Question

What are these operators doing?

(.) :: (b -> c) -> (a -> b) -> a -> c
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<*>) :: Applicative f => f (a -> b) -> f a -> f b

I don’t have any idea when I see the signatures. Perhaps some example with a simple and easy to understand explanation will help me.

Answer 1

I am also learning Haskell, and my recommendation is to have a look into Learn You a Haskell for Great Good!, and more precisely:

• for (.) read Function composition
• for <$> and <*> read Applicative functors

In essence:

• (.) is function composition: if you have g :: a -> b and f :: b -> c then f . g is essentially f(g(x)): first use g on an a to get a b and then use f on that b to get a c

• <$> takes a function taking an a and returning a b, and a functor that contains an a, and it returns a functor that contains a b. So <$> is the same as fmap :: (a -> b) -> f a -> f b

• <*> takes a functor that contains a function taking an a and returning a b, and a functor that contains an a, and it returns a functor that contains a b. So <*> kind of extract the function from a functor and applies it to an arguments also inside a functor, and finally returns the result into a functor

Note the explanations that you find in the book chapters are better than my attempt above