[robertbenjamin]

You don't prove that it's "correct," as there is no such thing as a "correct" program. You prove that it works.

[xixi77]

I think you may be assuming that the purpose of a CS degree is to teach people how to write programs that work, while it's really not :)

And there is such a thing as a correct implementation of an algorithm. Running it does not exactly prove things either, and it might not necessarily work on actual hardware, but it does show that the person understands at least part of the material.