Lower Type Bounds

While upper type bounds limit a type to a subtype of another type, lower type bounds declare a type to be a supertype of another type. The term B >: A expresses that the type parameter B or the abstract type B refer to a supertype of type A. In most cases, A will be the type parameter of the class and B will be the type parameter of a method.

Here is an example where this is useful:

trait List[+A] {
  def prepend(elem: A): NonEmptyList[A] = NonEmptyList(elem, this)
}

case class NonEmptyList[+A](head: A, tail: List[A]) extends List[A]

object Nil extends List[Nothing]

trait List[+A]:
  def prepend(elem: A): NonEmptyList[A] = NonEmptyList(elem, this)

case class NonEmptyList[+A](head: A, tail: List[A]) extends List[A]

object Nil extends List[Nothing]

This program implements a singly-linked list. Nil represents an empty list with no elements. class NonEmptyList is a node which contains an element of type A (head) and a reference to the rest of the list (tail). The trait List and its subtypes are covariant because we have +A.

However, this program does not compile because the parameter elem in prepend is of type A, which we declared covariant. This doesn’t work because functions are contravariant in their parameter types and covariant in their result types.

To fix this, we need to flip the variance of the type of the parameter elem in prepend. We do this by introducing a new type parameter B that has A as a lower type bound.

trait List[+A] {
  def prepend[B >: A](elem: B): NonEmptyList[B] = NonEmptyList(elem, this)
}

case class NonEmptyList[+A](head: A, tail: List[A]) extends List[A]

object Nil extends List[Nothing]

trait List[+A]:
  def prepend[B >: A](elem: B): NonEmptyList[B] = NonEmptyList(elem, this)

case class NonEmptyList[+A](head: A, tail: List[A]) extends List[A]

object Nil extends List[Nothing]

Now we can do the following:

trait Bird
case class AfricanSwallow() extends Bird
case class EuropeanSwallow() extends Bird

val africanSwallows: List[AfricanSwallow] = Nil.prepend(AfricanSwallow())
val swallowsFromAntarctica: List[Bird] = Nil
val someBird: Bird = EuropeanSwallow()

// assign swallows to birds
val birds: List[Bird] = africanSwallows

// add some bird to swallows, `B` is `Bird`
val someBirds = africanSwallows.prepend(someBird)

// add a swallow to birds
val moreBirds = birds.prepend(EuropeanSwallow())

// add disparate swallows together, `B` is `Bird` because that is the supertype common to both swallows
val allBirds = africanSwallows.prepend(EuropeanSwallow())

// but this is a mistake! adding a list of birds widens the type arg too much. -Xlint will warn!
val error = moreBirds.prepend(swallowsFromAntarctica)    // List[Object]

The covariant type parameter allows birds to get the value of africanSwallows.

The type bound on the type parameter for prepend allows adding different varieties of swallows and getting a wider type: instead of List[AfricanSwallow], we get a List[Bird].

Use -Xlint to warn if the inferred type arg is widened too much.