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+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+exception Empty
+
+type 'a t = {
+ face : 'a list;
+ rear : 'a list;
+ lenf : int;
+ lenr : int;
+}
+
+let rec split i accu l = match l with
+| [] ->
+ if Int.equal i 0 then (accu, []) else invalid_arg "split"
+| t :: q ->
+ if Int.equal i 0 then (accu, l)
+ else split (pred i) (t :: accu) q
+
+let balance q =
+ let avg = (q.lenf + q.lenr) / 2 in
+ let dif = q.lenf + q.lenr - avg in
+ if q.lenf > succ (2 * q.lenr) then
+ let (ff, fr) = split avg [] q.face in
+ { face = List.rev ff ; rear = q.rear @ List.rev fr; lenf = avg; lenr = dif }
+ else if q.lenr > succ (2 * q.lenf) then
+ let (rf, rr) = split avg [] q.rear in
+ { face = q.face @ List.rev rr ; rear = List.rev rf; lenf = dif; lenr = avg }
+ else q
+
+let empty = {
+ face = [];
+ rear = [];
+ lenf = 0;
+ lenr = 0;
+}
+
+let lcons x q =
+ balance { q with lenf = succ q.lenf; face = x :: q.face }
+
+let lhd q = match q.face with
+| [] ->
+ begin match q.rear with
+ | [] -> raise Empty
+ | t :: _ -> t
+ end
+| t :: _ -> t
+
+let ltl q = match q.face with
+| [] ->
+ begin match q.rear with
+ | [] -> raise Empty
+ | t :: _ -> empty
+ end
+| t :: r -> balance { q with lenf = pred q.lenf; face = r }
+
+let rcons x q =
+ balance { q with lenr = succ q.lenr; rear = x :: q.rear }
+
+let rhd q = match q.rear with
+| [] ->
+ begin match q.face with
+ | [] -> raise Empty
+ | t :: r -> t
+ end
+| t :: _ -> t
+
+let rtl q = match q.rear with
+| [] ->
+ begin match q.face with
+ | [] -> raise Empty
+ | t :: r -> empty
+ end
+| t :: r ->
+ balance { q with lenr = pred q.lenr; rear = r }
+
+let rev q = {
+ face = q.rear;
+ rear = q.face;
+ lenf = q.lenr;
+ lenr = q.lenf;
+}
+
+let length q = q.lenf + q.lenr
+
+let is_empty q = Int.equal (length q) 0
+
+let filter f q =
+ let fold (accu, len) x = if f x then (x :: accu, succ len) else (accu, len) in
+ let (rf, lenf) = List.fold_left fold ([], 0) q.face in
+ let (rr, lenr) = List.fold_left fold ([], 0) q.rear in
+ balance { face = List.rev rf; rear = List.rev rr; lenf = lenf; lenr = lenr }