The function checks if the word is valid given an arity n$,$ that is$,$ it satisfies the following inductive

definition:

$$ a symbol, with spaces allowed at both ends, is a valid word.

$$ a word of the form s$($w$1,...,$ wn$)$ with s denoting a symbol and w$1,...,$ wn denoting valid words,

with spaces allowed at both ends and around parentheses and commas, is a valid word.