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(***********************************************************************)
(* *)
(* Caml Special Light *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1995 Institut National de Recherche en Informatique et *)
(* Automatique. Distributed only by permission. *)
(* *)
(***********************************************************************)
(* $Id$ *)
(* Module [Set]: 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
val compare: t -> t -> int
end
(* The input signature of the functor [Set.Make].
[t] is the type of the set elements.
[compare] is 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].
Examples: a suitable ordering function for type [int]
is [(-)]. You can also use the generic structural comparison
function [compare]. *)
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 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
val inter: t -> t -> t
val diff: t -> t -> t
(* Union, intersection and 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 the same elements. *)
val iter: (elt -> 'a) -> t -> unit
(* [iter f s] applies [f] in turn to all elements of [s], and
discards the results. The elements of [s] are presented to [f]
in a non-specified order. *)
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].
The order in which elements of [s] are presented to [f] is
not specified. *)
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 elements appear in the list in some non-specified order. *)
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 not specified,
but equal elements will be chosen for equal sets. *)
end
module Make(Ord: OrderedType): (S with type elt = Ord.t)
(* Functor building an implementation of the set structure
given a totally ordered type. *)
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