ProtocolSwift

SetAlgebra

A type that provides mathematical set operations.

protocol SetAlgebra<Element> : Equatable, ExpressibleByArrayLiteral

Overview

You use types that conform to the SetAlgebra protocol when you need efficient membership tests or mathematical set operations such as intersection, union, and subtraction. In the standard library, you can use the Set type with elements of any hashable type, or you can easily create bit masks with SetAlgebra conformance using the OptionSet protocol. See those types for more information.

Conforming to the SetAlgebra Protocol

When implementing a custom type that conforms to the SetAlgebra protocol, you must implement the required initializers and methods. For the inherited methods to work properly, conforming types must meet the following axioms. Assume that S is a custom type that conforms to the SetAlgebra protocol, x and y are instances of S, and e is of type S.Element—the type that the set holds.

S() == []
x.intersection(x) == x
x.intersection([]) == []
x.union(x) == x
x.union([]) == x
x.contains(e) implies x.union(y).contains(e)
x.union(y).contains(e) implies x.contains(e) || y.contains(e)
x.contains(e) && y.contains(e) if and only if x.intersection(y).contains(e)
x.isSubset(of: y) implies x.union(y) == y
x.isSuperset(of: y) implies x.union(y) == x
x.isSubset(of: y) if and only if y.isSuperset(of: x)
x.isStrictSuperset(of: y) if and only if x.isSuperset(of: y) && x != y
x.isStrictSubset(of: y) if and only if x.isSubset(of: y) && x != y

Requirements

Associated Types

associatedtype Element
A type for which the conforming type provides a containment test.

Initializers

init()
Creates an empty set.
init<S>(S)
Creates a new set from a finite sequence of items.

Instance Properties

var isEmpty: Bool
A Boolean value that indicates whether the set has no elements.

Instance Methods

func contains(Self.Element) -> Bool
Returns a Boolean value that indicates whether the given element exists in the set.
func formIntersection(Self)
Removes the elements of this set that aren’t also in the given set.
func formSymmetricDifference(Self)
Removes the elements of the set that are also in the given set and adds the members of the given set that are not already in the set.
func formUnion(Self)
Adds the elements of the given set to the set.
func insert(Self.Element) -> (inserted: Bool, memberAfterInsert: Self.Element)
Inserts the given element in the set if it is not already present.
func intersection(Self) -> Self
Returns a new set with the elements that are common to both this set and the given set.
func isDisjoint(with: Self) -> Bool
Returns a Boolean value that indicates whether the set has no members in common with the given set.
func isSubset(of: Self) -> Bool
Returns a Boolean value that indicates whether the set is a subset of another set.
func isSuperset(of: Self) -> Bool
Returns a Boolean value that indicates whether the set is a superset of the given set.
func remove(Self.Element) -> Self.Element?
Removes the given element and any elements subsumed by the given element.
func subtract(Self)
Removes the elements of the given set from this set.
func subtracting(Self) -> Self
Returns a new set containing the elements of this set that do not occur in the given set.
func symmetricDifference(Self) -> Self
Returns a new set with the elements that are either in this set or in the given set, but not in both.
func union(Self) -> Self
Returns a new set with the elements of both this and the given set.
func update(with: Self.Element) -> Self.Element?
Inserts the given element into the set unconditionally.

Members

Instance Methods

func isStrictSubset(of: Self) -> Bool
Returns a Boolean value that indicates whether this set is a strict subset of the given set.
func isStrictSuperset(of: Self) -> Bool
Returns a Boolean value that indicates whether this set is a strict superset of the given set.

SetAlgebra

Overview

Conforming to the SetAlgebra Protocol

Refinements

Requirements

Associated Types

Initializers

Instance Properties

Instance Methods

Members

Instance Methods

Conforming Types

Implies