You can also look at the Scala implementations if you like. Scala has HKTs so you can write it all directly.

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

   trait Applicative[F[_]] extends Functor[F] {
     def pure[A](a: A): F[A]
     def apply[A, B](f: F[A => B])(x: F[A]): F[B]
     def product[A, B](xa: F[A], xb: F[B]): F[(A, B)]
   }

   trait Monad[F[_]] extends Applicative[F] {
     def bind[A, B](f: A => F[B])(x: F[A]): F[B]
     def join[A](x: F[F[A]]): F[A]
   }