Scalaで型レベルfizzbuzz

import shapeless.Nat
import shapeless.nat._
import shapeless.ops.nat._

trait FizzBuzz[N <: Nat] {
  def apply(): String
}

object FizzBuzz extends FizzBuzzLowerPriorityImplicits {
  def apply[N <: Nat](implicit lt: LT[_0, N], fizzbuzz: FizzBuzz[N]): String = fizzbuzz()

  implicit def fizzbuzz[N <: Nat](implicit mod: Mod.Aux[N, _15, _0]): FizzBuzz[N] =
    new FizzBuzz[N] {
      def apply(): String = "FizzBuzz"
    }
}

trait FizzBuzzLowestPriorityImplicits {
  implicit def number[N <: Nat](implicit toInt: ToInt[N]): FizzBuzz[N] =
    new FizzBuzz[N] {
      def apply(): String = toInt().toString
    }
}

trait FizzBuzzLowerPriorityImplicits extends FizzBuzzLowestPriorityImplicits {
  implicit def fizz[N <: Nat](implicit mod: Mod.Aux[N, _3, _0]): FizzBuzz[N] =
    new FizzBuzz[N] {
      def apply(): String = "Fizz"
    }
  implicit def buzz[N <: Nat](implicit mod: Mod.Aux[N, _5, _0]): FizzBuzz[N] =
    new FizzBuzz[N] {
      def apply(): String = "Buzz"
    }
}

FizzBuzz[_2] // => "2"
FizzBuzz[_3] // => "Fizz"
FizzBuzz[_5] // => "Buzz"
FizzBuzz[_6] // => "Fizz"
FizzBuzz[_15] // => "FizzBuzz"