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(** Module [Pred]: sets over infinite ordered types with complement. *)
(** 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 the Set library. *)
module type OrderedType =
sig
type t
val compare: t -> t -> int
end
(** The input signature of the functor [Pred.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].
Example: a suitable ordering function is
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 full: t
(** The whole type. *)
val is_empty: t -> bool
(** Test whether a set is empty or not. *)
val is_full: t -> bool
(** Test whether a set contains the whole type or not. *)
val mem: elt -> t -> bool
(** [mem x s] tests whether [x] belongs to the set [s]. *)
val singleton: elt -> t
(** [singleton x] returns the one-element set containing only [x]. *)
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
val complement: t -> t
(** Union, intersection, difference and set complement. *)
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 elements: t -> bool * elt list
(** Gives a finite representation of the predicate: if the
boolean is false, then the predicate is given in extension.
if it is true, then the complement is given *)
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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