test.scala

test.scala

import scala.language.higherKinds

object Test {

  // Functors
  trait Functor[F[_]] {
    def fmap[A, B](fa: F[A])(f: A => B): F[B]
  }
  implicit def OptionFunctor: Functor[Option] = new Functor[Option] {
    def fmap[A, B](fa: Option[A])(f: A => B) = fa map f
  }
  implicit def Tuple2Functor[C]: Functor[({type λ[α] = Tuple2[C, α]})#λ] = new Functor[({type λ[α] = Tuple2[C, α]})#λ] {
    def fmap[A, B](fa: (C, A))(f: A => B) = (fa._1, f(fa._2))
  }
  implicit def ListFunctor: Functor[List] = new Functor[List] {
    def fmap[A, B](fa: List[A])(f: A => B) = fa map f
  }

  // Functor Composition
  class Compose[F[_]: Functor, G[_]: Functor, A](val unCompose: F[G[A]])(implicit val F: Functor[F], implicit val G: Functor[G]) extends Functor[({type λ[α] = Compose[F, G, α]})#λ] {
    def fmap[A, B](composed: Compose[F, G, A])(f: A => B) =
      // new Compose(F.fmap(composed.unCompose)(G.fmap(_)(f)))(F, G, F, G)
      compose(F.fmap(composed.unCompose)(G.fmap(_)(f)))(F, G)
  }
  def compose[F[_]: Functor, G[_]: Functor, A](unCompose: F[G[A]]): Compose[F, G, A] =
    new Compose(unCompose)

  // The fixed-point of a Functor
  class Fix[F[_]: Functor](val unFix: F[Fix[F]])(implicit val F: Functor[F]) {
    def cata[A](fixed: Fix[F])(phi: F[A] => A): A = {
      phi(F.fmap(fixed.unFix)(cata(_)(phi)))
    }
  }
  def fix[F[_]: Functor](f: F[Fix[F]]): Fix[F] = new Fix(f)

}

Thanks to /u/real_huitz for help!