functor-cofunctor.scala

class Scratch

trait PartialApply1Of2[T[_, _], A] {
  type Apply[B] = T[A, B]
  type Flip[B] = T[B, A]
}

trait Cofunctor[F[_]] {
  def comap[A, B](r: F[A], f: B => A): F[B]
}

object Cofunctor {
  implicit def `(_ => X) ➝ Cofunctor`[X]: Cofunctor[PartialApply1Of2[Function1, X]#Flip] = new Cofunctor[PartialApply1Of2[Function1, X]#Flip] {
    def comap[A, B](r: A => X, f: B => A) = r compose f
  }
}

trait Functor[F[_]] {
  def fmap[A, B](a: F[A], f: A => B): F[B]
}

object Functor {
  implicit def `(X => _) ➝ Functor`[X]: Functor[PartialApply1Of2[Function1, X]#Apply] = new Functor[PartialApply1Of2[Function1, X]#Apply] {
    def fmap[A, B](r: X => A, f: A => B) = f compose r
  }

  implicit val ListFunctor: Functor[List] = new Functor[List] {
    def fmap[A, B](r: List[A], f: A => B) = r map f
  }
}

sealed trait MA[M[_], A] {
  val v: M[A]

  def ∙[B](f: B => A)(implicit t: Cofunctor[M]) = t.comap(v, f)

  def ∘[B](f: A => B)(implicit t: Functor[M]) = t.fmap(v, f)
}

trait MAsLow {
  def maImplicit[M[_], A](a: M[A]): MA[M, A] = new MA[M, A] {
    val v = a
  }
}

trait MAs extends MAsLow {
  def ma[M[_], A](a: M[A]): MA[M, A] = new MA[M, A] {
    val v = a
  }

  implicit def `(_ => A) ➝ MA`[A, R](f: R => A): MA[PartialApply1Of2[Function1, A]#Flip, R] = ma[PartialApply1Of2[Function1, A]#Flip, R](f)
  //
  implicit def `(R => _) ➝ MA`[A, R](f: A => R): MA[PartialApply1Of2[Function1, A]#Apply, R] = ma[PartialApply1Of2[Function1, A]#Apply, R](f)

  //   Seq[A] implements Function1[Int, A]. Without this, Function1FlipMA would be used.
  implicit def SeqMA[M[_] <: Seq[_], A](l: M[A]): MA[M, A] = ma[M, A](l)
}

////

object Example extends MAs {
  def main(args: Array[String]) {
    {
      val f: Int => Int = (3 +)

      println(List(1, 2, 3) ∘ f)

      // List(3, 4, 4, 5, 5)
      println(List(1, 2, 3, 4, 5) map (f ∙ ((_: Int) / 2)))
    }
  }
}