Yoneda Isomorphism between type A and the continuation/handler pattern

yoneda.scala

// Yoneda lemma
// - Yoneda Embedding is just another case of the lemma
// - implies that:
//      forall r . (a -> r) -> r ≅ a
//      Any type can be replaced (& back) by a continuation accepting a handler
trait Cont[A] {
  // handler which accepts a A and performs the rest of computation (like returningn a status R)
  def apply[R](handler: A => R): R
}

object Cont {
  def fromA[A](a: A) = new Cont[A] {
    def apply[R](handler: A => R): R = handler(a)
  }

  def toA[A](c: Cont[A]): A = c(identity)
}