+ 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
+ | 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.Equation (_,_,_,_), _, _ -> None
+ | _, Terms.Predicate _, _, _ -> assert false
+ ;;
+
+ let build_new_clause 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)
+ | None -> None
+ ;;
+ 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) ->
+ 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) ->
+ 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 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
+ 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)