4 ms·

This is a great point. In a computer proof system, you produce judgements like "the term x has type is T", where the type "T" encodes the statement of a theorem

This is a great point. In a computer proof system, you produce judgements like "the term x has type is T", where the type "T" encodes the statement of a theorem and "x" is the proof. We must be certain that whenever the type checker verifies that "x has type T", it means that the theorem "T" is actually true. Such a meta-proof must be done on pen and paper, before any code is written at all. Any bug in this meta-proof would destroy our ability to rely on the computer proof system.

cscheid 3y ago
> Such a meta-proof must be done on pen and paper, before any code is written at all. Not so fast; it could be done on a _different automated system_ (say, a smaller one) than the one you're building, in which case you're now relying on that system's correctness. Or it could even not be proven at all. This is not too different from what mathematicians do when they (often) say "assuming P != NP", or "assuming GRH", or "assuming FLT", etc etc. It's simply that it's worth being careful and precise.