module Utils = FoUtils.Utils(B)
module Pp = Pp.Pp(B)
+ 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
in
aux pos ctx 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, vl, 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) ->
+ let side, newside = if dir=Terms.Left2Right then l,r else r,l in
+ try
+ let subst, varlist =
+ 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
+ (* Riazanov, pp. 45 (ii) *)
+ if o = Terms.Lt 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)
+ ;;
+
+ (* 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 t =
+ match literal with
+ | Terms.Predicate t -> t
+ | Terms.Equation (l,r,ty,_) -> Terms.Node [ Terms.Leaf B.eqP; ty; l; r ]
+ in
+ match first_position [] (fun x -> x) t (demod table vl) with
+ | None -> None
+ | Some (newt, subst, varlist, id2, pos, dir) ->
+ build_clause bag (fun _ -> true) Terms.Demodulation
+ newt subst varlist id id2 pos dir
+ ;;
+
+ let rec demodulate bag clause table =
+ match demodulate_once bag clause table with
+ | None -> bag, clause
+ | Some (bag, clause) -> demodulate bag clause table
+ ;;
+
+ (* move away *)
+ let is_identity_clause = function
+ | _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
+ | _, Terms.Predicate _, _, _ -> assert false
+ | _ -> false
+ ;;
+
+ let is_subsumed (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 f b c =
+ let dir, l, r, vl =
+ match c with
+ | (d, (_,Terms.Equation (l,r,ty,_),vl,_))-> 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
+ 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)
+ ;;
+
+ (* demodulate and check for subsumption *)
+ let forward_simplify table 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)
+ ;;
+
+ (* =================== inference ===================== *)
let superposition_right table varlist subterm pos context =
let cands = IDX.DT.retrieve_unifiables table subterm in
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 =
(IDX.ClauseSet.elements cands)
;;
- let build_new_clause bag maxvar filter t subst vl id id2 pos dir =
+ 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)
- else
- ((*prerr_endline ("Filtering: " ^ Pp.pp_foterm t);*)None)
+ 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 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 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, new_clauses
+ bag, maxvar, res
;;
let superposition_right_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.SuperpositionRight
+ (fun _ -> true)
(all_positions [3]
(fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
r (superposition_right 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.SuperpositionRight
+ (fun _ -> true)
(all_positions [2]
(fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ])
l (superposition_right table vl))
| Terms.Equation (l,r,ty,Terms.Incomparable) ->
- fold_build_new_clause bag maxvar id
+ fold_build_new_clause bag maxvar id Terms.SuperpositionRight
(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
(* the current equation is normal w.r.t. demodulation with atable
* (and is not the identity) *)
- let superposition_right bag maxvar current (alist,atable) =
+ let infer_right bag maxvar current (alist,atable) =
let ctable = IDX.index_unit_clause IDX.DT.empty current in
let bag, maxvar, new_clauses =
List.fold_left
let bag, maxvar, additional_new_clauses =
superposition_right_with_table bag maxvar fresh_current atable
in
- bag, maxvar, (alist, atable), new_clauses @ additional_new_clauses
+ let new_clauses = new_clauses @ additional_new_clauses in
+ let bag, new_clauses =
+ HExtlib.filter_map_acc (forward_simplify atable) bag new_clauses
+ in
+ bag, maxvar, (alist, atable), new_clauses
;;
-
+
end
projects / helm.git / commitdiff