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 (the result of the function is then physically equal to s ).

       Before4.03 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 ).

       Before4.03 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 .)

       Since 4.04.0

       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 ).

       Before4.03 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 min_elt_opt : t -> elt option

       Return the smallest element of the given set (with respect to the  Ord.compare  ordering),
       or None if the set is empty.

       Since 4.05

       val max_elt : t -> elt

       Same as Set.S.min_elt , but returns the largest element of the given set.

       val max_elt_opt : t -> elt option

       Same as Set.S.min_elt_opt , but returns the largest element of the given set.

       Since 4.05

       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 choose_opt : t -> elt option

       Return one element of the given set, or None if the set is empty. Which element is  chosen
       is unspecified, but equal elements will be chosen for equal sets.

       Since 4.05

       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 find_opt : elt -> t -> elt option

       find_opt  x  s returns the element of s equal to x (according to Ord.compare ), or None if
       no such element exists.

       Since 4.05

       val find_first : (elt -> bool) -> t -> elt

       find_first f s , where f is  a  monotonically  increasing  function,  returns  the  lowest
       element e of s such that f e , or raises Not_found if no such element exists.

       For  example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e
       of s where Ord.compare e x >= 0 (intuitively: e >= x ), or raise Not_found if x is greater
       than any element of s .

       Since 4.05

       val find_first_opt : (elt -> bool) -> t -> elt option

       find_first_opt  f  s  ,  where f is a monotonically increasing function, returns an option
       containing the lowest element e of s such that f e , or None if no such element exists.

       Since 4.05

       val find_last : (elt -> bool) -> t -> elt

       find_last f s , where f is  a  monotonically  decreasing  function,  returns  the  highest
       element e of s such that f e , or raises Not_found if no such element exists.

       Since 4.05

       val find_last_opt : (elt -> bool) -> t -> elt option

       find_last_opt  f  s  ,  where  f is a monotonically decreasing function, returns an option
       containing the highest element e of s such that f e , or None if no such element exists.

       Since 4.05

       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