The halting problem applies when you are trying to check the properties of arbitrary programs. However, we are not writing arbitrary programs, we are writing very specific (hopefully useful) programs. The two are very different.
Pop-sci explanations of the halting problem have probably done incredible damage to formal verification as a whole. Mostly because it makes people with only the most cursory understanding of it go "why bother, it won't work anyway."
Pop-sci explanations of the halting problem have probably done incredible damage to formal verification as a whole. Mostly because it makes people with only the most cursory understanding of it go "why bother, it won't work anyway."