You're both right and wrong, it's just that "functional" has a lot of different definitions and nobody can agree on which one is correct.
As a result, "functional" has become pretty much meaningless when describing a programming language.
As a result, "functional" has become pretty much meaningless when describing a programming language.
Plenty of people will disagree with it too.
functions are invoked in an encapsulating way, and no state is kept between function-cup-up-segments-of-code, but there is a R.E.P.L that (replies) when you invoke a (parens) which is, in LISP-land known as a program.
However, now that I have mind-dumped that ^ I recall haskell and erlang also being called "functional" but I don't know their syntax any more than a chimpanzee knows that the sun is round.
Note that the above definition says nothing about how functions are to be evaluated: strictly, lazily, memoizing previously computed results, or using magic. No general-purpose programming paradigm can make such decisions for the programmer.