User blog comment:MilkyWay90/Finishing my very first notation - The Generalized Factorial/@comment-35470197-20190710234255/@comment-35470197-20190711225628

> \(F\) will be used to refer to any array notation where the exclamation mark is significant.

I could not understand the meaning. You meant that \(!\) does not appear in valid expression in \(F\), right?

> \(F_!(l!,!,l!), F_!(@,n,l!,@)\), and so on

The same symbols appearing in a a single equality is supposed to be the same value. Therefore you need to write something like \(F_!(@_1,n,l!,@_2)\) instead of \(F_!(@,n,l!,@)\).

> \(F_!(l!,1,l!) = F(l!,1,l!)\)


 * 1) If \(!\) does not appears in a valid expression in \(F\), then \(F\) is a typo of \(F_!\). Then You need an additional rule \(F_!(l) = F(l)\).
 * 2) If \(!\) appears in a valid expression in \(F\), then the rule includes non-unique division into substrings.