module BatSet:Sets over ordered types.`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.

**Note** OCaml, Batteries Included, provides two implementations
of sets: polymorphic sets and functorized sets. Functorized sets
(see `BatSet.S`

and `BatSet.Make`

) are slightly more complex to use but offer
stronger type-safety. Polymorphic sets make it easier to shoot
yourself in the foot. In case of doubt, you should use functorized
sets.

The functorized set implementation is built upon Stdlib's
Set
module, but provides the complete interface.

**Author(s):** Xavier Leroy, Nicolas Cannasse, Markus Mottl, David Rajchenbach-Teller

`module type OrderedType = ``BatInterfaces.OrderedType`

Input signature of the functor

`Set.Make`

.
module type S =`sig`

..`end`

Output signature of the functor

`Set.Make`

.
module StringSet:`S`

`with type elt = String.t`

A set of strings.

module IStringSet:`S`

`with type elt = String.t`

A set of strings.

module NumStringSet:`S`

`with type elt = String.t`

A set of strings.

module RopeSet:`S`

`with type elt = BatRope.t`

A set of ropes.

module IRopeSet:`S`

`with type elt = BatRope.t`

A set of ropes.

module IntSet:`S`

`with type elt = BatInt.t`

A set of integers.

module CharSet:`S`

`with type elt = Char.t`

A set of characters.

module Make:

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

The definitions below describe the polymorphic set interface.

They are similar in functionality to the functorized `BatSet.Make`

module, but the compiler cannot ensure that sets using different
element ordering have different types: the responsibility of not
mixing non-sensical comparison functions together is to the
programmer. If in doubt, you should rather use the `BatSet.Make`

functor for additional safety.

`type ``'a`

t

The type of sets.

`include BatEnum.Enumerable`

`include BatInterfaces.Mappable`

`val empty : ``'a t`

The empty set, using

`compare`

as comparison function`val create : ``('a -> 'a -> int) -> 'a t`

Creates a new empty set, using the provided function for key comparison.

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

Test whether a set is empty or not.

`val singleton : ``?cmp:('a -> 'a -> int) -> 'a -> 'a t`

Creates a new set with the single given element in it.

`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 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`

`union s t`

returns the union of `s`

and `t`

- the set containing
all elements in either `s`

and `t`

. The returned set uses `t`

's
comparison function. The current implementation works better for
small `s`

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

`intersect s t`

returns a new set of those elements that are in
both `s`

and `t`

. The returned set uses `s`

's comparison function.`val diff : ``'a t -> 'a t -> 'a t`

`diff s t`

returns the set of all elements in `s`

but not in
`t`

. The returned set uses `s`

's comparison function.`val subset : ``'a t -> 'a t -> bool`

`subset a b`

returns true if `a`

is a subset of `b`

. O(|a|).`val iter : ``('a -> unit) -> 'a 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 map : ``('a -> 'b) -> 'a t -> 'b t`

`map f x`

creates a new set with elements `f a0`

,
`f a1`

... `f aN`

, where `a0`

, `a1`

, ..., `aN`

are the
values contained in `x`

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

`filter p s`

returns the set of all elements in `s`

that satisfy predicate `p`

.`val filter_map : ``('a -> 'b option) -> 'a t -> 'b t`

`filter_map f m`

combines the features of `filter`

and
`map`

. It calls calls `f a0`

, `f a1`

, `f aN`

where `a0,a1..an`

are the elements of `m`

and returns the set of pairs `bi`

such as `f ai = Some bi`

(when `f`

returns `None`

, the
corresponding element of `m`

is discarded).`val fold : ``('a -> 'b -> 'b) -> 'a t -> 'b -> 'b`

`fold f s a`

computes `(f xN ... (f x1 (f x0 a))...)`

,
where `x0,x1..xN`

are the elements of `s`

, in increasing order.`val exists : ``('a -> bool) -> 'a t -> bool`

`exists p s`

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

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

Returns whether the given predicate applies to all elements in the set

`val partition : ``('a -> bool) -> 'a t -> 'a t * 'a t`

returns two disjoint subsets, those that satisfy the given
predicate and those that don't

`val split : ``'a -> 'a t -> 'a t * bool * 'a 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 cardinal : ``'a t -> int`

Return the number of elements of a set.

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

returns the smallest element of the set. Raises

`Invalid_argument`

if given an empty set.`val max_elt : ``'a t -> 'a`

returns the largest element of the set. Raises

`Invalid_argument`

if given an empty set.`val choose : ``'a t -> 'a`

returns an arbitrary (but deterministic) element of the given set.
Raises

`Invalid_argument`

if given an empty set.`val pop : ``'a t -> 'a * 'a t`

returns one element of the set and the set without that element.
Raises

`Not_found`

if given an empty set`val enum : ``'a t -> 'a BatEnum.t`

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

`val of_enum : ``'a BatEnum.t -> 'a t`

`val of_enum_cmp : ``cmp:('a -> 'a -> int) -> 'a BatEnum.t -> 'a t`

`val of_list : ``'a list -> 'a t`

builds a set from the given list, using the default comparison
function

Printing

`val print : ``?first:string ->`

?last:string ->

?sep:string ->

('a BatInnerIO.output -> 'b -> unit) ->

'a BatInnerIO.output -> 'b t -> unit