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 (the result of the function is then physically equal to s).
Before 4.03 Physical equality was not ensured.
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 (the result of the function is then physically equal to s).
Before 4.03 Physical equality was not ensured.
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 map : (elt -> elt) -> t -> t
map f s is the set whose elements are f a0,f a1... f
        aN, where a0,a1...aN are the elements of s.

The elements are passed to f in increasing order with respect to the ordering over the type of the elements.

If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.)

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. If p satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s).
Before 4.03 Physical equality was not ensured.
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.
val find : elt -> t -> elt
find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists.
Since 4.01.0
val of_list : elt list -> t
of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements.
Since 4.02.0
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