Set.S - Output signature of the functor Set.Make.

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.

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.

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 .

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 .