Gaining Intuition for Reader

[Kevin Meredith]

I'm working on the `Apply.hs` exercise.

I don't have a good intuition for how to define `Apply`. 

instance Apply ((->) t) where

  (<*>) ::

    ((->) t (a -> b))

    -> ((->) t a)

    -> ((->) t b)

  (<*>) = error "todo"

What's the meaning of ((->) t (a -> b))?

If you could please give me some intuition.

[Luis Fernando Milano Oliveira]

Hello, Kevin.

I'm also working through the course, currently I'm working on the "StateT.hs" exercises, so I've been where you are.

About your question, the first thing to notice is that '((->) t' is nothing more than the function type constructor partially applied to some value 't'.
It is in prefix notation, but we could think about that signature this way(although it's syntactically incorrect):
(<*>) :: (t -> (a -> b)) -> (t -> a) -> (t -> b)

So, the first argument you have (t -> (a ->b)) is a function that takes a 't' argument and gives another function, (a -> b), back.
The second argument (t -> a) is a function that also takes a 't' as argument and fives a 'a' back (tip: it's the same 't' the first function took).

If you remember the signature for function composition -  (.) - it goes like this:
(.) :: (b -> c) -> (a ->b) -> (a -> c)
It's somewhat similar to that from apply (<*>).

From this I think you could gain some intuition and work on your solution.

I hope this helps!

[Kevin Meredith]

That answered helped me out a lot. Thanks!