struct
module IDX = Index.Index(B)
module Unif = FoUnif.Founif(B)
- module Subst = FoSubst.Subst(B)
+ module Subst = FoSubst
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 debug s = prerr_endline s;;
+ let debug _ = ();;
let rec list_first f = function
| [] -> None
let rec aux pos ctx = function
| Terms.Leaf _ as t -> f t pos ctx
| Terms.Var _ -> None
- | Terms.Node l as t->
+ | Terms.Node l as t->
match f t pos ctx with
| Some _ as x -> x
| None ->
in
aux pos ctx t
;;
+
+ 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
| t -> Terms.Predicate t
in
let bag, uc =
- Utils.add_to_bag bag (0, literal, vl, proof)
+ Terms.add_to_bag (0, literal, vars_of_term t, proof) bag
in
Some (bag, uc)
else
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
+ if o = Terms.Lt then
Some (context newside, subst, varlist, id, pos, dir)
else
((*prerr_endline ("Filtering: " ^
(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 demodulate_once ~jump_to_right bag (id, literal, vl, pr) table =
+ match literal with
+ | Terms.Predicate t -> assert false
+ | Terms.Equation (l,r,ty,_) ->
+ let left_position = if jump_to_right then None else
+ first_position [2]
+ (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; x; r ]) l
+ (demod table vl)
+ in
+ match left_position with
+ | Some (newt, subst, varlist, id2, pos, dir) ->
+ begin
+ match build_clause bag (fun _ -> true) Terms.Demodulation
+ newt subst varlist id id2 pos dir
+ with
+ | None -> assert false
+ | Some x -> Some (x,false)
+ end
+ | None ->
+ match first_position
+ [3] (fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ]) r
+ (demod table vl)
+ with
+ | None -> None
+ | Some (newt, subst, varlist, id2, pos, dir) ->
+ match build_clause bag (fun _ -> true)
+ Terms.Demodulation newt subst varlist id id2 pos dir
+ with
+ | None -> assert false
+ | Some x -> Some (x,true)
;;
- let rec demodulate bag clause table =
- match demodulate_once bag clause table with
+ let rec demodulate ~jump_to_right bag clause table =
+ match demodulate_once ~jump_to_right bag clause table with
| None -> bag, clause
- | Some (bag, clause) -> demodulate bag clause table
+ | Some ((bag, clause),r) -> demodulate ~jump_to_right:r
+ bag clause table
+ ;;
+
+ let demodulate bag clause table = demodulate ~jump_to_right:false
+ bag clause table
;;
(* move away *)
- let is_identity_clause = function
+ let is_identity_clause ~unify = function
| _, Terms.Equation (_,_,_,Terms.Eq), _, _ -> true
- | _, Terms.Predicate _, _, _ -> assert false
- | _ -> false
+ | _, Terms.Equation (l,r,_,_), vl, proof when unify ->
+ (try ignore(Unif.unification vl [] l r); true
+ with FoUnif.UnificationFailure _ -> false)
+ | _, Terms.Equation (_,_,_,_), _, _ -> false
+ | _, Terms.Predicate _, _, _ -> assert false
;;
- let is_subsumed ~unify (id, lit, vl, _) table =
+ 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
+ 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 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, 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,vl1 = 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,_) ->
- 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)
+ 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
+ ;;
+ (* 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,vl1 = 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,vl1,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 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 "Orphan murdered"; res
;;
(* 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
+ let simplify table maxvar bag clause =
+ if is_identity_clause ~unify:false 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 ~unify:false clause then bag,None
else
- if is_subsumed ~unify:false clause table then None
- else Some (bag, clause)
+ 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 ->
+ Terms.replace_in_bag (clause,true) 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 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 rec keep_simplified (alist,atable) bag newc =
- match newc with
- | [] -> bag, (alist,atable)
- | hd::tl ->
- (match simplify atable bag hd with
- | None -> keep_simplified (alist,atable) bag tl
- | Some (bag, 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 ->
- let bag, c1 = demodulate bag c ctable in
- if (c1 == c) then
- bag, newa, c :: alist, IDX.index_unit_clause atable c
- else
- bag, c :: newa, alist, atable)
- (bag,[],[],IDX.DT.empty) alist
- in
- keep_simplified (alist, atable) bag newa)
+ 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 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 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
+;;
+
(* 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)
+ 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
+ if (is_identity_clause ~unify:true clause)
then raise (Success (bag, maxvar, clause))
- else bag, clause
+ else
+ let (id,lit,vl,_) = clause in
+ if vl = [] 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) ->
+ prerr_endline "Goal subsumed";
+ raise (Success (bag,maxvar,cl))
+(*
+ else 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))
+*)
;;
(* =================== inference ===================== *)
(IDX.ClauseSet.elements cands)
;;
- 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
- 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 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, res
- ;;
-
(* Superposes selected equation with equalities in table *)
let superposition_with_table bag maxvar (id,selected,vl,_) table =
match selected with
(fun _ -> true)
(all_positions [3]
(fun x -> Terms.Node [ Terms.Leaf B.eqP; ty; l; x ])
- r (superposition table vl))
+ r (superposition table vl))
| Terms.Equation (l,r,ty,Terms.Gt) ->
fold_build_new_clause bag maxvar id Terms.Superposition
(fun _ -> true)
(* 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 *)
+ (* 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, 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
+ in*)
debug "Simplified active clauses with fact";
(* We superpose active clauses with current *)
let bag, maxvar, new_clauses =
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
+ 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 "Another superposition";
let new_clauses = new_clauses @ additional_new_clauses in
+ debug (Printf.sprintf "Demodulating %d clauses"
+ (List.length new_clauses));
let bag, new_clauses =
- HExtlib.filter_map_acc (simplify atable) bag new_clauses
+ HExtlib.filter_map_monad (simplify atable maxvar) bag new_clauses
in
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 =
+ if (match goal with (_,_,[],_) -> true | _ -> false) then bag, maxvar, []
+ else
+ let bag, maxvar, new_goals =
superposition_with_table bag maxvar goal atable
in
- (* We demodulate the goal with active clauses *)
+ debug "Superposed goal with active clauses";
+ (* We simplify the new goals 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)
+ 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 "Simplified new goals with active clauses";
bag, maxvar, List.rev new_goals
;;
end
-
-
-
projects / helm.git / blobdiff