+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department, University of Bologna, Italy.
+ ||I||
+ ||T|| HELM is free software; you can redistribute it and/or
+ ||A|| modify it under the terms of the GNU General Public License
+ \ / version 2 or (at your option) any later version.
+ \ / This software is distributed as is, NO WARRANTY.
+ V_______________________________________________________________ *)
+
+(* $Id$ *)
+
+(* (weight of constants, [(meta, weight_of_meta)]) *)
+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, _) -> m2 - m1
+ in
+ (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
+;;
+
+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 =
+ match t1, t2 with
+ | [], [] -> Eq
+ | _, [] -> Gt
+ | [], _ -> Lt
+ | hd1::tl1, hd2::tl2 ->
+ let o =
+ kbo hd1 hd2
+ 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;;
+