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 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
aux pos ctx t
;;
- let superposition_right table varlist subterm pos context =
+ 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) ->
+ 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 newside side 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, pr) table =
+ (* debug ("Demodulating : " ^ (Pp.pp_unit_clause (id, literal, vl, pr)));*)
+ 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 ~unify (id, lit, vl, _) table =
+ match lit with
+ | Terms.Predicate _ -> assert false
+ | Terms.Equation (l,r,ty,_) ->
+ 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 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
+ let locked_vars = if unify then [] else vl in
+ List.exists
+ (fun (c, vl1) ->
+ try ignore(Unif.unification (vl@vl1) locked_vars c t); true
+ with FoUnif.UnificationFailure _ -> false)
+ (cands1 @ cands2)
+ ;;
+
+ (* demodulate and check for subsumption *)
+ let simplify table bag clause =
+ let bag, clause = demodulate bag clause table in
+ if is_identity_clause clause then None
+ else
+ if is_subsumed ~unify:false clause table then None
+ else Some (bag, clause)
+ ;;
+
+ let one_pass_simplification new_clause (alist,atable) bag =
+ match simplify atable bag new_clause with
+ | None -> None (* new_clause has been discarded *)
+ | Some (bag, clause) ->
+ let ctable = IDX.index_unit_clause IDX.DT.empty clause in
+ let bag, alist, atable =
+ List.fold_left
+ (fun (bag, alist, atable as acc) c ->
+ match simplify ctable bag c with
+ |None -> acc (* an active clause as been discarded *)
+ |Some (bag, c1) ->
+ bag, c :: alist, IDX.index_unit_clause atable c)
+ (bag,[],IDX.DT.empty) alist
+ in
+ Some (clause, bag, (alist,atable))
+ ;;
+
+ let simplification_step ~new_cl cl (alist,atable) bag 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 bag new_clause with
+ | None -> (Some cl, None) (* new_clause has been discarded *)
+ | Some (bag, 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 as acc) c ->
+ match simplify ctable bag c with
+ |None -> acc (* an active clause as been discarded *)
+ |Some (bag, 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
+ (Some cl, Some (clause, (alist,atable), newa, bag))
+ else
+ (* if new_clause is not cl, we simplify cl with clause *)
+ match simplify ctable bag cl with
+ | None ->
+ (* cl has been discarded *)
+ (None, Some (clause, (alist,atable), newa, bag))
+ | Some (bag,cl1) ->
+ (Some cl1, Some (clause, (alist,atable), newa, bag))
+ ;;
+
+ let keep_simplified cl (alist,atable) bag =
+ 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 cl with
+ | (None, _) -> assert false
+ | (Some _, None) -> None
+ | (Some _, Some (clause, (alist,atable), newa, bag)) ->
+ keep_simplified_aux ~new_cl:(cl!=clause) clause (alist,atable)
+ bag (newa@newc)
+ else
+ match newc with
+ | [] -> Some (cl, bag, (alist,atable))
+ | hd::tl ->
+ match simplification_step ~new_cl cl
+ (alist,atable) bag hd with
+ | (None,None) -> assert false
+ | (Some _,None) ->
+ keep_simplified_aux ~new_cl cl (alist,atable) bag tl
+ | (None, Some _) -> None
+ | (Some cl1, Some (clause, (alist,atable), newa, bag)) ->
+ 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 []
+ ;;
+
+ (* this is like simplify but raises Success *)
+ let simplify_goal maxvar table bag clause =
+ let bag, clause = demodulate bag clause table in
+ if (is_identity_clause clause) || (is_subsumed ~unify:true clause table)
+ then raise (Success (bag, maxvar, clause))
+ else bag, clause
+ ;;
+
+ (* =================== 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) ->
- 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 =
+ (* 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
;;
(* 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) =
+ (* 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_right_with_table bag maxvar active ctable
+ 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_right_with_table bag maxvar fresh_current atable
+ superposition_with_table bag maxvar fresh_current atable
+ in
+ debug "Another superposition";
+ let new_clauses = new_clauses @ additional_new_clauses in
+ let bag, new_clauses =
+ HExtlib.filter_map_acc (simplify atable) bag new_clauses
in
- bag, maxvar, (alist, atable), new_clauses @ additional_new_clauses
+ 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
+ (* We demodulate the goal with active clauses *)
+ let bag, new_goals =
+ List.fold_left
+ (fun (bag, acc) g ->
+ let bag, g = demodulate bag g atable in
+ bag, g :: acc)
+ (bag, []) new_goals
+ in
+ bag, maxvar, List.rev new_goals
+ ;;
+
end
projects / helm.git / blobdiff