build.sbt

scalaVersion := "2.12.6"

addCompilerPlugin("org.spire-math" %% "kind-projector" % "0.9.7")

ContT.scala

package generic_cont_example

trait ~> [-F[_], +G[_]] {
  def run[A](fa: F[A]): G[A]
}

final case class ContT[M[_], A](x: λ[a => A => M[a]] ~> M) {

  def map[B](f: A => B): ContT[M, B] =
    ContT[M, B](
      λ[~>[λ[a => B => M[a]], M]].run(k =>
        x.run(a => k(f(a)))
      )
    )

  def flatMap[B](f: A => ContT[M, B]): ContT[M, B] =
    ContT[M, B](
      λ[~>[λ[a => B => M[a]], M]].run(k =>
        x.run(a => f(a).x.run(k))
      )
    )

  def run[R](f: A => M[R]): M[R] =
    x.run(f)
}