NAME

       Set.Make - Functor building an implementation of the set structure given a totally ordered
       type.

Module

       Module   Set.Make

Documentation

       Module Make
        : functor (Ord : OrderedType) -> sig end

       Functor building an implementation of the set structure given a totally ordered type.

       Parameters:

       "Ord"

       Set.OrderedType

       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