asetmap
On This Page
Legend:
Library
Module
Module type
Parameter
Class
Class type

Signature for sets of values of a totally ordered type.

## Set

include Set.S
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 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.)

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 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 option

find e s is the element of s equal to e (if any).

val get : elt -> t -> elt

get is like find but

• raises Invalid_argument

if elt is not in s.

val min_elt : t -> elt option

min_elt s is the smallest element of s (if any).

val get_min_elt : t -> elt

get_min_elt is like min_elt but

• raises Invalid_argument

on the empty set.

val max_elt : t -> elt option

max_elt s is the greatest element of s (if any).

val get_max_elt : t -> elt

get_max_elt is like max_elt but

• raises Invalid_argument

on the empty set.

val choose : t -> elt option

choose s is an element of s or None is s empty. The chosen element is equal for equal sets.

val get_any_elt : t -> elt

get_any_elt is like choose but

• raises Invalid_argument

on the empty set.

## Conversions

val to_list : t -> elt list

to_list s is the elements of s in increasing order.

val of_list : elt list -> t

of_list l is a set from the elements of l

## Pretty-printers

val pp : ?sep:( unit -> unit) -> ( elt -> unit) -> t -> unit

pp ~sep pp_elt ppf s formats the elements of s on ppf. Each element is formatted with pp_elt and elements are separated by ~sep (defaults to Format.pp_print_cut). If the set is empty leaves ppf untouched.

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

dump pp_elt ppf s prints an unspecified representation of s on ppf using pp_elt to print elements.