NAME

       Set.S - Output signature of the functor Set.Make.

Module type

       Module type   Set.S

Documentation

       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