It is necessary to provide a comparison function to build a new set. * Binary operators on sets check that both arguments use the same comparison function, * otherwise, a failure is raised.

The empty set.

Test whether a set is empty or not.

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

find x s finds an element y in s which is equal to x. raise Not_found if no such element is in the set.

add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged.

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

remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged.

Set union.

Set intersection.

Set difference.

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

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

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

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.

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

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

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

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

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.

Return the number of elements of a set.

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.

Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty.

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

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.

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.