Sets over ordered types.
This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance.
The type of the set elements.
val empty : 'elt t
The empty set.
val is_empty : 'elt t -> bool
Test whether a set is empty or not.
val mem : 'elt -> 'elt t -> bool
mem x s tests whether
x belongs to the set
add x s returns a set containing all elements of
x was already in
s is returned unchanged.
val singleton : 'elt -> 'elt t
singleton x returns the one-element set containing only
remove x s returns a set containing all elements of
x was not in
s is returned unchanged.
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
equal s1 s2 tests whether the sets
s2 are equal, that is, contain equal elements.
subset s1 s2 tests whether the set
s1 is a subset of the set
val iter : ('elt -> unit) -> 'elt 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) -> 'elt 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) -> 'elt t -> bool
for_all p s checks if all elements of the set satisfy the predicate
val exists : ('elt -> bool) -> 'elt t -> bool
exists p s checks if at least one element of the set satisfies the predicate
filter p s returns the set of all elements in
s that satisfy predicate
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
s2 is the set of all the elements of
s that do not satisfy
val cardinal : 'elt t -> int
Return the number of elements of a set.
val elements : 'elt 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 is the argument given to
val min_elt : '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 : 'elt t -> 'elt
Set.S.min_elt, but returns the largest element of the given set.
val choose : 'elt 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.
split x s returns a triple
(l, present, r), where
l is the set of elements of
s that are strictly less than
r is the set of elements of
s that are strictly greater than
s contains no element equal to
s contains an element equal to
val of_list : 'elt list -> 'elt t