w5

nat.sc

abstract class Nat {
  def isZero: Boolean
  def predecessor: Nat
  def successor: Nat
  def +(that: Nat): Nat
  def -(that: Nat): Nat
}

object Zero extends Nat {
  def isZero: Boolean = true
  def predecessor: Nat = throw new NoSuchElementException()
  def successor: Nat = new Succ(this)
  def +(that: Nat): Nat = that
  def -(that: Nat): Nat =
    if (that.isZero) Zero else throw new NoSuchElementException()
  override def toString(): String = "zero"
}

class Succ(n: Nat) extends Nat {
  def isZero: Boolean = false
  def predecessor: Nat = n
  def successor: Nat = new Succ(this)
  def +(that: Nat): Nat =
    n + that.successor
  def -(that: Nat): Nat =
    if (that.isZero) this else n - that.predecessor
  override def toString(): String = predecessor + "->*"
}

val one = new Succ(Zero)
val two = new Succ(one)
val three = new Succ(two)
println(three + two)