epfl_wk4_2.scala

// Peano numbers

abstract class Nat {
  def isZero: Boolean
  def predecessor: Nat
  def successor: Nat = 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 is negative")
  def + (that: Nat) = that
  def - (that: Nat) = if (that.isZero) this else throw new Error("0.- is negative")
}

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