# View Source sets (stdlib v6.0)

Sets are collections of elements with no duplicate elements.

The data representing a set as used by this module is to be regarded as opaque by other modules. In abstract terms, the representation is a composite type of existing Erlang terms. See note on data types. Any code assuming knowledge of the format is running on thin ice.

This module provides the same interface as the `ordsets`

module but with an
undefined representation. One difference is that while this module considers two
elements as different if they do not match (`=:=`

), `ordsets`

considers two
elements as different if and only if they do not compare equal (`==`

).

Erlang/OTP 24.0 introduced a new internal representation for sets which is more
performant. Developers can use this new representation by passing the
`{version, 2}`

flag to `new/1`

and `from_list/2`

, such as
`sets:new([{version, 2}])`

. This new representation will become the default in
future Erlang/OTP versions. Functions that work on two sets, such as `union/2`

and similar, will work with sets of different versions. In such cases, there is
no guarantee about the version of the returned set. Explicit conversion from the
old version to the new one can be done with
`sets:from_list(sets:to_list(Old), [{version,2}])`

.

## Compatibility

The following functions in this module also exist and provide the same
functionality in the `gb_sets`

and `ordsets`

modules. That is, by only
changing the module name for each call, you can try out different set
representations.

`add_element/2`

`del_element/2`

`filter/2`

`filtermap/2`

`fold/3`

`from_list/1`

`intersection/1`

`intersection/2`

`is_element/2`

`is_empty/1`

`is_equal/2`

`is_set/1`

`is_subset/2`

`map/2`

`new/0`

`size/1`

`subtract/2`

`to_list/1`

`union/1`

`union/2`

## Note

While the three set implementations offer the same

functionalitywith respect to the aforementioned functions, their overallbehaviormay differ. As mentioned, this module considers elements as different if and only if they do not match (`=:=`

), while both`ordsets`

and`gb_sets`

consider elements as different if and only if they do not compare equal (`==`

).

Example:`1> sets:is_element(1.0, sets:from_list([1])). false 2> ordsets:is_element(1.0, ordsets:from_list([1])). true 2> gb_sets:is_element(1.0, gb_sets:from_list([1])). true`

## See Also

# Summary

## Functions

Returns a new set formed from `Set1`

with `Element`

inserted.

Returns `Set1`

, but with `Element`

removed.

Filters elements in `Set1`

with boolean function `Pred`

.

Filters and maps elements in `Set1`

with function `Fun`

.

Folds `Function`

over every element in `Set`

and returns the final value of the
accumulator. The evaluation order is undefined.

Returns a set of the elements in `List`

.

Returns a set of the elements in `List`

at the given version.

Returns the intersection of the non-empty list of sets.

Returns the intersection of `Set1`

and `Set2`

.

Returns `true`

if `Set1`

and `Set2`

are disjoint (have no elements in common),
otherwise `false`

.

Returns `true`

if `Element`

is an element of `Set`

, otherwise `false`

.

Returns `true`

if `Set`

is an empty set, otherwise `false`

.

Returns `true`

if `Set1`

and `Set2`

are equal, that is when every element of one
set is also a member of the respective other set, otherwise `false`

.

Returns `true`

if `Set`

appears to be a set of elements, otherwise `false`

.

Returns `true`

when every element of `Set1`

is also a member of `Set2`

,
otherwise `false`

.

Maps elements in `Set1`

with mapping function `Fun`

.

Returns a new empty set.

Returns a new empty set at the given version.

Returns the number of elements in `Set`

.

Returns only the elements of `Set1`

that are not also elements of `Set2`

.

Returns the elements of `Set`

as a list. The order of the returned elements is
undefined.

Returns the merged (union) set of the list of sets.

Returns the merged (union) set of `Set1`

and `Set2`

.

# Types

# Functions

Returns a new set formed from `Set1`

with `Element`

inserted.

Returns `Set1`

, but with `Element`

removed.

-spec filter(Pred, Set1) -> Set2 when Pred :: fun((Element) -> boolean()), Set1 :: set(Element), Set2 :: set(Element).

Filters elements in `Set1`

with boolean function `Pred`

.

-spec filtermap(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> boolean() | {true, Element2}), Set1 :: set(Element1), Set2 :: set(Element1 | Element2).

Filters and maps elements in `Set1`

with function `Fun`

.

-spec fold(Function, Acc0, Set) -> Acc1 when Function :: fun((Element, AccIn) -> AccOut), Set :: set(Element), Acc0 :: Acc, Acc1 :: Acc, AccIn :: Acc, AccOut :: Acc.

Folds `Function`

over every element in `Set`

and returns the final value of the
accumulator. The evaluation order is undefined.

-spec from_list(List) -> Set when List :: [Element], Set :: set(Element).

Returns a set of the elements in `List`

.

-spec from_list(List, [{version, 1..2}]) -> Set when List :: [Element], Set :: set(Element).

Returns a set of the elements in `List`

at the given version.

Returns the intersection of the non-empty list of sets.

-spec intersection(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).

Returns the intersection of `Set1`

and `Set2`

.

Returns `true`

if `Set1`

and `Set2`

are disjoint (have no elements in common),
otherwise `false`

.

Returns `true`

if `Element`

is an element of `Set`

, otherwise `false`

.

Returns `true`

if `Set`

is an empty set, otherwise `false`

.

Returns `true`

if `Set1`

and `Set2`

are equal, that is when every element of one
set is also a member of the respective other set, otherwise `false`

.

Returns `true`

if `Set`

appears to be a set of elements, otherwise `false`

.

Note that the test is shallow and will return `true`

for any term that coincides with
the possible representations of a set. See also note on data types.

Returns `true`

when every element of `Set1`

is also a member of `Set2`

,
otherwise `false`

.

-spec map(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> Element2), Set1 :: set(Element1), Set2 :: set(Element2).

Maps elements in `Set1`

with mapping function `Fun`

.

Returns a new empty set.

Returns a new empty set at the given version.

-spec size(Set) -> non_neg_integer() when Set :: set().

Returns the number of elements in `Set`

.

-spec subtract(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).

Returns only the elements of `Set1`

that are not also elements of `Set2`

.

-spec to_list(Set) -> List when Set :: set(Element), List :: [Element].

Returns the elements of `Set`

as a list. The order of the returned elements is
undefined.

Returns the merged (union) set of the list of sets.

-spec union(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).

Returns the merged (union) set of `Set1`

and `Set2`

.