Module typeModule type Set.S
= sig end
Output signature of the functor Set.Make .
The type of the set elements.
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.
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.
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
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 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 .
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.
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.