Scala Variances, Upper type Bounds and Lower type bounds

Filed Under: Scala

Variance refers as how subtyping between complex types relates to subtypes of their components. Scala supports variances annotations of type parameters of a generic class.

The type of variance annotations supported in Scala are;

TypesDefinitionScala Notation
CovariantC[T’] is a subclass of C[T][+T]
ContravariantC[T] is a subclass of C[T’][-T]
InvariantC[T] and C[T’] are not related[T]

class Array[+X] {
  def add[Y >: X](elem: Y): Array[Y] = new Array[Y] {
    override def first: Y = elem
    override def retrieve: Array[Y] = Array.this
    override def toString() = elem.toString() + "\n" + Array.this.toString()
  def first: X = sys.error("No elements in the Array")
  def retrieve: Array[X] = sys.error("Array is empty")
  override def toString() = ""
object ArrayTest extends App {

  var a: Array[Any] = new Array().add("US");
  //a = a.add(new Object())
  a = a.add(56)
  a = a.add(67.89)
  println("Array elements added are: " + a)


The annotation +X indicates that X can be used in covariant positions only. The annotation -X indicates that X can be used in contravariant positions only. Array[X] is a subtype of S if X is a subtype of S.

In this example we are defining a covariant type parameter X to define the method add. We have a polymorphic method in which we use the element type X as a lower bound of add method type variable thereby bringing the variance of X in sync with its declaration as covariant parameter. We are inserting elements of String,Integer and float types.

Upper type Bounds

An upper type bound X <: B declares that type variable X refers to a subtype of type B.

Consider an example below.

trait Employee {
  def EmployeeIdexists(x: Any): Boolean

case class EId(a: Int) extends Employee {
  def EmployeeIdexists(x: Any): Boolean =
    x.isInstanceOf[EId] &&
      x.asInstanceOf[EId].a == a

object TestEmployee extends App {
  def findEId[A <: Employee](d: A, ls: List[A]): Boolean =
    if (ls.isEmpty) false
    else if (d.EmployeeIdexists(ls.head)) true
    else findEId[A](d, ls.tail)
  val elist: List[EId] = List(EId(25), EId(26), EId(27), EId(28))
  if ((findEId[EId](EId(28), elist)))
    println("Employee Id exists")
  else println("Employee Id does not exist")


This example find whether the employee id exists or not. We are defining a method findEId which creates an integer list and checks whether the id specified is contained in the list.


Lower type Bounds

The term X >: B expresses that the type parameter X or the abstract type X refer to a supertype of type B. Lower type bounds declare a type to be a supertype of another type.

Create the scala class ListNode as;

case class ListNode[+T](h: T, t: ListNode[T]) {
  def head: T = h
  def tail: ListNode[T] = t
  def prepend[U >: T](elem: U): ListNode[U] =
    ListNode(elem, this)

We are creating a class ListNode and defining the prepend method where T only appears in covariant positions. U >: T specifies the abstract type U is a supertype of T.

The type variable T appears as a parameter type of method prepend, this rule is broken. With the help of a lower type bound, though, we can implement a prepend method.

Now create a scala object as;

object LowerBoundTest extends App {

  val empty: ListNode[Null] = ListNode(null, null)
  val strList: ListNode[String] = empty.prepend("hello")
  val anylist: ListNode[Any] = strList.prepend(12345)


That’s all for now, we will look into more scala features in future posts.

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