Never took off? In addition to the other replies, look at Mathematica/Wolfram Language where they are _the_ syntax:

    f[1, 2, 3]

And we can index it

    Part[f[1, 2, 3], 1] == 1

Now what would the 0th element be?

    Part[f[1, 2, 3], 0] == f

It is “head” or what corresponds to the first element in cons lists.

Also, as an appendix, there is no reason why you can’t have a “high-level” syntax and an abstract syntax which can both coexist. Mathematica has a syntax which can get quite cryptic (almost APL like at times), but it is possible to ask “freeze” expressions and print out the full m-expression form and thus inspect the structure of a function or similar.