As you know, most of the wellused programming languages (especially imperative) are complete by Turing. And some – even relative to the compilation time, as, say, C++ with their templates.
And how is it proved / disproved fullness of Turing? In itself, this concept looks difficult to formalizable.
Answer 1, Authority 100%

Formally it is necessary to prove it from the point of view of the theory of Recursive Functions – Language Polon By Turing then and only if it allows you to record every computing function. In practice, for this, it is usually quite depersely prohalilat to [Cherchasis]. (http: / /En.wikipedia.org/wiki/church%E2%80%93Turing_Thesis )

see Also, “How to Prove A PROGRAMMING LANGUAGE IS Turing Complete? . “
Answer 2, Authority 25%
for some reason it seems to me that if we can realize a Turing machine on some kind of language, it means that he is turingfull. Although I can make mistake.