Mon Sep 7 19:24:19 JST 2015

object Main {

  sealed abstract class Nat
  case class Z() extends Nat
  case class S(x:Nat) extends Nat

  def add(x: Nat, y: Nat): Nat = (x, y) match {
    case (_, Z()) => x
    case (Z(), _) => y
    case (S(a), _) => add(a, S(y))
  }

  def mult(x: Nat, y: Nat): Nat = {
    def sub(x: Nat, y: Nat, sum: Nat): Nat = x match {
      case Z() => sum
      case S(a) => sub(a, y, add(y, sum))
    }
    sub(x, y, Z())
  }

  def main(args: Array[String]) {
    println(Z())
    println(S(S(Z()))) // automatically derived Show

    val one = S(Z())
    val two = S(S(Z()))
    val three = S(S(S(Z())))
    println(add(one, two))
    println(add(one, two) == three) // true

    println(mult(two, three)) // six

  }
}