Comonad/Monad

gistfile1.scala

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

trait Extend[F[_]] extends Functor[F] {
  // coflatmap
  def extend[A, B](f: F[A] => B): F[A] => F[B]
}

trait Comonad[F[_]] extends Extend[F] {
  def copoint[A](a: F[A]): A
  override def fmap[A, B](f: A => B) =
    extend(q => f(copoint(q)))   
}

trait FlatMap[F[_]] extends Functor[F] { 
  def flatMap[A, B](f: A => F[B]): F[A] => F[B]
}

trait Monad[F[_]] extends FlatMap[F] {
  def point[A](a: A): F[A]
  override def fmap[A, B](f: A => B) =
    flatMap(q => point(f(q)))
}

case class Id[A](a: A)

object Comonad {
  val IdComonad: Comonad[Id] =
    new Comonad[Id] {
      def copoint[A](i: Id[A]) = i.a
      def extend[A, B](f: Id[A] => B) = 
        i => Id(f(i))
    }
}