Module type Set.S


module type S : sig ... end
Types
elt The type of the set elements.
Abstract
t The type of sets.
Abstract

Simple values
empty t
The empty set.

Functions

is_empty : t -> bool
Test whether a set is empty or not.

mem : elt -> t -> bool
mem x s tests whether x belongs to the set s.

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.

singleton : elt -> t
singleton x returns the one-element set containing only x.

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.

union : t -> t -> t

inter : t -> t -> t

diff : t -> t -> t
Union, intersection and set difference.

compare : t -> t -> int
Total ordering between sets. Can be used as the ordering function for doing sets of sets.

equal : t -> t -> bool
equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

subset : t -> t -> bool
subset s1 s2 tests whether the set s1 is a subset of the set s2.

iter : f:(elt -> unit) -> t -> unit
iter f s applies f in turn to all elements of s. The order in which the elements of s are presented to f is unspecified.

fold : f:(elt -> 'a -> 'a) -> t -> init:'a -> 'a
fold f s a computes (f xN ... (f x2 (f x1 a))...), where x1 ... xN are the elements of s. The order in which elements of s are presented to f is unspecified.

for_all : f:(elt -> bool) -> t -> bool
for_all p s checks if all elements of the set satisfy the predicate p.

exists : f:(elt -> bool) -> t -> bool
exists p s checks if at least one element of the set satisfies the predicate p.

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

partition : f:(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.

cardinal : t -> int
Return the number of elements of a set.

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.

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.

max_elt : t -> elt
Same as min_elt, but returns the largest element of the given set.

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.