The subject says it all really.  The :d, :f and :E argument specifiers
don't seem to be described anywhere.  If done as :w macros, I'd perhaps
have \exp_twice:w for \exp_not:d and \exp_first_once:w for \exp_not:E.
I've no idea about \exp_not:f as it is not really explained (I can see
\exp_stop_f: and \tlist_head_iii:f as the only other examples of this
Joseph Wright