module Float:S
with type elt = float
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 singleton : elt -> t
singleton x
returns the one-element set containing only x
.
val mem : elt -> t -> bool
mem x s
tests whether x
belongs to the set s
.
val find : elt -> t -> elt
find x s
returns the element in s that tests equal to x
under its comparison function.
Not_found
if no element is equalval find_opt : elt -> t -> elt option
find_opt x s
returns Some k
for the element k
in s
that
tests equal to x
under its comparison function.
If no element is equal, return None
val find_first : (elt -> bool) -> t -> elt
find_first f m
returns the first element e
for which f e
is true
or raises Not_found
if there is no such element.
f
must be monotonically increasing,
i.e. if k1 < k2 && f k1
is true then f k2
must also be true.
val find_first_opt : (elt -> bool) -> t -> elt option
find_first_opt f m
returns Some e
for the first element e
for which f e
is true or returns None
if there is no such element.
f
must be monotonically increasing,
i.e. if k1 < k2 && f k1
is true then f k2
must also be true.
val find_last : (elt -> bool) -> t -> elt
find_last f m
returns the last element e
for which f e
is true
or raises Not_found
if there is no such element.
f
must be monotonically decreasing,
i.e. if k1 < k2 && f k2
is true then f k1
must also be true.
val find_last_opt : (elt -> bool) -> t -> elt option
find_last_opt f m
returns Some e
for the last element e
for which f e
is true or returns None
if there is no such element.
f
must be monotonically decreasing,
i.e. if k1 < k2 && f k2
is true then f k1
must also be true.
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 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 remove_exn : elt -> t -> t
remove_exn x s
behaves like remove x s
except that it raises
an exception if x
is not in s
.
Not_found
if x
is not in s
.val update : elt -> elt -> t -> t
update x y s
replace x
by y
in s
.
update
is faster when x
compares equal to y
according
to the comparison function used by your set.
When x
and y
are physically equal, m
is returned unchanged.
Not_found
if x
is not in s
.val union : t -> t -> t
Set union.
val inter : t -> t -> t
Set intersection.
val diff : t -> t -> t
Set difference.
val sym_diff : t -> t -> t
sym_diff s t
returns the set of all elements in s
or t
but not both. This is the same as diff (union s t) (inter s
.
t)
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 disjoint : t -> t -> bool
disjoint s1 s2
tests whether the sets s1
and s2
contain no shared
elements. (i.e. inter s1 s2
is empty.)
val compare_subset : t -> t -> int
Partial ordering between sets as generated by subset
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 at_rank_exn : int -> t -> elt
at_rank_exn i s
returns element at rank i
in s
, that is
the i
-th element in increasing order
(the 0
-th element being the smallest element of s
).
Not_found
if s = empty
.Invalid_argument
error_message if i < 0 || i >= cardinal s
val map : (elt -> elt) -> t -> t
map f x
creates a new set with elements f a0
,
f a1
... f aN
, where a0
,a1
..aN
are the
values contained in x
if f
returns all elements unmodified then x
is returned unmodified.
val filter : (elt -> bool) -> t -> t
filter p s
returns the set of all elements in s
that satisfy predicate p
.
if p
returns true
for all elements then s
is returned unmodified.
val filter_map : (elt -> elt option) -> t -> t
filter_map f m
combines the features of filter
and
map
. It calls f a0
, f a1
, f aN
where a0
,a1
..aN
are the elements of m
and returns the set of elements bi
such as f ai = Some bi
(when f
returns None
, the
corresponding element of m
is discarded).
if f
returns true
for all elements then s
is returned unmodified.
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
fold f s a
computes (f xN ... (f x1 (f x0 a))...)
,
where x0
,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 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 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 split_opt : elt -> t -> t * elt option * t
split_opt x s
returns a triple (l, maybe_v, 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
;
maybe_v
is None
if s
contains no element equal to x
,
or Some v
if s
contains an element v
that compares equal to x
.
val split_lt : elt -> t -> t * t
split_lt x s
returns a pair of sets (l, r)
, such that
l
is the subset of s
with elements < x
;
r
is the subset of s
with elements >= x
.
val split_le : elt -> t -> t * t
split_le x s
returns a pair of sets (l, r)
, such that
l
is the subset of s
with elements <= x
;
r
is the subset of s
with elements > x
.
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 to_list : t -> elt list
Alias for elements
.
val to_array : t -> elt array
Same as to_list
but with an array instead of a list.
val min_elt : t -> elt
Return the smallest element of the given set
(with respect to the Ord.compare
ordering).
Not_found
if the set is empty.val min_elt_opt : t -> elt option
Return Some e
for the smallest element e
of the given set
(with respect to the Ord.compare
ordering).
Return None if the set is empty.
val pop_min : t -> elt * t
Returns the smallest element of the given set along with the rest of the set. Semantically equivalent and faster than
let mini = min_elt s in (mini, remove mini s)
Not_found
if the set is empty.val pop_max : t -> elt * t
Returns the biggest element of the given set along with the rest of the set. Semantically equivalent and faster than
let maxi = max_elt s in (maxi, remove maxi s)
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 max_elt_opt : t -> elt option
Same as Set.S.min_elt_opt
, but for the largest element of the
given set.
val choose : t -> elt
Return one element of the given set. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.
Not_found
if the set is empty.val choose_opt : t -> elt option
Return Some e
for one element e
of the given set.
Which element is chosen is unspecified, but equal elements will be
chosen for equal sets.
Return None
if the set is empty.
val any : t -> elt
Return one element of the given set. The difference with choose is that there is no guarantee that equals elements will be picked for equal sets. This merely returns the quickest element to get (O(1)).
Not_found
if the set is empty.val pop : t -> elt * t
returns one element of the set and the set without that element.
Not_found
if given an empty setval enum : t -> elt BatEnum.t
Return an enumeration of all elements of the given set.
The returned enumeration is sorted in increasing order with respect
to the ordering Ord.compare
, where Ord
is the argument
given to Set.Make
.
val backwards : t -> elt BatEnum.t
Return an enumeration of all elements of the given set.
The returned enumeration is sorted in decreasing order with respect
to the ordering Ord.compare
, where Ord
is the argument
given to Set.Make
.
val of_enum : elt BatEnum.t -> t
val of_list : elt list -> t
builds a set from the given list.
val of_array : elt array -> t
builds a set from the given array.
val to_seq : t -> elt BatSeq.t
Iterate on the whole set, in ascending order.
val to_rev_seq : t -> elt BatSeq.t
Iterate on the whole set, in descending order.
val to_seq_from : elt -> t -> elt BatSeq.t
to_seq_from x s
iterates on a subset of the elements in s
,
namely those greater or equal to x
, in ascending order.
val add_seq : elt BatSeq.t -> t -> t
add the given elements to the set, in order.
val of_seq : elt BatSeq.t -> t
build a set from the given elements
val print : ?first:string ->
?last:string ->
?sep:string ->
('a BatInnerIO.output -> elt -> unit) ->
'a BatInnerIO.output -> t -> unit
The following modules replace functions defined in Set
with functions
behaving slightly differently but having the same name. This is by design:
the functions meant to override the corresponding functions of Set
.
module Exceptionless:sig
..end
Operations on Set
without exceptions.
module Labels:sig
..end
Operations on Set
with labels.