Note that I was responding to post mentioning 'provably correct code' which is very different opportunistic efforts to improve code.
Valgrind and fuzzing are useful tools, but there is no general method. Being semi-decidable, with enumerable inputs. This means that fuzzing can be useful both with random walks and constrained random walks. But it doesn't come close to generating 'provably correct code'.
The 'Post correspondence problem' is maybe an easier way to see how this applies at the compiler level.
But tools that help are opportunistic, but that doesn't change the undecidability of generalizations.
While crossing domains, but because it is commonly used, considering the VC dimensionality of the problem also helps, or pure math problems like the Collatz conjecture that generalize to the same halting problem.
Generating 'provably correct code' in the general case is simply not possible without major advances in math. There is room to improve with many paths to do so, just not going down this particular path.