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(* *)
(* OCaml *)
(* *)
(* 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. *)
(* *)
(***********************************************************************)
(** 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 OrderedType =
sig
type t
(** The type of the set elements. *)
val compare : t -> 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 elt
(** The type of the set elements. *)
type t
(** The type of sets. *)
val empty: t
(** The empty set. *)
val is_empty: t -> bool
(** Test whether a set is empty or not. *)
val mem: elt -> t -> bool
(** [mem x s] tests whether [x] belongs to the set [s]. *)
val add: elt -> t -> 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: elt -> t
(** [singleton x] returns the one-element set containing only [x]. *)
val remove: elt -> t -> 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: t -> t -> t
(** Set union. *)
val inter: t -> t -> t
(** Set intersection. *)
val diff: t -> t -> t
(** Set difference. *)
val compare: t -> t -> int
(** Total ordering between sets. Can be used as the ordering function
for doing sets of sets. *)
val equal: t -> t -> bool
(** [equal s1 s2] tests whether the sets [s1] and [s2] are
equal, that is, contain equal elements. *)
val subset: t -> t -> bool
(** [subset s1 s2] tests whether the set [s1] is a subset of
the set [s2]. *)
val iter: (elt -> unit) -> t -> unit
(** [iter f s] applies [f] in turn to all elements of [s].
The elements of [s] are presented to [f] in increasing order
with respect to the ordering over the type of the elements. *)
val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
(** [fold f s a] computes [(f xN ... (f x2 (f x1 a))...)],
where [x1 ... xN] are the elements of [s], in increasing order. *)
val for_all: (elt -> bool) -> t -> bool
(** [for_all p s] checks if all elements of the set
satisfy the predicate [p]. *)
val exists: (elt -> bool) -> t -> bool
(** [exists p s] checks if at least one element of
the set satisfies the predicate [p]. *)
val filter: (elt -> bool) -> t -> t
(** [filter p s] returns the set of all elements in [s]
that satisfy predicate [p]. *)
val partition: (elt -> bool) -> t -> t * 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: t -> int
(** Return the number of elements of a set. *)
val elements: t -> 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: t -> 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: t -> elt
(** Same as {!Set.S.min_elt}, but returns the largest element of the
given set. *)
val choose: t -> 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. *)
val split: elt -> t -> t * bool * t
(** [split x s] returns a triple [(l, present, r)], where
[l] is the set of elements of [s] that are
strictly less than [x];
[r] is the set of elements of [s] that are
strictly greater than [x];
[present] is [false] if [s] contains no element equal to [x],
or [true] if [s] contains an element equal to [x]. *)
val find: elt -> t -> elt
(** [find x s] returns the element of [s] equal to [x] (according
to [Ord.compare]), or raise [Not_found] if no such element
exists.
@since 4.01.0 *)
end
(** Output signature of the functor {!Set.Make}. *)
module Make (Ord : OrderedType) : S with type elt = Ord.t
(** Functor building an implementation of the set structure
given a totally ordered type. *)
|