Scala-Metaprogramming: Towers of Hanoi

TowersOfHanoi.scala

import shapeless.ops.hlist.Prepend
import shapeless.{::, HList, HNil, Nat, Succ}

object Hanoi {
  // influenced by : https://gist.github.com/jrudolph/66925 
  // in action : https://youtu.be/mc6c_sX-ESc

  case class Left()
  case class Center()
  case class Right()

  case class Move[N<:Nat,A,B,C,History <: HList]()
  
  implicit def move0[A,B,C]:Move[Nat._1,A,B,C, (A,B) :: HNil] = {
    null
  }
  implicit def moveN[P<:Nat,A,B,C, H1 <: HList, H2 <: HList, H3 <: HList, H2andH3<:HList, Out <: HList]
    (implicit m1:Move[P,A,C,B, H1],
     m2:Move[Nat._1,A,B,C,H2],
     m3:Move[P,C,B,A,H3],
     prependH2andH3: Prepend.Aux[H2,H3, H2andH3],
     prepend: Prepend.Aux[H1,H2andH3, Out])
  :Move[Succ[P],A,B,C, Out] = null

  def run[N<:Nat,A,B,C,H <: HList](n: N, a: A, b: B, c: C)(implicit m:Move[N,A,B,C,H]) : H = null.asInstanceOf[H]

  val a = run(new Nat._3, Left(), Right(), Center())
  // type is calculated by intellj as
  // val a: ::[(Left, Right), HNil] = run(new Nat._1, Left(), Right(), Center())
  // val b: ::[(Left, Center), ::[(Left, Right), ::[(Center, Right), HNil]]] = run(new Nat._2, Left(), Right(), Center())
  // val c: ::[(Left, Right), ::[(Left, Center), ::[(Right, Center), ::[(Left, Right), ::[(Center, Left), ::[(Center, Right), ::[(Left, Right), HNil]]]]]]] = run(new Nat._3, Left(), Right(), Center())

}