// Peano numbers
object Natural
{
  abstract class Nat
  {
    def isZero: Boolean
    def predecessor: Nat
    def successor = new Succ(this)
    def + (that: Nat): Nat
    def - (that: Nat): Nat
  }


  object Zero extends Nat
  {
    def isZero = true
    def predecessor = throw new Error("0.predecessor")
    def + (that: Nat) = that
    def - (that: Nat) = if (that.isZero) this else throw new Error("negative number")
  }

  class Succ(n: Nat) extends Nat
  {
    def isZero = false
    def predecessor = n
    def + (that: Nat) = new Succ(n + that)
    def - (that: Nat) = if (that.isZero) this else n - that.predecessor
  }

  def run = {
    println("Natural")
  }
}