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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)         *)
+(************************************************************************)
+
+(** A native integer module with usual utility functions. *)
+
+type t = int
+
+external equal : t -> t -> bool = "%eq"
+
+external compare : t -> t -> int = "caml_int_compare"
+
+val hash : t -> int
+
+module Set : Set.S with type elt = t
+module Map : CMap.ExtS with type key = t and module Set := Set
+
+module List : sig
+  val mem : int -> int list -> bool
+  val assoc : int -> (int * 'a) list -> 'a
+  val mem_assoc : int -> (int * 'a) list -> bool
+  val remove_assoc : int -> (int * 'a) list -> (int * 'a) list
+end
+
+module PArray :
+sig
+  type 'a t
+  (** Persistent, auto-resizable arrays. The [get] and [set] functions never
+      fail whenever the index is between [0] and [Sys.max_array_length - 1]. *)
+  val empty : int -> 'a t
+  (** The empty array, with a given starting size. *)
+  val get : 'a t -> int -> 'a option
+  (** Get a value at the given index. Returns [None] if undefined. *)
+  val set : 'a t -> int -> 'a option -> 'a t
+  (** Set/unset a value at the given index. *)
+end
+
+module PMap :
+sig
+  type key = int
+  type 'a t
+  val empty : 'a t
+  val is_empty : 'a t -> bool
+  val mem : key -> 'a t -> bool
+  val add : key -> 'a -> 'a t -> 'a t
+  val singleton : key -> 'a -> 'a t
+  val remove : key -> 'a t -> 'a t
+(*   val merge : (key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t *)
+(*   val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int *)
+(*   val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool *)
+  val iter : (key -> 'a -> unit) -> 'a t -> unit
+  val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
+  val for_all : (key -> 'a -> bool) -> 'a t -> bool
+  val exists : (key -> 'a -> bool) -> 'a t -> bool
+(*   val filter : (key -> 'a -> bool) -> 'a t -> 'a t *)
+(*   val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t *)
+(*   val cardinal : 'a t -> int *)
+(*   val bindings : 'a t -> (key * 'a) list *)
+(*   val min_binding : 'a t -> key * 'a *)
+(*   val max_binding : 'a t -> key * 'a *)
+(*   val choose : 'a t -> key * 'a *)
+(*   val split : key -> 'a t -> 'a t * 'a option * 'a t *)
+  val find : key -> 'a t -> 'a
+(*   val map : ('a -> 'b) -> 'a t -> 'b t *)
+(*   val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t *)
+  val domain : 'a t -> Set.t
+  val cast : 'a t -> 'a Map.t
+end
+(** This is a (partial) implementation of a [Map] interface on integers, except
+    that it internally uses persistent arrays. This ensures O(1) accesses in
+    non-backtracking cases. It is thus better suited for zero-starting,
+    contiguous keys, or otherwise a lot of space will be empty. To keep track of
+    the present keys, a binary tree is also used, so that adding a key is
+    still logarithmic. It is therefore essential that most of the operations
+    are accesses and not add/removes. *)