Provided by: ocaml-nox_4.02.3-5ubuntu2_amd64
Set.S - Output signature of the functor Set.Make.
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. 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 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 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. 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