>what makes it functional is that the state / memory must be explicitly acknowledged
Isn't state/memory assumed by default when talking about computation?
What kind of computations you can perform on a Turing machine without a ticker tape?
Isn't state/memory assumed by default when talking about computation?
What kind of computations you can perform on a Turing machine without a ticker tape?
What are you applying your α-conversion and β-reduction operations to?