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
(the result of the function is then physically equal to `s`

).**Before 4.03**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`

).**Before 4.03**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`

.)

`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`

).**Before 4.03**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 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