Why is `($ 4) (> 3)` equivalent to `4 > 3`?

Question

I noticed as I was playing around with Haskell today that it is possible to do something like

($ 4) (> 3)

which yields True

Answer 1

($ 4) is what's called a section. It's a way of partially applying an infix operator, but providing the right-hand side instead of the left. It's exactly equivalent to (flip ($) 4).

Similarly, (> 3) is a section.

($ 4) (> 3)

can be rewritten as

(flip ($) 4) (> 3)

which is the same as

flip ($) 4 (> 3)

which is the same as

(> 3) $ 4

And at this point, it should be clear that this boils down to (4 > 3).