# 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.

    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 (the result of the function is then physically equal to `s`).
Before 4.03 Physical equality was not ensured.

    val singleton : elt -> t

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

    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 (the result of the function is then physically equal to `s`).
Before 4.03 Physical equality was not ensured.

    val union : t -> t -> t

Set union.

    val inter : t -> t -> t

Set intersection.

    val diff : t -> t -> t

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 equal elements.

    val subset : t -> t -> bool

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

    val 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.

    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`, in increasing order.

    val for_all : (elt -> bool) -> t -> bool

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

    val exists : (elt -> bool) -> t -> bool

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

    val filter : (elt -> bool) -> t -> t

`filter p s` returns the set of all elements in `s` that satisfy predicate `p`. If `p` satisfies every element in `s`, `s` is returned unchanged (the result of the function is then physically equal to `s`).
Before 4.03 Physical equality was not ensured.

    val 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`.

    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 returned list is sorted in increasing order with respect to the ordering `Ord.compare`, where `Ord` is the argument given to `Set.Make`.

    val 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.

    val max_elt : t -> elt

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

    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 unspecified, but equal elements will be chosen for equal sets.

    val 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`.

    val 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

    val of_list : elt list -> 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