Scala Variance

Intro

Variance lets you control how type parameters behave with regards to subtyping. Scala supports variance annotations of type parameters of generic classes, to allow them to be covariant, contravariant, or invariant if no annotations are used. The use of variance in the type system allows us to make intuitive connections between complex types.

Variance: If B Extends A, Should List[B] extend List[A] ?

Invariance

By default, type parameters in Scala are invariant: subtyping relationships between the type parameters aren’t reflected in the parameterized type.

trait List[A]

Example

class Box[A](var content: A)

We’re going to be putting values of type Animal in it. This type is defined as follows:

abstract class Animal {
  def name: String
}
case class Cat(name: String) extends Animal
case class Dog(name: String) extends Animal

We can say that Cat is a subtype of Animal, and that Dog is also a subtype of Animal. That means that the following is well-typed:

val myAnimal: Animal = Cat("Felix")

What about boxes? Is Box[Cat] a subtype of Box[Animal], like Cat is a subtype of Animal? 

val myCatBox: Box[Cat] = new Box[Cat](Cat("Felix"))
val myAnimalBox: Box[Animal] = myCatBox // this doesn't compile

Although this is valid

val myAnimal: Animal = myAnimalBox.content
myAnimalBox.content = Dog("Fido")

From this, we have to conclude that Box[Cat] and Box[Animal] can’t have a subtyping relationship, even though Cat and Animal do.

Covarience

The The problem we ran in to above, is that because we could put a Dog in an Animal Box, a Cat Box can’t be an Animal Box.

trait List[+A]

Example:

class ImmutableBox[+A](val content: A)
val catbox: ImmutableBox[Cat] = new ImmutableBox[Cat](Cat("Felix"))
val animalBox: ImmutableBox[Animal] = catbox // now this compiles

We say that ImmutableBox is covariant in A, and this is indicated by the + before the A.

Contravarience

We’ve seen we can accomplish covariance by making sure that we can’t put something in the covariant type, but only get something out. What if we had the opposite, something you can put something in, but can’t take out?

trait List[-A]

Example:

abstract class Serializer[-A] {
  def serialize(a: A): String
}

val animalSerializer: Serializer[Animal] = new Serializer[Animal] {
  def serialize(animal: Animal): String = s"""{ "name": "${animal.name}" }"""
}
val catSerializer: Serializer[Cat] = animalSerializer
catSerializer.serialize(Cat("Felix"))

We say that Serializer is contravariant in A, and this is indicated by the - before the A. A more general serializer is a subtype of a more specific serializer.

More formally, that gives us the reverse relationship: given some class Contra[-T], then if A is a subtype of B, Contra[B] is a subtype of Contra[A].

Bounded Types

The type of Variance would lead to have members defined with upper or lower bounded types like the following example.

class Car
class SuperCar extends Car
class Garage[T <: Car>](car: T)

More deatils on bounded values on the following articles:

Immutability and Variance

Immutability constitutes an important part of the design decision behind using variance. For example, Scala’s collections systematically distinguish between mutable and immutable collections. The main issue is that a covariant mutable collection can break type safety. This is why List is a covariant collection, while scala.collection.mutable.ListBuffer is an invariant collection.

Comparison With Other Languages

Variance is supported in different ways by some languages that are similar to Scala. Scala’s tendency towards immutable types makes it that covariant and contravariant types are more common than in other languages, since a mutable generic type must be invariant.

Reference