Scala Type Level Programming: The Natural Numbers: Multiplication

type-level-programming-natural-numbers-mult.scala

sealed trait Nat {
  type mult[That <: Nat] <: Nat
}

sealed trait MsbZero extends Nat {
  override type mult[That <: Nat] = MsbZero
}

sealed trait MsbOne extends Nat {
  override type mult[That <: Nat] = That
}

sealed trait B0[HigherBits <: Nat] extends Nat {
  override type mult[That <: Nat] = HigherBits#mult[That]#dbl
}

sealed trait B1[HigherBits <: Nat] extends Nat {
  override type mult[That <: Nat] = HigherBits#mult[That]#dbl#add[That]
}