type-level FizzBuzz

gistfile1.scala

trait Nat {
  type IsZero <: Bool
  type Prev <: Nat
  type Divisable[A <: Nat] = DivisableImpl[A, A]
  type DivisableImpl[A <: Nat, B <: Nat] <: Bool
}

trait Z extends Nat {
  type IsZero = True
  type Prev = Nothing
  type DivisableImpl[A <: Nat, B <: Nat] = B#IsZero
}

trait S[N <: Nat] extends Nat {
  type IsZero = False
  type Prev = N
  type DivisableImpl[A <: Nat, B <: Nat] = B#IsZero#If[Bool, N#DivisableImpl[A, A#Prev], N#DivisableImpl[A, B#Prev]]
}

trait FizzBuzzBase extends Nat {
  type IsZero = Nothing
  type Prev = Nothing
  type DivisableImpl[A <: Nat, B <: Nat] = Nothing
}

trait Fizz extends FizzBuzzBase
trait Buzz extends FizzBuzzBase
trait FizzBuzz extends FizzBuzzBase

type _0 = Z
type _1 = S[_0]
type _2 = S[_1]
type _3 = S[_2]
type _4 = S[_3]
type _5 = S[_4]
type _6 = S[_5]
type _7 = S[_6]
type _8 = S[_7]
type _9 = S[_8]
type _10 = S[_9]
type _11 = S[_10]
type _12 = S[_11]
type _13 = S[_12]
type _14 = S[_13]
type _15 = S[_14]

trait Bool {
  type If[Ty, T <: Ty, F <: Ty] <: Ty
}

trait True extends Bool {
  type If[Ty, T <: Ty, F <: Ty] = T
}

trait False extends Bool {
  type If[Ty, T <: Ty, F <: Ty] = F
}

trait Fun {
  type Apply[A <: Nat] <: Nat
}
  
trait List {
  type Map[F <: Fun] <: List
}
  
trait Nil extends List {
  type Map[F <: Fun] = Nil
}
  
trait ::[A <: Nat, L <: List] extends List {
  type Map[F <: Fun] = ::[F#Apply[A], L#Map[F]]
}

type NumList = _1 :: _2 :: _3 :: _4 :: _5 :: _6 :: _7 :: _8 :: _9 :: _10 :: Nil

type FizzBuzzList = _1 :: _2 :: Fizz :: _4 :: Buzz :: Fizz :: _7 :: _8 :: Fizz :: Buzz :: Nil

println(implicitly[
  NumList#Map[
    Fun {
      type Apply[A <: Nat] = A#Divisable[_15]#If[Nat, FizzBuzz, A#Divisable[_3]#If[Nat, Fizz, A#Divisable[_5]#If[Nat, Buzz, A]]]
    }
  ] =:= FizzBuzzList])