Just note that F# is not functional by your definition, because all it's core datastructures (tuples, arrays, lists) are actually objects, with methods on them etc.
Yeah, but it's not possible (I think, but am not 100% sure) to reason about F# code without object semantics because of how it's implemented: it probably could be implemented on top of MSIL without objects, but (again, not 100%, but 95% sure :)) it isn't.
I thought about another language I think you'd call functional: Lua. It supports first- and higher-order functions and has no objects at all in the core language. What do you think?
Also, now that I understand what you mean I can agree with you, but you do realize that this is not very common definition of "functional", right? :)
Also, it seems that only languages you think worthy of being called "funtional" are various (typed or not) lambda calculi implementations?
What is Scala, then? Not functional at all, too?
Could you maybe provide a few examples of languages you'd call "functional" or "supporting functional programming paradigm"?