(* $Id$ *)
-(* (weight of constants, [(meta, weight_of_meta)]) *)
-type weight = int * (int * int) list;;
+type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE
-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
-;;
+module Orderings (B : Terms.Blob) = struct
-let weight_of_term term =
- let vars_dict = Hashtbl.create 5 in
- let rec aux = function
- | Terms.Var i ->
- (try
- let oldw = Hashtbl.find vars_dict i in
- Hashtbl.replace vars_dict i (oldw+1)
- with Not_found ->
- Hashtbl.add vars_dict i 1);
- 0
- | Terms.Leaf _ -> 1
- | Terms.Node l -> List.fold_left (+) 0 (List.map aux l)
- in
- let w = aux term in
- let l =
- Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict []
- in
- let compare w1 w2 =
- match w1, w2 with
- | (m1, _), (m2, _) -> m2 - m1
- in
- (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
-;;
+ type weight = int * (int * int) list;;
+
+ 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 vars_dict = Hashtbl.create 5 in
+ let rec aux = function
+ | Terms.Var i ->
+ (try
+ let oldw = Hashtbl.find vars_dict i in
+ Hashtbl.replace vars_dict i (oldw+1)
+ with Not_found ->
+ Hashtbl.add vars_dict i 1);
+ 0
+ | Terms.Leaf _ -> 1
+ | Terms.Node l -> List.fold_left (+) 0 (List.map aux l)
+ in
+ let w = aux term in
+ let l =
+ Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict []
+ in
+ let compare w1 w2 =
+ match w1, w2 with
+ | (m1, _), (m2, _) -> m1 - m2
+ in
+ (w, List.sort compare l) (* from the smallest meta to the bigest *)
+ ;;
+
+ 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
+ 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.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) ->
+ let wl, ml = weight_of_term l in
+ let wr, mr = weight_of_term r in
+ weight_of_polynomial (wl+wr) (ml@mr)
+ ;;
-let compute_clause_weight = assert false (*
- let factor = 2 in
- match o with
- | Lt ->
- let w, m = (weight_of_term
- ~consider_metas:true ~count_metas_occurrences:false right) in
- w + (factor * (List.length m)) ;
- | Le -> assert false
- | Gt ->
- let w, m = (weight_of_term
- ~consider_metas:true ~count_metas_occurrences:false left) in
- w + (factor * (List.length m)) ;
- | Ge -> assert false
- | Eq
- | Incomparable ->
- let w1, m1 = (weight_of_term
- ~consider_metas:true ~count_metas_occurrences:false right) in
- let w2, m2 = (weight_of_term
- ~consider_metas:true ~count_metas_occurrences:false left) in
- w1 + w2 + (factor * (List.length m1)) + (factor * (List.length m2))
-*)
-;;
-
-(* 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)
-;;
-
-(* Riazanov: 3.1.5 pag 38 *)
-let compare_weights ((h1, w1) as weight1) ((h2, w2) as weight2)=
- 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 Lt
- else if hdiff > 0 then Gt
- else Eq
- | (m, _, 0) ->
- if hdiff <= 0 then Lt
- else if (- diffs) >= hdiff then Le else Incomparable
- | (0, _, m) ->
- if hdiff >= 0 then Gt
- else if diffs >= (- hdiff) then Ge else Incomparable
- | (m, _, n) when m > 0 && n > 0 ->
- Incomparable
- | _ -> assert false
-;;
-
-
-let rec aux_ordering ?(recursion=true) t1 t2 =
- let module C = Cic in
- let compare_uris u1 u2 =
- let res =
- compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
- if res < 0 then Lt
- else if res = 0 then Eq
- else Gt
- in
- match t1, t2 with
- | C.Meta _, _
- | _, C.Meta _ -> Incomparable
-
- | t1, t2 when t1 = t2 -> Eq
-
- | C.Rel n, C.Rel m -> if n > m then Lt else Gt
- | C.Rel _, _ -> Lt
- | _, C.Rel _ -> Gt
-
- | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
- | C.Const _, _ -> Lt
- | _, C.Const _ -> Gt
-
- | C.MutInd (u1, tno1, _), C.MutInd (u2, tno2, _) ->
- let res = compare_uris u1 u2 in
- if res <> Eq then res
- else
- let res = compare tno1 tno2 in
- if res = 0 then Eq else if res < 0 then Lt else Gt
- | C.MutInd _, _ -> Lt
- | _, C.MutInd _ -> Gt
-
- | C.MutConstruct (u1, tno1, cno1, _), C.MutConstruct (u2, tno2, cno2, _) ->
- let res = compare_uris u1 u2 in
- if res <> Eq then res
- else
- let res = compare (tno1,cno1) (tno2,cno2) in
- if res = 0 then Eq else if res < 0 then Lt else Gt
- | C.MutConstruct _, _ -> Lt
- | _, C.MutConstruct _ -> Gt
-
- | C.Appl l1, C.Appl l2 when recursion ->
- let rec cmp t1 t2 =
- match t1, t2 with
- | [], [] -> Eq
- | _, [] -> Gt
- | [], _ -> Lt
- | hd1::tl1, hd2::tl2 ->
- let o = aux_ordering hd1 hd2 in
- if o = Eq then cmp tl1 tl2
- else o
- in
- cmp l1 l2
- | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
- aux_ordering h1 h2
-
- | t1, t2 ->
- debug_print
- (lazy
- (Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
- (CicPp.ppterm t1) (CicPp.ppterm t2)));
- Incomparable
-;;
-
-let nonrec_kbo t1 t2 =
- let w1 = weight_of_term t1 in
- let w2 = weight_of_term t2 in
- match compare_weights ~normalize:true w1 w2 with
- | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
- | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
- | Eq -> aux_ordering t1 t2
- | res -> res
-;;
-
-let rec kbo t1 t2 =
- let aux = aux_ordering ~recursion:false in
- let w1 = weight_of_term t1
- and w2 = weight_of_term t2 in
- let rec cmp t1 t2 =
+let compute_goal_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
+ match l with
+ | Terms.Predicate t ->
+ let w, m = weight_of_term t in
+ weight_of_polynomial w m
+ | Terms.Equation (l,r,_,_) ->
+ let wl, ml = weight_of_term l in
+ let wr, mr = weight_of_term r in
+ let wl = weight_of_polynomial wl ml in
+ let wr = weight_of_polynomial wr mr in
+ - (abs (wl-wr))
+ ;;
+
+ (* 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 = 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 ?(head_only=false) t1 t2 =
match t1, t2 with
- | [], [] -> Eq
- | _, [] -> Gt
- | [], _ -> Lt
- | hd1::tl1, hd2::tl2 ->
- let o =
- kbo hd1 hd2
+ (* 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
+ | [], _ -> 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
- if o = Eq then cmp tl1 tl2
- else o
- in
- let comparison = compare_weights ~normalize:true w1 w2 in
- match comparison with
- | Le ->
- let r = aux t1 t2 in
- if r = Lt then Lt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Lt then Lt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Ge ->
- let r = aux t1 t2 in
- if r = Gt then Gt
- else if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- if cmp tl1 tl2 = Gt then Gt else Incomparable
- | _, _ -> Incomparable
- ) else Incomparable
- | Eq ->
- let r = aux t1 t2 in
- if r = Eq then (
- match t1, t2 with
- | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
- cmp tl1 tl2
- | _, _ -> Incomparable
- ) else r
- | res -> res
-;;
-
-let compare_terms = nonrec_kbo;;
+ cmp l1 l2
+ ;;
+
+ (* Riazanov: p. 40, relation >_n *)
+ let nonrec_kbo t1 t2 =
+ let w1 = weight_of_term t1 in
+ let w2 = weight_of_term t2 in
+ match compare_weights w1 w2 with
+ | XLE -> (* this is .> *)
+ if aux_ordering t1 t2 = XLT then XLT else XINCOMPARABLE
+ | XGE ->
+ if aux_ordering t1 t2 = XGT then XGT else XINCOMPARABLE
+ | XEQ -> aux_ordering t1 t2
+ | res -> res
+ ;;
+
+ (* Riazanov: p. 38, relation > *)
+ let rec kbo t1 t2 =
+ let aux = aux_ordering ~head_only:true in
+ let rec cmp t1 t2 =
+ match t1, t2 with
+ | [], [] -> XEQ
+ | _, [] -> XGT
+ | [], _ -> XLT
+ | hd1::tl1, hd2::tl2 ->
+ let o = kbo hd1 hd2 in
+ if o = XEQ then cmp tl1 tl2
+ else o
+ in
+ let w1 = weight_of_term t1 in
+ let w2 = weight_of_term t2 in
+ let comparison = compare_weights w1 w2 in
+ match comparison with
+ | XLE ->
+ let r = aux t1 t2 in
+ if r = XLT then XLT
+ else if r = XEQ then (
+ match t1, t2 with
+ | Terms.Node (_::tl1), Terms.Node (_::tl2) ->
+ if cmp tl1 tl2 = XLT then XLT else XINCOMPARABLE
+ | _, _ -> assert false
+ ) else XINCOMPARABLE
+ | XGE ->
+ let r = aux t1 t2 in
+ if r = XGT then XGT
+ else if r = XEQ then (
+ match t1, t2 with
+ | Terms.Node (_::tl1), Terms.Node (_::tl2) ->
+ if cmp tl1 tl2 = XGT then XGT else XINCOMPARABLE
+ | _, _ -> assert false
+ ) else XINCOMPARABLE
+ | XEQ ->
+ let r = aux t1 t2 in
+ if r = XEQ then (
+ match t1, t2 with
+ | Terms.Node (_::tl1), Terms.Node (_::tl2) -> cmp tl1 tl2
+ | _, _ -> XINCOMPARABLE
+ ) else r
+ | res -> res
+ ;;
+
+ let rec lpo s t =
+ match s,t with
+ | Terms.Var i, Terms.Var j when i = j ->
+ XEQ
+ | Terms.Var _, Terms.Var _ ->
+ XINCOMPARABLE
+ | Terms.Var _, _ ->
+ (match lpo t s with
+ | XGT -> XLT
+ | XLT -> XGT
+ | o -> o)
+ | _, Terms.Var i ->
+ if (List.mem i (Terms.vars_of_term s)) then XGT
+ else XINCOMPARABLE
+ | 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.Node (hd1::tl1), Terms.Node (hd2::tl2) ->
+ (match lpo hd1 hd2 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 s x = XLT) tl2 then XLT
+ else XINCOMPARABLE
+ | XEQ -> List.fold_left2
+ (fun acc si ti -> if acc = XEQ then lpo si ti else acc)
+ XEQ tl1 tl2
+ | XINCOMPARABLE -> XINCOMPARABLE
+ | _ -> assert false)
+ | _ -> assert false
+
+ ;;
+
+ let compare_terms x y =
+ match kbo x y with
+ | XINCOMPARABLE -> Terms.Incomparable
+ | XGT -> Terms.Gt
+ | XLT -> Terms.Lt
+ | XEQ -> Terms.Eq
+ | _ -> assert false
+ ;;
+end
projects / helm.git / blobdiff