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105 changes: 90 additions & 15 deletions _tour/variances.md
Original file line number Diff line number Diff line change
Expand Up @@ -12,55 +12,99 @@ redirect_from: "/tutorials/tour/variances.html"

Variance lets you control how type parameters behave with regards to subtyping. Scala supports variance annotations of type parameters of [generic classes](generic-classes.html), 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.

{% tabs variances_1 %}
{% tab 'Scala 2 and 3' for=variances_1 %}
```scala mdoc
class Foo[+A] // A covariant class
class Bar[-A] // A contravariant class
class Baz[A] // An invariant class
```
{% endtab %}
{% endtabs %}

### Invariance

By default, type parameters in Scala are invariant: subtyping relationships between the type parameters aren't reflected in the parameterized type. To explore why this works the way it does, we look at a simple parameterized type, the mutable box.

{% tabs invariance_1 %}
{% tab 'Scala 2 and 3' for=invariance_1 %}
```scala mdoc
class Box[A](var content: A)
```
{% endtab %}
{% endtabs %}

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

{% tabs invariance_2 class=tabs-scala-version %}
{% tab 'Scala 2' for=invariance_2 %}
```scala mdoc
abstract class Animal {
def name: String
}
case class Cat(name: String) extends Animal
case class Dog(name: String) extends Animal
```
{% endtab %}
{% tab 'Scala 3' for=invariance_2 %}
```scala
abstract class Animal:
def name: String

case class Cat(name: String) extends Animal
case class Dog(name: String) extends Animal
```
{% endtab %}
{% endtabs %}

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:

{% tabs invariance_3 %}
{% tab 'Scala 2 and 3' for=invariance_3 %}
```scala mdoc
val myAnimal: Animal = Cat("Felix")
val myAnimal: Animal = Cat("Felix")
```
{% endtab %}
{% endtabs %}

What about boxes? Is `Box[Cat]` a subtype of `Box[Animal]`, like `Cat` is a subtype of `Animal`? At first sight, it looks like that may be plausible, but if we try to do that, the compiler will tell us we have an error:

{% tabs invariance_4 class=tabs-scala-version %}
{% tab 'Scala 2' for=invariance_4 %}
```scala mdoc:fail
val myCatBox: Box[Cat] = new Box[Cat](Cat("Felix"))
val myAnimalBox: Box[Animal] = myCatBox // this doesn't compile
val myAnimal: Animal = myAnimalBox.content
```
{% endtab %}
{% tab 'Scala 3' for=invariance_4 %}
```scala
val myCatBox: Box[Cat] = new Box[Cat](Cat("Felix"))
val myAnimalBox: Box[Animal] = myCatBox // this doesn't compile
val myAnimal: Animal = myAnimalBox.content
val myCatBox: Box[Cat] = Box[Cat](Cat("Felix"))
val myAnimalBox: Box[Animal] = myCatBox // this doesn't compile
val myAnimal: Animal = myAnimalBox.content
```
{% endtab %}
{% endtabs %}

Why could this be a problem? We can get the cat from the box, and it's still an Animal, isn't it? Well, yes. But that's not all we can do. We can also replace the cat in the box with a different animal

{% tabs invariance_5 %}
{% tab 'Scala 2 and 3' for=invariance_5 %}
```scala
myAnimalBox.content = Dog("Fido")
```
{% endtab %}
{% endtabs %}

There now is a Dog in the Animal box. That's all fine, you can put Dogs in Animal boxes, because Dogs are Animals. But our Animal Box is a Cat Box! You can't put a Dog in a Cat box. If we could, and then try to get the cat from our Cat Box, it would turn out to be a dog, breaking type soundness.

{% tabs invariance_6 %}
{% tab 'Scala 2 and 3' for=invariance_6 %}
```scala
val myCat: Cat = myCatBox.content //myCat would be Fido the dog!
```
{% endtab %}
{% endtabs %}

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

Expand All @@ -70,18 +114,31 @@ The problem we ran in to above, is that because we could put a Dog in an Animal

But what if we couldn't put a Dog in the box? Then we could just get our Cat back out and that's not a problem, so than it could follow the subtyping relationship. It turns out, that's indeed something we can do.

{% tabs covariance_1 class=tabs-scala-version %}
{% tab 'Scala 2' for=covariance_1 %}
```scala mdoc
class ImmutableBox[+A](val content: A)
val catbox: ImmutableBox[Cat] = new ImmutableBox[Cat](Cat("Felix"))
val animalBox: ImmutableBox[Animal] = catbox // now this compiles
class ImmutableBox[+A](val content: A)
val catbox: ImmutableBox[Cat] = new ImmutableBox[Cat](Cat("Felix"))
val animalBox: ImmutableBox[Animal] = catbox // now this compiles
```
{% endtab %}
{% tab 'Scala 3' for=covariance_1 %}
```scala
class ImmutableBox[+A](val content: A)
val catbox: ImmutableBox[Cat] = ImmutableBox[Cat](Cat("Felix"))
val animalBox: ImmutableBox[Animal] = catbox // now this compiles
```
{% endtab %}
{% endtabs %}

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

More formally, that gives us the following relationship: given some `class Cov[+T]`, then if `A` is a subtype of `B`, `Cov[A]` is a subtype of `Cov[B]`. This allows us to make very useful and intuitive subtyping relationships using generics.

In the following less contrived example, the method `printAnimalNames` will accept a list of animals as an argument and print their names each on a new line. If `List[A]` were not covariant, the last two method calls would not compile, which would severely limit the usefulness of the `printAnimalNames` method.

{% tabs covariance_2 %}
{% tab 'Scala 2 and 3' for=covariance_2 %}
```scala mdoc
def printAnimalNames(animals: List[Animal]): Unit =
animals.foreach {
Expand All @@ -97,22 +154,40 @@ printAnimalNames(cats)
// prints: Fido, Rex
printAnimalNames(dogs)
```
{% endtab %}
{% endtabs %}

### Contravariance

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? This situation arises if we have something like a serializer, that takes values of type A, and converts them to a serialized format.

{% tabs contravariance_1 class=tabs-scala-version %}
{% tab 'Scala 2' for=contravariance_1 %}
```scala mdoc
abstract class Serializer[-A] {
def serialize(a: A): String
}
abstract class Serializer[-A] {
def serialize(a: A): String
}

val animalSerializer: Serializer[Animal] = new Serializer[Animal] {
def serialize(animal: Animal): String = s"""{ "name": "${animal.name}" }"""
}
val catSerializer: Serializer[Cat] = animalSerializer
catSerializer.serialize(Cat("Felix"))
val animalSerializer: Serializer[Animal] = new Serializer[Animal] {
def serialize(animal: Animal): String = s"""{ "name": "${animal.name}" }"""
}
val catSerializer: Serializer[Cat] = animalSerializer
catSerializer.serialize(Cat("Felix"))
```
{% endtab %}
{% tab 'Scala 3' for=contravariance_1 %}
```scala
abstract class Serializer[-A]:
def serialize(a: A): String

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

val catSerializer: Serializer[Cat] = animalSerializer
catSerializer.serialize(Cat("Felix"))
```
{% endtab %}
{% endtabs %}

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.

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