Haskell Cookbook

How it works...

The Applicative must follow these laws: 

• Identity Law: An application of identity should not change the data:

        pure id <*> v == v

• Homomorphism: An application of a function to a data (f x) is equivalent to the application of Applicative of the function applied to pure data (data inducted in Applicative):

       pure f <*> pure x == pure (f x)

• Interchange: This is equivalent to saying that  f (a -> b) -> f a == f b, which should be equivalent to f ((a -> b) -> b) -> f (a -> b) == f b:

       u <*> pure y = pure ($ y) <*> u

• Composition: Stipulates that an Applicative compose operator is similar to the function composition (.): 

       pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

Here, the application of the composition pure (.) <*> u ...