clause table with | None -> Some (bag, clause) | Some ((bag,maxvar),c) -> debug (lazy "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