yoneda.scala

package yoneda
import language.higherKinds
import scalaz._
import Scalaz._

/**
 * A => ? to F is nature transformation, encoded as ~>[(A => ?), F]
 * f and g are the witness of the fact that:
 * the nature transformation of A => ? to F is isomorphic to F[A]  
 */
object Lemma {
  def f[F[_], A, R](k: ~>[(A => ?), F]): F[A] = k(identity)
  def g[F[_]: Functor, A](fa: F[A]): ~>[(A => ?), F] = new ~>[(A => ?), F] {
    def apply[R](aa: A => R): F[R] = fa.map(aa)
  }
}