Module type Set.S

module type S = sig .. end

Output signature of the functor Set.Make.

type elt;

The type of the set elements.

type t;

The type of sets.

let empty: t;

The empty set.

let is_empty: t => bool;

Test whether a set is empty or not.

let mem: (elt, t) => bool;

mem x s tests whether x belongs to the set s.

let 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.

let singleton: elt => t;

singleton x returns the one-element set containing only x.

let 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.

let union: (t, t) => t;

Set union.

let inter: (t, t) => t;

Set intersection.

let diff: (t, t) => t;

Set difference.

let compare: (t, t) => int;

Total ordering between sets. Can be used as the ordering function for doing sets of sets.

let equal: (t, t) => bool;

equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

let subset: (t, t) => bool;

subset s1 s2 tests whether the set s1 is a subset of the set s2.

let 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.

let 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.

let for_all: (elt => bool, t) => bool;

for_all p s checks if all elements of the set satisfy the predicate p.

let exists: (elt => bool, t) => bool;

exists p s checks if at least one element of the set satisfies the predicate p.

let filter: (elt => bool, t) => t;

filter p s returns the set of all elements in s that satisfy predicate p.

let 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.

let cardinal: t => int;

Return the number of elements of a set.

let elements: t => list(elt);

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.

let 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.

let max_elt: t => elt;

Same as Set.S.min_elt, but returns the largest element of the given set.

let 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.

let 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.

let 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

let of_list: list(elt) => t;

of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements.
Since 4.02.0