The standard example of correct software and in fact where most work on formal correctness tends to happen is in compiler design and distributed systems. So when you say that there is a tradeoff between speed and correctness that is simply not true. All those compilers you use are correct, for a very precise definition of correct, and fast and constantly improving.
I appreciate your concern that a shouting match was imminent, but with gems like "running your mouth" and "parroting it over and over again" I think, ironically, the only one risking that is yourself.
Are they? How do we know? And if they are, why is GCC's list of major and critical bugs[1], for example, longer than a laundry list?
[1] https://gcc.gnu.org/bugzilla/buglist.cgi?bug_severity=critic...
Beware of bugs in the above code; I have only proved it correct, not tried it.
- Donald Knuth
Formal correctness and implementation correctness are still separate issues in compilers like gcc but that doesn't change the fact that there are correctness specifications for gcc. There are projects that try to bridge the gap: https://en.wikipedia.org/wiki/CompCert.