module Make:
Functor building an implementation of the set structure given a totally ordered type.
Parameters: 

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
).
val singleton : elt > t
singleton x
returns the oneelement 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
).
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
, where
aNa0
,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
).
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.
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.
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.
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.
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.
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
.
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.
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.
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.
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.