Nat.scala

package week4

//Peano Numbers
abstract class Nat {
  def isZero: Boolean
  def predecessor: Nat
  def successor: Nat = new NonZero(this) //holds no matter if Zero or NonZero
  def + (that: Nat): Nat
  def - (that: Nat): Nat
}
//Zero Natural Numbers
object Zero extends Nat {
  def isZero: Boolean = true
  def predecessor: Nat = throw new NoSuchElementException("Zero has no predecessor")

  def + (that: Nat): Nat = that
  def - (that: Nat): Nat = {
    if(that.isZero) this
    else throw new Error("Cannot substract to get negative")
  }
  override def toString = "0"
}
//NonZero Natural Numbers
class NonZero(n: Nat) extends Nat {
  def isZero: Boolean = false
  def predecessor: Nat = n

  def + (that: Nat): Nat =  new NonZero(this + that)
  def - (that: Nat): Nat = {
    if(that.isZero) this
    else n - that.predecessor //this is the same as (this - that) because n = this.predessor
  }
    override def toString = {
    def count(n: Nat, ct: Int): Int = n.isZero match {
      case true => ct
      case false => count(n.predecessor, ct+1)
    }
    ""+count(this, 0)
  }
}

object NonZero {
  def apply[T](x: Nat): Nat = new NonZero(x)
  
  def main(args: Array[String]) = {
    println(Zero)
    println(NonZero(NonZero(Zero)))
  }
}