This is a horrible idea. This means I can't read Tool::Box::func( LIST ) and can't know from reading the function name whether it returns the function-appropriate result or an accumulator function. It also means that once I've understood that I'm going to get an average (or whatever), that if I read the function name somewhere else, it doesn't necessarilly mean the same thing.

The function in different modes must have different names. You're just making obfuscated code otherwise.