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

You can partially apply an infix operator from either side. For commutative operators such as +, it doesn't matter if you say (+ 1) or (1 +), but for example for division you can supply either the dividend (5 /) or the divisor (/ 5).

The function application operator takes a function as the left-hand operand and a parameter as the right-hand operand (f $ x), so you can partially apply it either with a function (f $) or with a parameter ($ x). So given

($ 4) (> 3)

You first partially apply the $-operator with the parameter 4 and supply it with the function (> 3). So what this essentially becomes is

(> 3) $ 4

Which is the same as (4 > 3).