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|
(*
*
* Copyright (c) 2001-2002,
* John Kodumal <jkodumal@eecs.berkeley.edu>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* 3. The names of the contributors may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
* IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
* PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
* OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*)
(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the GNU Library General Public License, with *)
(* the special exception on linking described in file ../LICENSE. *)
(* *)
(***********************************************************************)
(* $Id: setp.mli,v 1.3 2003-02-19 19:26:31 jkodumal Exp $ *)
(** Sets over ordered types.
This module implements the set data structure, given a total ordering
function over the set elements. All operations over sets
are purely applicative (no side-effects).
The implementation uses balanced binary trees, and is therefore
reasonably efficient: insertion and membership take time
logarithmic in the size of the set, for instance.
*)
module type PolyOrderedType =
sig
type 'a t
(** The type of the set elements. *)
val compare : 'a t -> 'a t -> int
(** A total ordering function over the set elements.
This is a two-argument function [f] such that
[f e1 e2] is zero if the elements [e1] and [e2] are equal,
[f e1 e2] is strictly negative if [e1] is smaller than [e2],
and [f e1 e2] is strictly positive if [e1] is greater than [e2].
Example: a suitable ordering function is
the generic structural comparison function {!Pervasives.compare}. *)
end
(** Input signature of the functor {!Set.Make}. *)
module type S =
sig
type 'a elt
(** The type of the set elements. *)
type 'a t
(** The type of sets. *)
val empty: 'a t
(** The empty set. *)
val is_empty: 'a t -> bool
(** Test whether a set is empty or not. *)
val mem: 'a elt -> 'a t -> bool
(** [mem x s] tests whether [x] belongs to the set [s]. *)
val add: 'a elt -> 'a t -> 'a t
(** [add x s] returns a set containing all elements of [s],
plus [x]. If [x] was already in [s], [s] is returned unchanged. *)
val singleton: 'a elt -> 'a t
(** [singleton x] returns the one-element set containing only [x]. *)
val remove: 'a elt -> 'a t -> 'a t
(** [remove x s] returns a set containing all elements of [s],
except [x]. If [x] was not in [s], [s] is returned unchanged. *)
val union: 'a t -> 'a t -> 'a t
(** Set union. *)
val inter: 'a t -> 'a t -> 'a t
(** Set interseection. *)
(** Set difference. *)
val diff: 'a t -> 'a t -> 'a t
val compare: 'a t -> 'a t -> int
(** Total ordering between sets. Can be used as the ordering function
for doing sets of sets. *)
val equal: 'a t -> 'a t -> bool
(** [equal s1 s2] tests whether the sets [s1] and [s2] are
equal, that is, contain equal elements. *)
val subset: 'a t -> 'a t -> bool
(** [subset s1 s2] tests whether the set [s1] is a subset of
the set [s2]. *)
val iter: ('a elt -> unit) -> 'a t -> unit
(** [iter f s] applies [f] in turn to all elements of [s].
The order in which the elements of [s] are presented to [f]
is unspecified. *)
val fold: ('a elt -> 'b -> 'b) -> 'a t -> 'b -> 'b
(** [fold f s a] computes [(f xN ... (f x2 (f x1 a))...)],
where [x1 ... xN] are the elements of [s].
The order in which elements of [s] are presented to [f] is
unspecified. *)
val for_all: ('a elt -> bool) -> 'a t -> bool
(** [for_all p s] checks if all elements of the set
satisfy the predicate [p]. *)
val exists: ('a elt -> bool) -> 'a t -> bool
(** [exists p s] checks if at least one element of
the set satisfies the predicate [p]. *)
val filter: ('a elt -> bool) -> 'a t -> 'a t
(** [filter p s] returns the set of all elements in [s]
that satisfy predicate [p]. *)
val partition: ('a elt -> bool) -> 'a t -> 'a t * 'a t
(** [partition p s] returns a pair of sets [(s1, s2)], where
[s1] is the set of all the elements of [s] that satisfy the
predicate [p], and [s2] is the set of all the elements of
[s] that do not satisfy [p]. *)
val cardinal: 'a t -> int
(** Return the number of elements of a set. *)
val elements: 'a t -> 'a elt list
(** Return the list of all elements of the given set.
The returned list is sorted in increasing order with respect
to the ordering [Ord.compare], where [Ord] is the argument
given to {!Set.Make}. *)
val min_elt: 'a t -> 'a elt
(** Return the smallest element of the given set
(with respect to the [Ord.compare] ordering), or raise
[Not_found] if the set is empty. *)
val max_elt: 'a t -> 'a elt
(** Same as {!Set.S.min_elt}, but returns the largest element of the
given set. *)
val choose: 'a t -> 'a elt
(** Return one element of the given set, or raise [Not_found] if
the set is empty. Which element is chosen is unspecified,
but equal elements will be chosen for equal sets. *)
end
(** Output signature of the functor {!Set.Make}. *)
module Make (Ord : PolyOrderedType) : S with type 'a elt = 'a Ord.t
(** Functor building an implementation of the set structure
given a totally ordered type. *)
|
