You're saying that the type system has something to do with functional programming.
I'm saying that if Scheme, LISP and Haskell are all functional languages, obviously the type system is besides the point -- they're radically different in that aspect. Functional programming is about functions.
I'd say Scheme and Haskell are functional languages, as they emphasize programming in a functional style: Composing functions to process values. "Value-oriented programming".
I never understood why anyone classified Lisp (typically CL) as a functional language, as it isn't any more functional than Python, Ruby or Perl.