Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only on

Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only one thing, C. There are no special considerations to single out that theory from a huge pool of similar ones. It's like devoting your life to the study of one particular differential equation with a thousand terms, which was written by a committee. Why not the other equation which has a minus instead of a plus over there? Why not study differential equations in general? Compare with a formal theory like PA, which fits on a page and describes the natural numbers. Proving a theorem about PA has implications everywhere, because natural numbers are everywhere. Or if we want to talk about computation, there are many formal theories with short descriptions that have much more to say about computation in general.