How does get function typecheck in lens

Question

I have been reading this post to understand lens. They initially define a type synonym like this:

type RefF a b = forall f. Functor f => (b -> f b) -> (a -> f a)

Const is defined like this:

newtype Const a b = Const { getConst :: a }

How does the get function typecheck:

get :: RefF a b -> a -> b
get r = getConst . r Const

The type of getConst is something like this:

getConst :: Const a b -> a

The type of r Const which I guess is something like this:

r Const = (b -> f b) -> (Const -> f Const)

Then how does both getConst and r Const get's composed to give a -> b?

Answer 1

The type of r is obtained by substituting the const functor for f; since we'll need a b result that has to be the first argument (only x is actually found in the Const x y type)

    r :: (b -> Const b b) -> (a -> Const b a)

Now the argument is simple: that's merely the Const constructor.

    r Const :: a -> Const b a

And if you post-compose that with getConst :: Const b a -> b, you end up with

    getConst . r Const :: a -> b