`type elt = string`

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 is_singleton : t -> bool`

Test if the set is a singleton.

`val singleton : elt -> t`

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

`val mem : elt -> t -> bool`

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

`val find : elt -> t -> elt`

`find x s` returns the element in s that tests equal to `x` under its comparison function.

- raises `Not_found`

  if no element is equal

`val find_opt : elt -> t -> elt option`

`find_opt x s` returns `Some k` for the element `k` in `s` that tests equal to `x` under its comparison function. If no element is equal, return `None`

- since 3.3.0

`val find_first : (elt -> bool) -> t -> elt`

`find_first f m` returns the first element `e` for which `f e` is true or raises `Not_found` if there is no such element. `f` must be monotonically increasing, i.e. if `k1 < k2 && f k1` is true then `f k2` must also be true.

- since 3.3.0

`val find_first_opt : (elt -> bool) -> t -> elt option`

`find_first_opt f m` returns `Some e` for the first element `e` for which `f e` is true or returns `None` if there is no such element. `f` must be monotonically increasing, i.e. if `k1 < k2 && f k1` is true then `f k2` must also be true.

- since 3.3.0

`val find_last : (elt -> bool) -> t -> elt`

`find_last f m` returns the last element `e` for which `f e` is true or raises `Not_found` if there is no such element. `f` must be monotonically decreasing, i.e. if `k1 < k2 && f k2` is true then `f k1` must also be true.

- since 3.3.0

`val find_last_opt : (elt -> bool) -> t -> elt option`

`find_last_opt f m` returns `Some e` for the last element `e` for which `f e` is true or returns `None` if there is no such element. `f` must be monotonically decreasing, i.e. if `k1 < k2 && f k2` is true then `f k1` must also be true.

- since 3.3.0

`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.

- before 3.3.0

  or OCaml 4.03 Physical equality was not ensured.

`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.

- before 3.3.0

  or OCaml 4.03 Physical equality was not ensured.

`val remove_exn : elt -> t -> t`

`remove_exn x s` behaves like `remove x s` except that it raises an exception if `x` is not in `s`.

- raises `Not_found`

  if `x` is not in `s`.

- since 3.2.0

`val update : elt -> elt -> t -> t`

`update x y s` replace `x` by `y` in `s`. `update` is faster when `x` compares equal to `y` according to the comparison function used by your set. When `x` and `y` are physically equal, `m` is returned unchanged.

- raises `Not_found`

  if `x` is not in `s`.

- before 3.3.0

  Physical equality was not ensured.

- since 2.4

`val union : t -> t -> t`

Set union.

`val inter : t -> t -> t`

Set intersection.

`val diff : t -> t -> t`

Set difference.

`val sym_diff : t -> t -> t`

`sym_diff s t` returns the set of all elements in `s` or `t` but not both. This is the same as `diff (union s t) (inter s t)`.

`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 disjoint : t -> t -> bool`

`disjoint s1 s2` tests whether the sets `s1` and `s2` contain no shared elements. (i.e. `inter s1 s2` is empty.)

`val compare_subset : t -> t -> int`

Partial ordering between sets as generated by `subset`

`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 at_rank_exn : int -> t -> elt`

`at_rank_exn i s` returns element at rank `i` in `s`, that is the `i`-th element in increasing order (the `0`-th element being the smallest element of `s`).

- raises `Not_found`

  if `s = empty`.

- raises `Invalid_argument`

  error_message if `i < 0 || i >= cardinal s`

- since 2.4

`val map : (elt -> elt) -> t -> 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`

if `f` returns all elements unmodified then `x` is returned unmodified.

- before 3.3.0

  Physical equality was not ensured.

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

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

if `p` returns `true` for all elements then `s` is returned unmodified.

- before 3.3.0

  or OCaml 4.03 Physical equality was not ensured.

`val filter_map : (elt -> elt option) -> t -> t`

`filter_map f m` combines the features of `filter` and `map`. It calls `f a0`, `f a1`, `f aN` where `a0`,`a1`..`aN` are the elements of `m` and returns the set of elements `bi` such as `f ai = Some bi` (when `f` returns `None`, the corresponding element of `m` is discarded).

if `f` returns `true` for all elements then `s` is returned unmodified.

- before 3.3.0

  Physical equality was not ensured.

`val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a`

`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 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 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 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 split_opt : elt -> t -> t * elt option * t`

`split_opt x s` returns a triple `(l, maybe_v, 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`; `maybe_v` is `None` if `s` contains no element equal to `x`, or `Some v` if `s` contains an element `v` that compares equal to `x`.

- since 2.2.0

`val split_lt : elt -> t -> t * t`

`split_lt x s` returns a pair of sets `(l, r)`, such that `l` is the subset of `s` with elements < `x`; `r` is the subset of `s` with elements >= `x`.

- since 2.2.0

`val split_le : elt -> t -> t * t`

`split_le x s` returns a pair of sets `(l, r)`, such that `l` is the subset of `s` with elements <= `x`; `r` is the subset of `s` with elements > `x`.

- since 2.2.0

`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 to_list : t -> elt list`

Alias for `elements`.

- since 2.2.0

`val to_array : t -> elt array`

Same as `to_list` but with an array instead of a list.

- since 2.4

`val min_elt : t -> elt`

Return the smallest element of the given set (with respect to the `Ord.compare` ordering).

- raises `Not_found`

  if the set is empty.

`val min_elt_opt : t -> elt option`

Return `Some e` for the smallest element `e` of the given set (with respect to the `Ord.compare` ordering). Return None if the set is empty.

- since 3.3.0

`val pop_min : t -> elt * t`

Returns the smallest element of the given set along with the rest of the set. Semantically equivalent and faster than

`let mini = min_elt s in (mini, remove mini s)`

- raises `Not_found`

  if the set is empty.

- since 2.4

`val pop_max : t -> elt * t`

Returns the biggest element of the given set along with the rest of the set. Semantically equivalent and faster than

`let maxi = max_elt s in (maxi, remove maxi s)`

- raises `Not_found`

  if the set is empty.

- since 2.4

`val max_elt : t -> elt`

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

`val max_elt_opt : t -> elt option`

Same as `Set.S.min_elt_opt`, but for the largest element of the given set.

- since 3.3.0

`val choose : t -> elt`

Return one element of the given set. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

- raises `Not_found`

  if the set is empty.

`val choose_opt : t -> elt option`

Return `Some e` for one element `e` of the given set. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. Return `None` if the set is empty.

- since 3.3.0

`val any : t -> elt`

Return one element of the given set. The difference with choose is that there is no guarantee that equals elements will be picked for equal sets. This merely returns the quickest element to get (O(1)).

- raises `Not_found`

  if the set is empty.

`val pop : t -> elt * t`

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

- raises `Not_found`

  if given an empty set

`val enum : t -> elt 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 `Ord.compare`, where `Ord` is the argument given to `Set.Make`.

`val backwards : t -> elt BatEnum.t`

Return an enumeration of all elements of the given set. The returned enumeration is sorted in decreasing order with respect to the ordering `Ord.compare`, where `Ord` is the argument given to `Set.Make`.

`val of_enum : elt BatEnum.t -> t`
`val of_list : elt list -> t`

builds a set from the given list.

- since 2.3.0

`val of_array : elt array -> t`

builds a set from the given array.

- since 2.4

`val to_seq : t -> elt BatSeq.t`

Iterate on the whole set, in ascending order.

- since 3.3.0

`val to_rev_seq : t -> elt BatSeq.t`

Iterate on the whole set, in descending order.

- since 3.3.0

`val to_seq_from : elt -> t -> elt BatSeq.t`

`to_seq_from x s` iterates on a subset of the elements in `s`, namely those greater or equal to `x`, in ascending order.

- since 3.3.0

`val add_seq : elt BatSeq.t -> t -> t`

add the given elements to the set, in order.

- since 3.3.0

`val of_seq : elt BatSeq.t -> t`

build a set from the given elements

- since 3.3.0

## Boilerplate code

### Printing

`val print : ?first:string -> ?last:string -> ?sep:string -> ('a BatInnerIO.output -> elt -> unit) -> 'a BatInnerIO.output -> t -> unit`

## Override modules

The following modules replace functions defined in `Set` with functions behaving slightly differently but having the same name. This is by design: the functions meant to override the corresponding functions of `Set`.

`module Exceptionless : sig ... end`

Operations on `Set` without exceptions.

`module Labels : sig ... end`

Operations on `Set` with labels.