Lab 4. Algebraic Datatype definition

Consider the following type defined to represent natural numbers:

trait Nat 
case object Zero extends Nat
case class Succ(n: Nat) extends Nat

4.1.1. Implement the following function:

def isZero(n: Nat): Nat = 
   n match {
       case Zero => ???
       case Succ(np) => ???
   }

4.1.2. Implement the addition function over natural numbers:

def add(n: Nat, m: Nat): Nat = 
   n match {
       case Zero => ???
       case Succ(np) => ???
   }

4.1.3. Implement the subtraction function over natural numbers. If $ n > m$ then $ m - n = 0$ .

def subtract(n: Nat, m: Nat): Nat = ???