fmap函数组成如何工作

Question

I am trying to understand how function composition works.

The common example is:

(.) :: (b -> c) -> (a -> b) -> a -> c  
f . g = \x -> f (g x)  

It is easy to understand, what a function composition is.

Now consider:

(fmap . fmap) (+5) (Just (Just 4))

Let's consider first fmap implementation:

fmap . fmap = \x -> fmap ( fmap x )

How does the example is going to execute?

Does fmap (+5) is going to execute first?

What is the x value in connection of the example?

Answer 1

(fmap . fmap) (+5) (Just (Just 4))
= { def. (.) }
fmap (fmap (+5)) (Just (Just 4))
= { fmap g (Just x) = Just (g x), where g = fmap (+5) ; x = Just 4 }
Just (fmap (+5) (Just 4))
= { fmap g (Just x) = Just (g x), where g = (+5) ; x = 4 }
Just (Just ((+5) 4))
= { def. (+) }
Just (Just 9)