A simplified model for the natural numbers (Peano numbers), from week 4 of Functional Programming in Scala

gistfile1.scala

abstract class Nat {
  def isZero: Boolean
  def predecessor: Nat
  def successor: Nat = new Succ(this)
  def +(that: Nat): Nat
  def -(that: Nat): Nat =
    if (that.isZero)
      this
    else
      predecessor - that.predecessor
}

object Zero extends Nat {
  def isZero = true
  def predecessor = throw new NoSuchElementException
  def +(that: Nat) = that
}

class Succ(n: Nat) extends Nat {
  def isZero = false
  def predecessor = n
  def +(that: Nat) = new Succ(n + that)
}