>Also, I've seen plenty of programs that provably have no bugs, but still grow to exhaust all system memory or occasionally take several hours to return from a function call for no apparent reason
I think you mean programs that type checked, not programs that provably had no bugs.
What if those programs were guaranteed to do the right thing, if only that had enough time or space to finish? Maybe they're still "correct".
Or, to put it another way: our existing type systems don't make code "provably correct", and when people say that it does (like the commenter above), they're trying to talk you into something.
What you posted was wrong, like I said. There are programs that have proofs demonstrating they are free of bugs. You have not seen them do either of the things you claim to have seen. You were stating something false.
I think you mean programs that type checked, not programs that provably had no bugs.