Though it calculates function using “x^2 + y^2”,  it is better to write the name of it as the output of $x^2 + y^2$.
Is it possible to write  it as in mathematical form?

       functionstyle = "math”,

Is there any reason to use two different names “function” and “code” to define functions?

we can still decide as it's beta ...

 function | functions

or

 code | codelist

(it's basically lua code ...)

i have no preference and as you're the first to bring it up you may decide ... (unless others can convince you otherwise)