ApplicativeとApplicativeの合成

Applicative.scala

trait Applicative[F[_]] extends Functor[F] {
  // この2つが必要
  def point[A](a: A): F[A]
  def ap[A, B](a: F[A])(f: F[A => B]): F[B]

  // pureはpointのalias?
  def pure[A](a: A): F[A] = point(a)

  // 以下はap/pointを使って実装できるもの
  def apF[A,B](f: => F[A => B]): F[A] => F[B] = ap(_)(f)

  def apply2[A, B, C](fa: => F[A], fb: => F[B])(f: (A, B) => C): F[C] =
    ap(fb)(ap(fa)(point(f.curried)))

  def ap2[A,B,C](fa: => F[A], fb: => F[B])(f: F[(A,B) => C]): F[C] =
    ap(fb)(ap(fa)(map(f)(_.curried)))

  // mapはapとpointから実装できる
  def map[A, B](fa: F[A])(f: A => B): F[B] = ap(fa)(point(f))
}

composeApplicative.scala

def composeApplicative[F[_]: Applicative, G[_]: Applicative] = new Applicative[({ type f[x] = F[G[x]] })#f] {
  val F = implicitly[Applicative[F]]
  val G = implicitly[Applicative[G]]

  def point[A](a: A): F[G[A]] = F.point(G.point(a))
  def ap[A, B](a: F[G[A]])(f: F[G[A => B]]): F[G[B]] = F.apply2(a, f)((ga, g) => G.ap(ga)(g))
}

implicit val optionalApplicative = new Applicative[Option] {
  override def point[A](a: A) = Some(a)
  override def ap[A, B](a: Option[A])(f: Option[A => B]): Option[B] = f match {
    case Some(f) => a.map(f)
    case None => None
  }
}