✎ fp2023:lab08 [books]

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====== Lab 08: Polymorphism =======

===== 8.1. Ad-hoc polymorphism =====

Consider the following implementation of the type ''Nat'', which you are well-familiar with:
<code scala>
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)
}

</code> 

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).

<code scala>
object Nat { // a companion object for trait Nat 

}
</code>

We can now populate the companion objects with any methods we would like. In particular, we can add a method:
<code>
def apply(i: Int): Nat = ???
</code>

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.

===== 8.2. Dictionaries =====