Quick A: Yes, a final class cannot have its methods overriden.

Recently on SO:

Does C++ final imply final in all aspects?

To quote the draft C++ standard from here [class.virtual/4]:

If a virtual function f in some class B is marked with the virt-specifier final and in a class D derived from B a function D::f overrides B::f, the program is ill-formed.

And here [class/3]:

If a class is marked with the class-virt-specifier final and it appears as a base-type-specifier in a base-clause (Clause [class.derived]), the program is ill-formed.

So, in answer to the question;

 

Does a final class implicitly imply its virtual functions to be final as well? Should it? Please clarify.

So, at least not formally. But attempts to violate either rule will be the same result in both cases; the program is ill-formed and so won't compile. A final class means the class cannot be derived from, so as a consequence of this, its virtual methods cannot be overridden.

 

Should it? Probably not, they are related but they not the same thing. There is also no need formally require the one to imply the other, the effect follows naturally. Any violations have the same result, a failed compile (hopefully with appropriate error messages to distinguish the two).