(************************************************************************)
(*         *   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)         *)
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(** Heaps *)

module type Ordered = sig
  type t
  val compare : t -> t -> int
end

module type S =sig

  (** Type of functional heaps *)
  type t

  (** Type of elements *)
  type elt

  (** The empty heap *)
  val empty : t

  (** [add x h] returns a new heap containing the elements of [h], plus [x];
     complexity {% $ %}O(log(n)){% $ %} *)
  val add : elt -> t -> t

  (** [maximum h] returns the maximum element of [h]; raises [EmptyHeap]
     when [h] is empty; complexity {% $ %}O(1){% $ %} *)
  val maximum : t -> elt

  (** [remove h] returns a new heap containing the elements of [h], except
     the maximum of [h]; raises [EmptyHeap] when [h] is empty;
     complexity {% $ %}O(log(n)){% $ %} *)
  val remove : t -> t

  (** usual iterators and combinators; elements are presented in
     arbitrary order *)
  val iter : (elt -> unit) -> t -> unit

  val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a

end

exception EmptyHeap

(** {6 Functional implementation. } *)

module Functional(X: Ordered) : S with type elt=X.t