(* $Id$ *)
-type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE
+type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE | XINVERTIBLE
-module Orderings (B : Terms.Blob) = struct
+module type Blob =
+ sig
+ include Terms.Blob
- type weight = int * (int * int) list;;
+ (* This order relation should be:
+ * - stable for instantiation
+ * - total on ground terms
+ *
+ *)
+ val compare_terms :
+ t Terms.foterm -> t Terms.foterm -> Terms.comparison
+
+ val compute_clause_weight : 't Terms.clause -> int
+
+ val name : string
+
+ end
- let string_of_weight (cw, mw) =
- let s =
- String.concat ", "
- (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
- in
- Printf.sprintf "[%d; %s]" cw s
- ;;
+type weight = int * (int * int) list;;
+
+let rec eq_foterm f x y =
+ x == y ||
+ match x, y with
+ | Terms.Leaf t1, Terms.Leaf t2 -> f t1 t2
+ | Terms.Var i, Terms.Var j -> i = j
+ | Terms.Node l1, Terms.Node l2 -> List.for_all2 (eq_foterm f) l1 l2
+ | _ -> false
+;;
+
+let string_of_weight (cw, mw) =
+ let s =
+ String.concat ", "
+ (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
+ in
+ Printf.sprintf "[%d; %s]" cw s
+;;
- let weight_of_term term =
+let weight_of_term term =
let vars_dict = Hashtbl.create 5 in
let rec aux = function
| Terms.Var i ->
in
let compare w1 w2 =
match w1, w2 with
- | (m1, _), (m2, _) -> m2 - m1
+ | (m1, _), (m2, _) -> m1 - m2
in
- (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
- ;;
+ (w, List.sort compare l) (* from the smallest meta to the bigest *)
+;;
- let compute_unit_clause_weight =
+let compute_literal_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
- | Terms.Equation (_,x,_,Terms.Lt)
+ | Terms.Equation (_,x,_,Terms.Lt)
| Terms.Equation (x,_,_,Terms.Gt) ->
let w, m = weight_of_term x in
weight_of_polynomial w m
| Terms.Equation (l,r,_,Terms.Eq)
- | Terms.Equation (l,r,_,Terms.Incomparable) ->
+ | Terms.Equation (l,r,_,Terms.Incomparable)
+ | Terms.Equation (l,r,_,Terms.Invertible) ->
let wl, ml = weight_of_term l in
let wr, mr = weight_of_term r in
weight_of_polynomial (wl+wr) (ml@mr)
- ;;
-
- (* returns a "normalized" version of the polynomial weight wl (with type
- * weight list), i.e. a list sorted ascending by meta number,
- * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
- * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
- * (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
- let normalize_weight maxmeta (cw, wl) =
- let rec aux = function
- | 0 -> []
- | m -> (m, 0)::(aux (m-1))
- in
- let tmpl = aux maxmeta in
- let wl =
- List.sort
- (fun (m, _) (n, _) -> Pervasives.compare m n)
- (List.fold_left
- (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
- in
- (cw, wl)
- ;;
-
-
- let normalize_weights (cw1, wl1) (cw2, wl2) =
- let rec aux wl1 wl2 =
- match wl1, wl2 with
- | [], [] -> [], []
- | (m, w)::tl1, (n, w')::tl2 when m = n ->
- let res1, res2 = aux tl1 tl2 in
- (m, w)::res1, (n, w')::res2
- | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
- let res1, res2 = aux tl1 wl2 in
- (m, w)::res1, (m, 0)::res2
- | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
- let res1, res2 = aux wl1 tl2 in
- (n, 0)::res1, (n, w')::res2
- | [], (n, w)::tl2 ->
- let res1, res2 = aux [] tl2 in
- (n, 0)::res1, (n, w)::res2
- | (m, w)::tl1, [] ->
- let res1, res2 = aux tl1 [] in
- (m, w)::res1, (m, 0)::res2
- | _, _ -> assert false
- in
- let cmp (m, _) (n, _) = compare m n in
- let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
- (cw1, wl1), (cw2, wl2)
- ;;
+;;
+
+let compute_clause_weight (_,nl,pl,_,_) =
+ List.fold_left (fun acc (lit,_) -> compute_literal_weight lit + acc) 0 (nl@pl)
+
+let compute_goal_weight = compute_clause_weight;;
- (* Riazanov: 3.1.5 pag 38 *)
- (* TODO: optimize early detection of XINCOMPARABLE case *)
- let compare_weights (h1, w1) (h2, w2) =
- let res, diffs =
- try
- List.fold_left2
- (fun ((lt, eq, gt), diffs) w1 w2 ->
- match w1, w2 with
- | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
- let diffs = (w1 - w2) + diffs in
- let r = compare w1 w2 in
- if r < 0 then (lt+1, eq, gt), diffs
- else if r = 0 then (lt, eq+1, gt), diffs
- else (lt, eq, gt+1), diffs
- | _ -> assert false)
- ((0, 0, 0), 0) w1 w2
- with Invalid_argument _ -> assert false
- in
- let hdiff = h1 - h2 in
- match res with
- | (0, _, 0) ->
- if hdiff < 0 then XLT
- else if hdiff > 0 then XGT
- else XEQ
- | (m, _, 0) ->
- if hdiff <= 0 then XLT
- else if (- diffs) >= hdiff then XLE else XINCOMPARABLE
- | (0, _, m) ->
- if hdiff >= 0 then XGT
- else if diffs >= (- hdiff) then XGE else XINCOMPARABLE
- | (m, _, n) when m > 0 && n > 0 -> XINCOMPARABLE
- | _ -> assert false
- ;;
+(* Riazanov: 3.1.5 pag 38 *)
+(* Compare weights normalized in a new way :
+ * Variables should be sorted from the lowest index to the highest
+ * Variables which do not occur in the term should not be present
+ * in the normalized polynomial
+ *)
+let compare_weights (h1, w1) (h2, w2) =
+ let rec aux hdiff (lt, gt) diffs w1 w2 =
+ match w1, w2 with
+ | ((var1, w1)::tl1) as l1, (((var2, w2)::tl2) as l2) ->
+ if var1 = var2 then
+ let diffs = (w1 - w2) + diffs in
+ let r = Pervasives.compare w1 w2 in
+ let lt = lt or (r < 0) in
+ let gt = gt or (r > 0) in
+ if lt && gt then XINCOMPARABLE else
+ aux hdiff (lt, gt) diffs tl1 tl2
+ else if var1 < var2 then
+ if lt then XINCOMPARABLE else
+ aux hdiff (false,true) (diffs+w1) tl1 l2
+ else
+ if gt then XINCOMPARABLE else
+ aux hdiff (true,false) (diffs-w2) l1 tl2
+ | [], (_,w2)::tl2 ->
+ if gt then XINCOMPARABLE else
+ aux hdiff (true,false) (diffs-w2) [] tl2
+ | (_,w1)::tl1, [] ->
+ if lt then XINCOMPARABLE else
+ aux hdiff (false,true) (diffs+w1) tl1 []
+ | [], [] ->
+ if lt then
+ if hdiff <= 0 then XLT
+ else if (- diffs) >= hdiff then XLE else XINCOMPARABLE
+ else if gt then
+ if hdiff >= 0 then XGT
+ else if diffs >= (- hdiff) then XGE else XINCOMPARABLE
+ else
+ if hdiff < 0 then XLT
+ else if hdiff > 0 then XGT
+ else XEQ
+ in
+ aux (h1-h2) (false,false) 0 w1 w2
+;;
+
+(* Riazanov: p. 40, relation >>>
+ * if head_only=true then it is not >>> but helps case 2 of 3.14 p 39 *)
+let rec aux_ordering b_compare ?(head_only=false) t1 t2 =
+ match t1, t2 with
+ (* We want to discard any identity equality. *
+ * If we give back XEQ, no inference rule *
+ * will be applied on this equality *)
+ | Terms.Var i, Terms.Var j when i = j ->
+ XEQ
+ (* 1. *)
+ | Terms.Var _, _
+ | _, Terms.Var _ -> XINCOMPARABLE
+ (* 2.a *)
+ | Terms.Leaf a1, Terms.Leaf a2 ->
+ let cmp = b_compare a1 a2 in
+ if cmp = 0 then XEQ else if cmp < 0 then XLT else XGT
+ | Terms.Leaf _, Terms.Node _ -> XLT
+ | Terms.Node _, Terms.Leaf _ -> XGT
+ (* 2.b *)
+ | Terms.Node l1, Terms.Node l2 ->
+ let rec cmp t1 t2 =
+ match t1, t2 with
+ | [], [] -> XEQ
+ | _, [] -> (* XGT *) assert false (* hd symbols were eq *)
+ | [], _ -> (* XLT *) assert false (* hd symbols were eq *)
+ | hd1::tl1, hd2::tl2 ->
+ let o = aux_ordering b_compare ~head_only hd1 hd2 in
+ if o = XEQ && not head_only then cmp tl1 tl2 else o
+ in
+ cmp l1 l2
+;;
- (* Riazanov: p. 40, relation >>>
- * if head_only=true then it is not >>> but helps case 2 of 3.14 p 39 *)
- let rec aux_ordering ?(head_only=false) t1 t2 =
- match t1, t2 with
- (* 1. *)
- | Terms.Var _, _
- | _, Terms.Var _ -> XINCOMPARABLE
- (* 2.a *)
- | Terms.Leaf a1, Terms.Leaf a2 ->
- let cmp = B.compare a1 a2 in
- if cmp = 0 then XEQ else if cmp < 0 then XLT else XGT
- | Terms.Leaf _, Terms.Node _ -> XLT
- | Terms.Node _, Terms.Leaf _ -> XGT
- (* 2.b *)
- | Terms.Node l1, Terms.Node l2 ->
- let rec cmp t1 t2 =
- match t1, t2 with
- | [], [] -> XEQ
- | _, [] -> XGT
- | [], _ -> XLT
- | hd1::tl1, hd2::tl2 ->
- let o = aux_ordering ~head_only hd1 hd2 in
- if o = XEQ && not head_only then cmp tl1 tl2 else o
- in
- cmp l1 l2
- ;;
+let compare_terms o x y =
+ match o x y with
+ | XINCOMPARABLE -> Terms.Incomparable
+ | XGT -> Terms.Gt
+ | XLT -> Terms.Lt
+ | XEQ -> Terms.Eq
+ | XINVERTIBLE -> Terms.Invertible
+ | _ -> assert false
+;;
+
+module NRKBO (B : Terms.Blob) = struct
+ let name = "nrkbo"
+ include B
+
+ module Pp = Pp.Pp(B)
+
+ let eq_foterm = eq_foterm B.eq;;
+
+ let compute_clause_weight = compute_clause_weight;;
+ let compute_goal_weight = compute_goal_weight;;
(* Riazanov: p. 40, relation >_n *)
let nonrec_kbo t1 t2 =
let w1 = weight_of_term t1 in
let w2 = weight_of_term t2 in
- let w1, w2 = normalize_weights w1 w2 in
match compare_weights w1 w2 with
| XLE -> (* this is .> *)
- if aux_ordering t1 t2 = XLT then XLT else XINCOMPARABLE
+ if aux_ordering B.compare t1 t2 = XLT then XLT else XINCOMPARABLE
| XGE ->
- if aux_ordering t1 t2 = XGT then XGT else XINCOMPARABLE
- | XEQ -> aux_ordering t1 t2
+ if aux_ordering B.compare t1 t2 = XGT then XGT else XINCOMPARABLE
+ | XEQ -> let res = aux_ordering B.compare t1 t2 in
+ if res = XINCOMPARABLE && are_invertible t1 t2 then XINVERTIBLE
+ else res
| res -> res
;;
+
+ let compare_terms = compare_terms nonrec_kbo;;
+
+ let profiler = HExtlib.profile ~enable:true "compare_terms(nrkbo)";;
+ let compare_terms x y =
+ profiler.HExtlib.profile (compare_terms x) y
+ ;;
+
+end
+module KBO (B : Terms.Blob) = struct
+ let name = "kbo"
+ include B
+
+ module Pp = Pp.Pp(B)
+
+ let eq_foterm = eq_foterm B.eq;;
+
+ let compute_clause_weight = compute_clause_weight;;
+ let compute_goal_weight = compute_goal_weight;;
+
(* Riazanov: p. 38, relation > *)
let rec kbo t1 t2 =
- let aux = aux_ordering ~head_only:true in
+ let aux = aux_ordering B.compare ~head_only:true in
let rec cmp t1 t2 =
match t1, t2 with
| [], [] -> XEQ
in
let w1 = weight_of_term t1 in
let w2 = weight_of_term t2 in
- let w1, w2 = normalize_weights w1 w2 in
let comparison = compare_weights w1 w2 in
match comparison with
| XLE ->
let r = aux t1 t2 in
if r = XEQ then (
match t1, t2 with
+ | Terms.Var i, Terms.Var j when i=j -> XEQ
| Terms.Node (_::tl1), Terms.Node (_::tl2) -> cmp tl1 tl2
| _, _ -> XINCOMPARABLE
) else r
| res -> res
;;
+
+ let compare_terms = compare_terms kbo;;
+
+ let profiler = HExtlib.profile ~enable:true "compare_terms(kbo)";;
+ let compare_terms x y =
+ profiler.HExtlib.profile (compare_terms x) y
+ ;;
+
+end
+
+module LPO (B : Terms.Blob) = struct
+ let name = "lpo"
+ include B
+
+ module Pp = Pp.Pp(B)
+
+ let eq_foterm = eq_foterm B.eq;;
+
+ let compute_clause_weight = compute_clause_weight;;
+ let compute_goal_weight = compute_goal_weight;;
+
+ let rec lpo s t =
+ match s,t with
+ | s, t when eq_foterm s t ->
+ XEQ
+ | Terms.Var _, Terms.Var _ ->
+ XINCOMPARABLE
+ | _, Terms.Var i ->
+ if (List.mem i (Terms.vars_of_term s)) then XGT
+ else XINCOMPARABLE
+ | Terms.Var i,_ ->
+ if (List.mem i (Terms.vars_of_term t)) then XLT
+ else XINCOMPARABLE
+ | Terms.Node (hd1::tl1), Terms.Node (hd2::tl2) ->
+ let rec ge_subterm t ol = function
+ | [] -> (false, ol)
+ | x::tl ->
+ let res = lpo x t in
+ match res with
+ | XGT | XEQ -> (true,res::ol)
+ | o -> ge_subterm t (o::ol) tl
+ in
+ let (res, l_ol) = ge_subterm t [] tl1 in
+ if res then XGT
+ else let (res, r_ol) = ge_subterm s [] tl2 in
+ if res then XLT
+ else begin
+ let rec check_subterms t = function
+ | _,[] -> true
+ | o::ol,_::tl ->
+ if o = XLT then check_subterms t (ol,tl)
+ else false
+ | [], x::tl ->
+ if lpo x t = XLT then check_subterms t ([],tl)
+ else false
+ in
+ match aux_ordering B.compare hd1 hd2 with
+ | XGT -> if check_subterms s (r_ol,tl2) then XGT
+ else XINCOMPARABLE
+ | XLT -> if check_subterms t (l_ol,tl1) then XLT
+ else XINCOMPARABLE
+ | XEQ ->
+ let lex = List.fold_left2
+ (fun acc si ti -> if acc = XEQ then lpo si ti else acc)
+ XEQ tl1 tl2
+ in
+ (match lex with
+ | XGT ->
+ if List.for_all (fun x -> lpo s x = XGT) tl2 then XGT
+ else XINCOMPARABLE
+ | XLT ->
+ if List.for_all (fun x -> lpo x t = XLT) tl1 then XLT
+ else XINCOMPARABLE
+ | o -> o)
+ | XINCOMPARABLE -> XINCOMPARABLE
+ | _ -> assert false
+ end
+ | _,_ -> aux_ordering B.compare s t
- let compare_terms x y =
- match nonrec_kbo x y with
- | XINCOMPARABLE -> Terms.Incomparable
- | XGT -> Terms.Gt
- | XLT -> Terms.Lt
- | XEQ -> Terms.Eq
- | _ -> assert false
- ;;
+ ;;
+
+ let compare_terms = compare_terms lpo;;
+
+ let profiler = HExtlib.profile ~enable:true "compare_terms(lpo)";;
+ let compare_terms x y =
+ profiler.HExtlib.profile (compare_terms x) y
+ ;;
end
+
projects / helm.git / blobdiff