When and why should one use Applicative Functors in Scala

Question

I know that Monad can be expressed in Scala as follows:

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

Answer 1

Functor is for lifting computations to a category.

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

And it works perfectly for a function of one variable.

val f = (x : Int) => x + 1

But for a function of 2 and more, after lifting to a category, we have the following signature:

val g = (x: Int) => (y: Int) => x + y
Option(5) map g // Option[Int => Int]

And it is the signature of a applicative functor. And to apply the following value to a function g — an aplicative functor is needed.

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

And finally:

(Applicative[Option] apply (Functor[Option] map g)(Option(5)))(Option(10))

Applicative functor is a functor for applying a special value (value in category) to a lifted function.