Implemented OrderedSet for passive clauses.
Selection is now based on weight (fairness condition to be added).
let empty_bag = Terms.M.empty ;;
+ let mk_passive_clause cl =
+ (Order.compute_unit_clause_weight cl, cl)
+ ;;
+
+ let compare_passive_clauses (w1,(id1,_,_,_)) (w2,(id2,_,_,_)) =
+ if w1 = w2 then id1 - id2
+ else w1 - w2
+ ;;
+
end
int -> B.t Terms.foterm -> B.t Terms.foterm ->
B.t Terms.unit_clause * int
+ val mk_passive_clause :
+ B.t Terms.unit_clause -> B.t Terms.passive_clause
+
val eq_unit_clause : B.t Terms.unit_clause -> B.t Terms.unit_clause -> bool
val compare_unit_clause : B.t Terms.unit_clause -> B.t Terms.unit_clause -> int
val empty_bag : B.t Terms.bag
+ val compare_passive_clauses :
+ B.t Terms.passive_clause -> B.t Terms.passive_clause -> int
+
end
(w, List.sort compare l) (* from the smallest meta to the bigest *)
;;
- let compute_unit_clause_weight =
+ let compute_unit_clause_weight (_,l, _, _) =
let weight_of_polynomial w m =
let factor = 2 in
w + factor * List.fold_left (fun acc (_,occ) -> acc+occ) 0 m
in
- function
+ match l with
| Terms.Predicate t ->
let w, m = weight_of_term t in
weight_of_polynomial w m
val compare_terms :
B.t Terms.foterm -> B.t Terms.foterm -> Terms.comparison
+ val compute_unit_clause_weight :
+ B.t Terms.unit_clause -> int
+
end
-let nparamod metasenv subst context t table =
+(*let nparamod metasenv subst context t table =
prerr_endline "========================================";
let module C = struct
let metasenv = metasenv
let module FU = FoUnif.Founif(B) in
let module IDX = Index.Index(B) in
let module Sup = Superposition.Superposition(B) in
- let module Utils = FoUtils.Utils(B) in
+ let module Utils = FoUtils.Utils(B) in*)
(*
let test_unification _ = function
| Terms.Node [_; _; lhs; rhs] ->
prerr_endline "Substitution :";
prerr_endline (Pp.pp_substitution subst)
*)
+(*
+
let mk_clause maxvar t =
let ty = B.embed t in
let proof = B.embed (NCic.Rel ~-1) in
in
prerr_endline "Output clauses :";
List.iter (fun c -> prerr_endline (Pp.pp_unit_clause c)) newclauses;
- prerr_endline "Proofs: ";
- prerr_endline (Pp.pp_bag bag);
+ (* prerr_endline "Proofs: ";
+ prerr_endline (Pp.pp_bag bag); *)
prerr_endline "========================================";
;;
-
-let select = function
- | [] -> None
- | x::tl -> Some (x, tl)
+*)
+let debug s =
+ prerr_endline s
;;
let nparamod metasenv subst context t table =
let module IDX = Index.Index(B) in
let module Sup = Superposition.Superposition(B) in
let module Utils = FoUtils.Utils(B) in
-
+
+ let module OrderedPassives =
+ struct
+ type t = B.t Terms.passive_clause
+
+ let compare = Utils.compare_passive_clauses
+ end
+ in
+ let module PassiveSet = Set.Make(OrderedPassives)
+ in
+ let add_passive_clause passives cl =
+ PassiveSet.add (Utils.mk_passive_clause cl) passives
+ in
+ (* TODO : fairness condition *)
+ let select passives =
+ if PassiveSet.is_empty passives then None
+ else let cl = PassiveSet.min_elt passives in
+ Some (snd cl,PassiveSet.remove cl passives)
+ in
let rec given_clause bag maxvar actives passives g_actives g_passives =
-
+
(* keep goals demodulated w.r.t. actives and check if solved *)
(* we may move this at the end of infer_right and simplify with
* just new_clauses *)
let bag, g_actives =
List.fold_left
(fun (bag,acc) c ->
- let bag, c = Sup.backward_simplify maxvar (snd actives) bag c in
- bag, c::acc)
+ let bag, c = Sup.backward_simplify maxvar (snd actives) bag c in
+ bag, c::acc)
(bag,[]) g_actives
in
-
- (* backward step *)
- let bag, maxvar, g_actives, g_passives =
- match select g_passives with
+
+ (* backward step : superposition left, simplifications on goals *)
+ debug "Backward infer step...";
+ let bag, maxvar, g_actives, g_passives =
+ match select g_passives with
| None -> bag, maxvar, g_actives, g_passives
| Some (g_current, g_passives) ->
+ debug ("Selected goal : " ^ Pp.pp_unit_clause g_current);
let bag, g_current =
Sup.backward_simplify maxvar (snd actives) bag g_current
in
let bag, maxvar, new_goals =
Sup.infer_left bag maxvar g_current actives
in
- bag, maxvar, g_current::g_actives, g_passives @ new_goals
+ let new_goals = List.fold_left add_passive_clause
+ PassiveSet.empty new_goals
+ in
+ bag, maxvar, g_current::g_actives,
+ (PassiveSet.union new_goals g_passives)
in
+ prerr_endline
+ (Printf.sprintf "Number of active goals : %d"
+ (List.length g_actives));
+ prerr_endline
+ (Printf.sprintf "Number of passive goals : %d"
+ (PassiveSet.cardinal g_passives));
- (* forward step *)
- let bag, maxvar, actives, passives =
+ (* forward step *)
+
+ (* e = select P *
+ * e' = demod A e *
+ * A' = demod [e'] A *
+ * A'' = A' + e' *
+ * e'' = fresh e' *
+ * new = supright e'' A'' *
+ * new'= demod A'' new *
+ * P' = P + new' *)
+ debug "Forward infer step...";
+ let bag, maxvar, actives, passives, g_passives =
match select passives with
- | None -> bag, maxvar, actives, passives
+ | None -> bag, maxvar, actives, passives, g_passives
| Some (current, passives) ->
+ debug ("Selected fact : " ^ Pp.pp_unit_clause current);
match Sup.forward_simplify (snd actives) bag current with
- | None -> bag, maxvar, actives, passives
+ | None -> debug ("Discarded fact");
+ bag, maxvar, actives, passives, g_passives
| Some (bag, current) ->
+ debug ("Fact after simplification :" ^ Pp.pp_unit_clause current);
let bag, maxvar, actives, new_clauses =
Sup.infer_right bag maxvar current actives
in
- bag, maxvar, actives, passives @ new_clauses
+ let ctable = IDX.index_unit_clause IDX.DT.empty current in
+ let bag, maxvar, new_goals =
+ List.fold_left
+ (fun (bag,m,acc) g ->
+ let bag, m, ng = Sup.infer_left bag maxvar g
+ ([current],ctable) in
+ bag,m,ng@acc)
+ (bag,maxvar,[]) g_actives
+ in
+ let new_clauses = List.fold_left add_passive_clause
+ PassiveSet.empty new_clauses in
+ let new_goals = List.fold_left add_passive_clause
+ PassiveSet.empty new_goals in
+ bag, maxvar, actives,
+ PassiveSet.union new_clauses passives,
+ PassiveSet.union new_goals g_passives
in
-
+ prerr_endline
+ (Printf.sprintf "Number of actives : %d" (List.length (fst actives)));
+ prerr_endline
+ (Printf.sprintf "Number of passives : %d"
+ (PassiveSet.cardinal passives));
given_clause bag maxvar actives passives g_actives g_passives
in
- let mk_clause bag maxvar ty =
- let ty = B.embed ty in
- let proof = B.embed (NCic.Rel ~-1) in
+ let mk_clause bag maxvar (t,ty) =
+ let (proof,ty) = B.saturate t ty in
let c, maxvar = Utils.mk_unit_clause maxvar ty proof in
let bag, c = Utils.add_to_bag bag c in
bag, maxvar, c
in
let bag, maxvar, goal = mk_clause Terms.M.empty 0 t in
let g_actives = [] in
- let g_passives = [goal] in
+ let g_passives = PassiveSet.singleton (Utils.mk_passive_clause goal) in
let passives, bag, maxvar =
List.fold_left
(fun (cl, bag, maxvar) t ->
let bag, maxvar, c = mk_clause bag maxvar t in
- c::cl, bag, maxvar)
- ([], bag, maxvar) table
+ (add_passive_clause cl c), bag, maxvar)
+ (PassiveSet.empty, bag, maxvar) table
in
let actives = [], IDX.DT.empty in
try given_clause bag maxvar actives passives g_actives g_passives
- with Sup.Success _ -> prerr_endline "YES!"
+ with Sup.Success (bag, _, mp) ->
+ prerr_endline "YES!";
+ prerr_endline "Meeting point :"; prerr_endline (Pp.pp_unit_clause mp);
+ (* prerr_endline "Bag :"; prerr_endline (Pp.pp_bag bag) *)
;;
val nparamod :
NCic.metasenv -> NCic.substitution -> NCic.context ->
- NCic.term -> NCic.term list ->
+ (NCic.term * NCic.term) -> (NCic.term * NCic.term) list ->
unit
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
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
+ 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)
(* 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 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
| _ -> false
;;
- let is_subsumed (id, lit, vl, _) table =
+ let is_subsumed ~unify (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 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
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)
+ 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 bag, clause = demodulate bag clause table in
if is_identity_clause clause then None
else
- if is_subsumed clause table then None
+ if is_subsumed ~unify:false clause table then None
else Some (bag, clause)
;;
(* this is like forward_simplify but raises Success *)
let backward_simplify maxvar table bag clause =
let bag, clause = demodulate bag clause table in
- if is_identity_clause clause then raise (Success (bag, maxvar, clause))
+ if (is_identity_clause clause) || (is_subsumed ~unify:true clause table)
+ then raise (Success (bag, maxvar, clause))
else bag, clause
;;
bag, maxvar, res
;;
+ (* Superposes selected equation with equalities in table *)
let superposition_with_table bag maxvar (id,selected,vl,_) table =
match selected with
| Terms.Predicate _ -> 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 *)
let ctable = IDX.index_unit_clause IDX.DT.empty current in
let bag, (alist, atable) =
let 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 ->
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_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 (forward_simplify atable) 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 =
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 ->
module Superposition (B : Terms.Blob) :
sig
+ (* bag, maxvar, meeting point *)
exception Success of B.t Terms.bag * int * B.t Terms.unit_clause
(* The returned active set is the input one + the selected clause *)
(fun (status, l) t ->
let status, t = disambiguate status t None (ctx_of gty) in
let status, ty = typeof status (ctx_of t) t in
+ let status, t = term_of_cic_term status t (ctx_of gty) in
let status, ty = term_of_cic_term status ty (ctx_of ty) in
- (status, ty :: l))
+ (status, (t,ty) :: l))
(status,[]) l
in
- Paramod.nparamod metasenv subst (ctx_of gty) t l;
+ Paramod.nparamod metasenv subst (ctx_of gty) (NCic.Rel ~-1,t) l;
status
;;
include "nat/plus.ma".
-ntheorem boo:
- ((λx.x = x) ?) → 0 = 0.
-##[ #H; nwhd in H ⊢ %; nauto by H.
+(*ntheorem boo:
+ (∀x. x = x) → 0 = 0.
+##[ #H; nwhd in H ⊢ %; nauto by H.*)
+
+ntheorem bboo:
+ (∀x. x + 0 = x) ->
+ (∀x, y. x + S y = S (x + y)) →
+ (∀x, y. x + y = y + x) →
+ 3 + 2 = 5.
+#H; #H1; #H2; nauto by H, H1. H2.
ntheorem foo:
((λx.x + 0 = x) ?) →
((λx,y.x + S y = S (x + y)) ? ?) →
- ((λx,y.y + x = x + y) ? ?) →
- ∀x. ((λz. x + x = z + S z) ?).
+ ((λx,y.x y = x y) ? ?) →
+ ∀x. ((λz. x + x = z + z) ?).
##[ #H; #H1; #H2; #x; nwhd in H H1 H2 ⊢ %; nauto by H, H1, H2.
\ No newline at end of file
projects / helm.git / commitdiff