module Sette:Sets over ordered types (extension of standard library module and polymorphic variant)`sig`

..`end`

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.

Modified by B. Jeannet to get a generic type and a few additions
(like conversions form and to maps and pretty-printing).

`type `

`'a`

set =

`|` |
`Empty` |
|||

`|` |
`Node of ` |
`(*` | Meant to be internal, but exporting needed for Mappe.maptoset. | `*)` |

type`'a`

t =`'a set`

The type of sets over elements of type 'a.

`val empty : ``'a t`

The empty set.

`val is_empty : ``'a t -> bool`

Test whether a set is empty or not.

`val mem : ``'a -> 'a t -> bool`

`mem x s`

tests whether `x`

belongs to the set `s`

.`val add : ``'a -> '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 -> 'a t`

`singleton x`

returns the one-element set containing only `x`

.`val remove : ``'a -> '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`

`val inter : ``'a t -> 'a t -> 'a t`

`val diff : ``'a t -> 'a t -> 'a t`

Union, intersection and set difference.

`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 -> 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 -> '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.`Not_found`

if no fount`val for_all : ``('a -> bool) -> 'a t -> bool`

`for_all p s`

checks if all elements of the set
satisfy the predicate `p`

.`val exists : ``('a -> bool) -> 'a t -> bool`

`exists p s`

checks if at least one element of
the set satisfies the predicate `p`

.`val filter : ``('a -> bool) -> 'a t -> 'a t`

`filter p s`

returns the set of all elements in `s`

that satisfy predicate `p`

.`val partition : ``('a -> 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 list`

Return the list of all elements of the given set. The returned list
is sorted in increasing order with respect to the ordering

`Pervasives.compare`

.`val min_elt : ``'a t -> 'a`

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`

Same as

`min_elt`

, but returns the largest element of the given
set.`val choose : ``'a t -> 'a`

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 print : ``?first:(unit, Format.formatter, unit) Pervasives.format ->`

?sep:(unit, Format.formatter, unit) Pervasives.format ->

?last:(unit, Format.formatter, unit) Pervasives.format ->

(Format.formatter -> 'a -> unit) -> Format.formatter -> 'a t -> unit

module type S =`sig`

..`end`

Output signature of the functor

`Sette.Make`

.
module Make:

Functor building an implementation of the set structure
given a totally ordered type.

module Compare:`sig`

..`end`