module type S = sig .. endOutput signature of the functor Set.Make.
type elt;
The type of the set elements.
type t;
The type of sets.
let empty: t;
The empty set.
let is_empty: t => bool;
Test whether a set is empty or not.
let mem: (elt, t) => bool;
mem x s tests whether x belongs to the set s.
let 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).
let singleton: elt => t;
singleton x returns the one-element set containing only x.
let 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).
let union: (t, t) => t;
Set union.
let inter: (t, t) => t;
Set intersection.
let disjoint: (t, t) => bool;
Test if two sets are disjoint.
let diff: (t, t) => t;
Set difference: diff s1 s2 contains the elements of s1
that are not in s2.
let compare: (t, t) => int;
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
let equal: (t, t) => bool;
equal s1 s2 tests whether the sets s1 and s2 are
equal, that is, contain equal elements.
let subset: (t, t) => bool;
subset s1 s2 tests whether the set s1 is a subset of
the set s2.
let 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.
let 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.)
let fold: ((elt, 'a) => 'a, t, 'a) => 'a;
fold f s init computes (f xN ... (f x2 (f x1 init))...),
where x1 ... xN are the elements of s, in increasing order.
let for_all: (elt => bool, t) => bool;
for_all f s checks if all elements of the set
satisfy the predicate f.
let exists: (elt => bool, t) => bool;
exists f s checks if at least one element of
the set satisfies the predicate f.
let filter: (elt => bool, t) => t;
filter f s returns the set of all elements in s
that satisfy predicate f. If f satisfies every element in s,
s is returned unchanged (the result of the function is then
physically equal to s).
let filter_map: (elt => option(elt), t) => t;
filter_map f s returns the set of all v such that
f x = Some v for some element x of s.
For example,
filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s
is the set of halves of the even elements of s.
If no element of s is changed or dropped by f (if
f x = Some x for each element x), then
s is returned unchanged: the result of the function
is then physically equal to s.
let partition: (elt => bool, t) => (t, t);
partition f s returns a pair of sets (s1, s2), where
s1 is the set of all the elements of s that satisfy the
predicate f, and s2 is the set of all the elements of
s that do not satisfy f.
let cardinal: t => int;
Return the number of elements of a set.
let elements: t => list(elt);
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.
let 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.
let min_elt_opt: t => option(elt);
Return the smallest element of the given set
(with respect to the Ord.compare ordering), or None
if the set is empty.
let max_elt: t => elt;
Same as Set.S.min_elt, but returns the largest element of the
given set.
let max_elt_opt: t => option(elt);
Same as Set.S.min_elt_opt, but returns the largest element of the
given set.
let 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.
let choose_opt: t => option(elt);
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.
let 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.
let 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.
let find_opt: (elt, t) => option(elt);
find_opt x s returns the element of s equal to x (according
to Ord.compare), or None if no such element
exists.
let 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.
let find_first_opt: (elt => bool, t) => option(elt);
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.
let 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.
let find_last_opt: (elt => bool, t) => option(elt);
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.
let of_list: list(elt) => 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.
let to_seq_from: (elt, t) => Seq.t(elt);
to_seq_from x s iterates on a subset of the elements of s
in ascending order, from x or above.
let to_seq: t => Seq.t(elt);
Iterate on the whole set, in ascending order
let to_rev_seq: t => Seq.t(elt);
Iterate on the whole set, in descending order
let add_seq: (Seq.t(elt), t) => t;
Add the given elements to the set, in order.
let of_seq: Seq.t(elt) => t;
Build a set from the given bindings