Module Set


structure Set = struct ... end
Sets over types ordered by Pervasives.compare. If you want sets over types with specific order, use MakeSet.
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.

type 'a t
The type of sets.

val empty : 'a t
The empty set.
val is_empty : 'a t -> bool
Test whether a set is empty or not.
val mem : 'a -> 'a t -> bool
mem x s tests whether x belongs to the set s.
val add : 'a -> 'a t -> 'a 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 : 'a -> 'a t
singleton x returns the one-element set containing only x.
val remove : 'a -> 'a t -> 'a 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 : 'a t -> 'a t -> 'a t
Set union.
val inter : 'a t -> 'a t -> 'a t
Set interseection.
val diff : 'a t -> 'a t -> 'a t
Set difference.
val compare : 'a t -> 'a t -> int
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
val equal : 'a t -> 'a t -> bool
equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.
val subset : 'a t -> 'a t -> bool
subset s1 s2 tests whether the set s1 is a subset of the set s2.
val iter : ('a -> unit) -> 'a 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.
val fold : ('a -> 'b -> 'b) -> 'a t -> 'b -> 'b
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.
val for_all : ('a -> bool) -> 'a t -> bool
for_all p s checks if all elements of the set satisfy the predicate p.
val exists : ('a -> bool) -> 'a t -> bool
exists p s checks if at least one element of the set satisfies the predicate p.
val filter : ('a -> bool) -> 'a t -> 'a t
filter p s returns the set of all elements in s that satisfy predicate p.
val partition : ('a -> bool) -> 'a t -> 'a t * 'a 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 : 'a t -> int
Return the number of elements of a set.
val elements : 'a t -> 'a list
Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Pervasives.compare. 
val min_elt : 'a t -> 'a
Return the smallest element of the given set (with respect to the Pervasives.compare ordering), or raise Not_found if the set is empty.
val max_elt : 'a t -> 'a
Same as Set.min_elt, but returns the largest element of the given set.
val choose : 'a t -> 'a
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.