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+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+(* $Id: gmap.ml,v 1.3.16.1 2004/07/16 19:30:29 herbelin Exp $ *)
+
+(* Maps using the generic comparison function of ocaml. Code borrowed from
+ the ocaml standard library. *)
+
+ type ('a,'b) t =
+ Empty
+ | Node of ('a,'b) t * 'a * 'b * ('a,'b) t * int
+
+ let empty = Empty
+
+ let height = function
+ Empty -> 0
+ | Node(_,_,_,_,h) -> h
+
+ let create l x d r =
+ let hl = height l and hr = height r in
+ Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
+
+ let bal l x d r =
+ let hl = match l with Empty -> 0 | Node(_,_,_,_,h) -> h in
+ let hr = match r with Empty -> 0 | Node(_,_,_,_,h) -> h in
+ if hl > hr + 2 then begin
+ match l with
+ Empty -> invalid_arg "Map.bal"
+ | Node(ll, lv, ld, lr, _) ->
+ if height ll >= height lr then
+ create ll lv ld (create lr x d r)
+ else begin
+ match lr with
+ Empty -> invalid_arg "Map.bal"
+ | Node(lrl, lrv, lrd, lrr, _)->
+ create (create ll lv ld lrl) lrv lrd (create lrr x d r)
+ end
+ end else if hr > hl + 2 then begin
+ match r with
+ Empty -> invalid_arg "Map.bal"
+ | Node(rl, rv, rd, rr, _) ->
+ if height rr >= height rl then
+ create (create l x d rl) rv rd rr
+ else begin
+ match rl with
+ Empty -> invalid_arg "Map.bal"
+ | Node(rll, rlv, rld, rlr, _) ->
+ create (create l x d rll) rlv rld (create rlr rv rd rr)
+ end
+ end else
+ Node(l, x, d, r, (if hl >= hr then hl + 1 else hr + 1))
+
+ let rec add x data = function
+ Empty ->
+ Node(Empty, x, data, Empty, 1)
+ | Node(l, v, d, r, h) as t ->
+ let c = Pervasives.compare x v in
+ if c = 0 then
+ Node(l, x, data, r, h)
+ else if c < 0 then
+ bal (add x data l) v d r
+ else
+ bal l v d (add x data r)
+
+ let rec find x = function
+ Empty ->
+ raise Not_found
+ | Node(l, v, d, r, _) ->
+ let c = Pervasives.compare x v in
+ if c = 0 then d
+ else find x (if c < 0 then l else r)
+
+ let rec mem x = function
+ Empty ->
+ false
+ | Node(l, v, d, r, _) ->
+ let c = Pervasives.compare x v in
+ c = 0 || mem x (if c < 0 then l else r)
+
+ let rec merge t1 t2 =
+ match (t1, t2) with
+ (Empty, t) -> t
+ | (t, Empty) -> t
+ | (Node(l1, v1, d1, r1, h1), Node(l2, v2, d2, r2, h2)) ->
+ bal l1 v1 d1 (bal (merge r1 l2) v2 d2 r2)
+
+ let rec remove x = function
+ Empty ->
+ Empty
+ | Node(l, v, d, r, h) as t ->
+ let c = Pervasives.compare x v in
+ if c = 0 then
+ merge l r
+ else if c < 0 then
+ bal (remove x l) v d r
+ else
+ bal l v d (remove x r)
+
+ let rec iter f = function
+ Empty -> ()
+ | Node(l, v, d, r, _) ->
+ iter f l; f v d; iter f r
+
+ let rec map f = function
+ Empty -> Empty
+ | Node(l, v, d, r, h) -> Node(map f l, v, f d, map f r, h)
+
+ let rec fold f m accu =
+ match m with
+ Empty -> accu
+ | Node(l, v, d, r, _) ->
+ fold f l (f v d (fold f r accu))
+
+(* Added with respect to ocaml standard library. *)
+
+ let dom m = fold (fun x _ acc -> x::acc) m []
+
+ let rng m = fold (fun _ y acc -> y::acc) m []
+
+ let to_list m = fold (fun x y acc -> (x,y)::acc) m []
+