[ukj]

>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?

[kchamplewski]

Lambda calculus, for example, has no ticker tape.

[ukj]

What kind of computations can you perform with Lambda calculus without any input variables?

What are you applying your α-conversion and β-reduction operations to?