Question

when you split a list using x:xs syntax why is it wrapped in a parentheses? what is the significance of the parentheses? why not [x:xs] or just x:xs?

Answer 1

The cons cell doesn’t have to be parenthesized in every context, but in most contexts it is because

Function application binds tighter than any infix operator.

Burn this into your brain in letters of fire.

Example:

length [] = 0
length (x:xs) = 1 + length xs

If parentheses were omitted the compiler would think you had an argument x followed by an ill-placed infix operator, and it would complain bitterly. On the other hand this is OK

length l = case l of [] -> 0
                     x:xs -> 1 + length xs

In this case neither x nor xs can possibly be construed as part of a function application so no parentheses are needed.

Note that the same wonderful rule function application binds tighter than any infix operator is what allows us to write length xs in 1 + length xs without any parentheses. The infix rule giveth and the infix rule taketh away.