Applicative exercise

Applicative.scala

object Applicative {
  // pick any monad, I have picked Option for you
  type F[A] = Option[A]

  // Applicative primitive given concrete
  // AKA point, pure, return
  def lift0[A](a: A): F[A] =
    Some(a)

  // Applicative primitive given concrete
  // AKA <*>
  def ap[A, B](f: F[A => B]): F[A] => F[B] =
    a => f flatMap (ff => a map (ff(_)))
  
  // Implement using lift0 + ap
  // AKA map
  def lift1[A, B](f: A => B): F[A] => F[B] =
    sys.error("todo")

  // Implement using:
  // lift1 + ap
  def lift2[A, B, C](f: A => B => C): F[A] => F[B] => F[C] =
    sys.error("todo")

  // Implement using:
  // lift2 + ap
  def lift3[A, B, C, D](f: A => B => C => D): F[A] => F[B] => F[C] => F[D] =
    sys.error("todo")

  // Implement using:
  // lift3 + ap
  def lift4[A, B, C, D, E](f: A => B => C => D => E): F[A] => F[B] => F[C] => F[D]  => F[E] =
    sys.error("todo")

  // Implement using:
  // lift4 + ap
  def lift5[A, B, C, D, E, G](f: A => B => C => D => E => G): F[A] => F[B] => F[C] => F[D]  => F[E] => F[G] =
    sys.error("todo")

  // lift6, lift7, etc.

}