Module type Set.S

Output signature of the functor Make.

Sets

type elt

type elt;

The type of the set elements.

type t

type t;

The type of sets.

val empty : t

let empty: t;

The empty set.

val add : elt -> t -> t

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 (the result of the function is then physically equal to s).

before 4.03 Physical equality was not ensured.

val singleton : elt -> t

let singleton: elt => t;

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

val remove : elt -> t -> t

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 (the result of the function is then physically equal to s).

before 4.03 Physical equality was not ensured.

val union : t -> t -> t

let union: t => t => t;

Set union.

val inter : t -> t -> t

let inter: t => t => t;

Set intersection.

val disjoint : t -> t -> bool

let disjoint: t => t => bool;

Test if two sets are disjoint.

since 4.08

val diff : t -> t -> t

let diff: t => t => t;

Set difference: diff s1 s2 contains the elements of s1 that are not in s2.

val cardinal : t -> int

let cardinal: t => int;

Return the number of elements of a set.

Elements

val elements : t -> elt list

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.

val min_elt : t -> elt

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.

val min_elt_opt : t -> elt option

let min_elt_opt: t => option(elt);

Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the set is empty.

since 4.05

val max_elt : t -> elt

let max_elt: t => elt;

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

val max_elt_opt : t -> elt option

let max_elt_opt: t => option(elt);

Same as min_elt_opt, but returns the largest element of the given set.

since 4.05

val choose : t -> elt

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.

val choose_opt : t -> elt option

let choose_opt: t => option(elt);

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

since 4.05

Searching

val find : elt -> t -> elt

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

val find_opt : elt -> t -> elt option

let find_opt: elt => t => option(elt);

find_opt x s returns the element of s equal to x (according to Ord.compare), or None if no such element exists.

since 4.05

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

let find_first: (elt => bool) => t => elt;

find_first f s, where f is a monotonically increasing function, returns the lowest element e of s such that f e, or raises Not_found if no such element exists.

For example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e of s where Ord.compare e x >= 0 (intuitively: e >= x), or raise Not_found if x is greater than any element of s.

since 4.05

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

let find_first_opt: (elt => bool) => t => option(elt);

find_first_opt f s, where f is a monotonically increasing function, returns an option containing the lowest element e of s such that f e, or None if no such element exists.

since 4.05

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

let find_last: (elt => bool) => t => elt;

find_last f s, where f is a monotonically decreasing function, returns the highest element e of s such that f e, or raises Not_found if no such element exists.

since 4.05

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

let find_last_opt: (elt => bool) => t => option(elt);

find_last_opt f s, where f is a monotonically decreasing function, returns an option containing the highest element e of s such that f e, or None if no such element exists.

since 4.05

Traversing

val iter : (elt -> unit) -> t -> unit

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.

val fold : (elt -> 'acc -> 'acc) -> t -> 'acc -> 'acc

let fold: (elt => 'acc => 'acc) => t => 'acc => 'acc;

fold f s init computes (f xN ... (f x2 (f x1 init))...), where x1 ... xN are the elements of s, in increasing order.

Transforming

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

let map: (elt => elt) => t => t;

map f s is the set whose elements are f a0,f a1... f aN, where a0,a1...aN are the elements of s.

The elements are passed to f in increasing order with respect to the ordering over the type of the elements.

If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.)

since 4.04

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

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

filter f s returns the set of all elements in s that satisfy predicate f. If f 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 filter_map : (elt -> elt option) -> t -> t

let filter_map: (elt => option(elt)) => t => t;

filter_map f s returns the set of all v such that f x = Some v for some element x of s.

For example,

filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s

filter_map(
  n =>
    if (n mod 2 == 0) {
      Some(n / 2);
    } else {
      None;
    },
  s,
);

is the set of halves of the even elements of s.

If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s.

since 4.11

val partition : (elt -> bool) -> t -> t * t

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

partition f s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate f, and s2 is the set of all the elements of s that do not satisfy f.

val split : elt -> t -> t * bool * t

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.

Predicates and comparisons

val is_empty : t -> bool

let is_empty: t => bool;

Test whether a set is empty or not.

val mem : elt -> t -> bool

let mem: elt => t => bool;

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

val equal : t -> t -> bool

let equal: t => t => bool;

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

val compare : t -> t -> int

let compare: t => t => int;

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

val subset : t -> t -> bool

let subset: t => t => bool;

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

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

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

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

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

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

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

Converting

val to_list : t -> elt list

let to_list: t => list(elt);

to_list s is elements s.

since 5.1

val of_list : elt list -> t

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

val to_seq_from : elt -> t -> elt Seq.t

let to_seq_from: elt => t => Seq.t(elt);

to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above.

since 4.07

val to_seq : t -> elt Seq.t

let to_seq: t => Seq.t(elt);

Iterate on the whole set, in ascending order

since 4.07

val to_rev_seq : t -> elt Seq.t

let to_rev_seq: t => Seq.t(elt);

Iterate on the whole set, in descending order

since 4.12

val add_seq : elt Seq.t -> t -> t

let add_seq: Seq.t(elt) => t => t;

Add the given elements to the set, in order.

since 4.07

val of_seq : elt Seq.t -> t

let of_seq: Seq.t(elt) => t;

Build a set from the given bindings

since 4.07