more SK

[xacid]

import cats._
import cats.data._
import cats.implicits._
import scala.concurrent._
import duration.Duration._
import ExecutionContext.Implicits.global

object Sk extends App {
  val PLUS = ((_: Int) + (_: Int)).curried

  trait SK[F[_]] {
    def S[E, A, B]: Kleisli[F, E, A => B] =>
      Kleisli[F, E, A] => Kleisli[F, E, B]

    def K[E, A]: (E => A) => Kleisli[F, E, E => A]

    def I[A]: Kleisli[F, A, A]
  }

  object SK {
    def apply[F[_] : SK] = implicitly[SK[F]]
  }

  implicit def ska[F[_] : Applicative]: SK[F] =
    new SK[F] {
      def AP[E] = Applicative[Kleisli[F, E, ?]]

      def S[E, A, B] = AP[E].ap[A, B]

      def K[E, A] = AP[E].pure[E => A]

      def I[A] = Kleisli.ask[F, A]
    }

  def answer[F[_] : SK] = {
    val sk = SK[F]
    import sk._
    S(S(K(PLUS))(I))(I)
  }

  def main[F[_] : SK : Functor] =
    answer[F].map(println)

  main[Id].apply(21)
  Await.ready(main[Future].apply(21), Inf)

}