Scala Metaprogrammatic Hanoi's Tower Solver

hanoi.scala

object TowerOfHanoi {
  import scala.reflect.Manifest

  def name(manifest:Manifest[_]):String = {
    manifest.erasure.getName
  }

  trait NaturalNumber
  final class Zero extends NaturalNumber
  final class Successor[Previous<:NaturalNumber] extends NaturalNumber

  type One   = Successor[Zero]
  type Two   = Successor[One]
  type Three = Successor[Two]
  type Four  = Successor[Three]
  type Five  = Successor[Four]
  type Six   = Successor[Five]
  type Seven = Successor[Six]
  type Eight = Successor[Seven]
  type Nine  = Successor[Eight]
  type Ten   = Successor[Nine]

  case class Move[N<:NaturalNumber, Peg1, Peg2, Peg3]()
 
  implicit def move[Peg1, Peg2, Peg3](implicit peg1:Manifest[Peg1], peg2:Manifest[Peg2]):Move[Zero, Peg1, Peg2, Peg3] = { 
    System.out.println("Move from " + name(peg1) + " to " + name(peg2))
    null
  }
 
  implicit def prepare[COUNT<:NaturalNumber, Peg1, Peg2, Peg3](
    implicit move1:Move[COUNT, Peg1, Peg3, Peg2], move2:Move[ZERO, Peg1, Peg2, Peg3], move3:Move[COUNT, Peg3, Peg2, Peg1])
      :Move[Successor[COUNT], Peg1, Peg2, Peg3] = null
  
  def run[HEIGHT<:NaturalNumber, Peg1, Peg2, Peg3](implicit move:Move[HEIGHT, Peg1, Peg2, Peg3]) = null
  
  case class Left()
  case class Center()
  case class Right()
  
  def main(args:Array[String]){
    run[Ten, Left, Right, Center]
  }
}