Natural numbers implementation in scala

Nat.scala

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 = error("no predecessor")
    def + (that: Nat): Nat = that
    def - (that: Nat): Nat = 
        if (that == Zero) this
        else error("zero minus is not possible")
    override def toString = "0"
}

class Succ(n: Nat) extends Nat{
    def isZero = false
    def predecessor= n
    def - (that:Nat): Nat = 
        if (that == Zero) this
        else this.predecessor - that.predecessor
    def + (that:Nat): Nat =
        if (that == Zero) this
        else this.successor + that.predecessor
    override def toString = "1+" ++ this.predecessor.toString
}