Reimplementing Mizar in Rust

Abstract

This paper describes a new open-source proof processing tool, \texttt{mizar-rs}, a wholesale reimplementation of the Mizar proof system, written in Rust. In particular, the main Mizar processing tool \texttt{verifier} is implemented, which can be used to verify the Mizar Mathematical Library (MML). This is to our knowledge the first and only external implementation of the system. We have used this to verify the entire MML in 11.8 minutes on 8 cores, a 4.8$\times$ speedup over the original Pascal implementation. Since Mizar is not designed to have a small trusted core, checking Mizar proofs entails following Mizar closely, so our ability to detect bugs is limited. Nevertheless, we were able to find multiple memory errors, four soundness bugs in the original (which were not being exploited in MML), in addition to one non-critical bug which was being exploited in 46 different MML articles. We hope to use this checker as a base for proof export tooling, as well as revitalizing development of the language.