Applicative functor

Because Maybe is a Functor, we can lift the (+2) function so that it can be applied directly to a Maybe value (Just or Nothing):

  fmap (+2) (Just 3)

However, fmap does not enable us to apply a function to multiple Functor values:

  fmap (+) (Just 2) (Just 3)

For that, we need the Applicative Functor type-class, which enables us to raise a function to act on multiple Functor values:

–- Applicative inherits from Functor
class (Functor f) => Applicative f where
  pure  :: a -> f a
  (<*>) :: f (a -> b) -> f a -> f b

The pure function lifts a value into the Functor type­class while the <*> operator generalizes function application to Functor (hence the term Applicative Functor). Let's see how this works by making Maybe' an instance of Applicative:

import Control.Applicative

data Maybe' a = Just' a | Nothing'
  deriving (Show)

–- we still need the Functor instance
instance Functor Maybe' where
  fmap _ Nothing' =   Nothing'
  fmap f (Just' x) = Just...