(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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(*i $Id: heap.mli 14641 2011-11-06 11:59:10Z herbelin $ i*)

(* 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

(*S Functional implementation. *)

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