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+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+type 'a tree =
+| Leaf of 'a
+| Node of 'a * 'a tree * 'a tree
+
+type 'a t = Nil | Cons of int * 'a tree * 'a t
+
+let oob () = invalid_arg "index out of bounds"
+
+let empty = Nil
+
+let cons x l = match l with
+| Cons (h1, t1, Cons (h2, t2, rem)) ->
+  if Int.equal h1 h2 then Cons (1 + h1 + h2, Node (x, t1, t2), rem)
+  else Cons (1, Leaf x, l)
+| _ -> Cons (1, Leaf x, l)
+
+let is_empty = function
+| Nil -> true
+| _ -> false
+
+let rec tree_get h t i = match t with
+| Leaf x ->
+  if i = 0 then x else oob ()
+| Node (x, t1, t2) ->
+  if i = 0 then x
+  else
+    let h = h / 2 in
+    if i <= h then tree_get h t1 (i - 1) else tree_get h t2 (i - h - 1)
+
+let rec get l i = match l with
+| Nil -> oob ()
+| Cons (h, t, rem) ->
+  if i < h then tree_get h t i else get rem (i - h)
+
+let length l =
+  let rec length accu = function
+  | Nil -> accu
+  | Cons (h, _, l) -> length (h + accu) l
+  in
+  length 0 l
+
+let rec tree_map f = function
+| Leaf x -> Leaf (f x)
+| Node (x, t1, t2) -> Node (f x, tree_map f t1, tree_map f t2)
+
+let rec map f = function
+| Nil -> Nil
+| Cons (h, t, l) -> Cons (h, tree_map f t, map f l)
+
+let rec tree_fold_left f accu = function
+| Leaf x -> f accu x
+| Node (x, t1, t2) ->
+  tree_fold_left f (tree_fold_left f (f accu x) t1) t2
+
+let rec fold_left f accu = function
+| Nil -> accu
+| Cons (_, t, l) -> fold_left f (tree_fold_left f accu t) l
+
+let rec tree_fold_right f t accu = match t with
+| Leaf x -> f x accu
+| Node (x, t1, t2) ->
+  f x (tree_fold_right f t1 (tree_fold_right f t2 accu))
+
+let rec fold_right f l accu = match l with
+| Nil -> accu
+| Cons (_, t, l) -> tree_fold_right f t (fold_right f l accu)
+
+let hd = function
+| Nil -> failwith "hd"
+| Cons (_, Leaf x, _) -> x
+| Cons (_, Node (x, _, _), _) -> x
+
+let tl = function
+| Nil -> failwith "tl"
+| Cons (_, Leaf _, l) -> l
+| Cons (h, Node (_, t1, t2), l) ->
+  let h = h / 2 in
+  Cons (h, t1, Cons (h, t2, l))
+
+let rec skipn n l =
+  if n = 0 then l
+  else if is_empty l then failwith "List.skipn"
+  else skipn (pred n) (tl l)