Lab 08: Polymorphism

Consider the following implementation of the type Nat, which you are well-familiar with:

trait Nat {
   def +(other: Nat): Nat
}
case object Zero extends Nat{
   override def +(other: Nat): Nat = other
}
case class Succ(n: Nat) extends Nat{
   override def +(other: Nat): Nat = Succ(n + other)
}

It might be the case that we would like to use nat values from different sources, e.g. fromInteger(1) + Zero + fromString(“2”). Keeping track of all different functions that convert other values to Nat might be tedious. A work-around is to: (1) define a companion object for Nat by creating a new object with the same name as Nat, in the same scala file (or worksheet).

object Nat { // a companion object for trait Nat 
 
}

We can now populate the companion objects with any methods we would like. In particular, we can add a method:

def apply(i: Int): Nat = ???

which can be called simply as: Nat(5). Also, we can (2) overload apply in order to support creating naturals with the call Nat(.) from different other types.

8.1. Create a companion object for Nat and add appropriate apply functions in order to make the expression Nat(1) + Zero + Nat(“2”) successfully compile and run.