Safe, Fast, Concurrent Proof Checking for the lambda-Pi Calculus Modulo Rewriting

TL;DR

This paper introduces Kontroli, a concurrent proof checker for the lambda-Pi calculus modulo rewriting, which significantly improves proof checking speed and efficiency on multi-core processors compared to existing tools.

Contribution

The work presents a memory- and thread-safe kernel design for concurrent proof checking, implemented in Kontroli, demonstrating substantial speed improvements over Dedukti.

Findings

Kontroli outperforms Dedukti on all tested datasets.

Using eight threads, proof checking time is reduced by up to 6.6x.

Kontroli efficiently supports concurrent proof verification.

Abstract

Several proof assistants, such as Isabelle or Coq, can concurrently check multiple proofs. In contrast, the vast majority of today's small proof checkers either does not support concurrency at all or only limited forms thereof, restricting the efficiency of proof checking on multi-core processors. This work shows the design of a small, memory- and thread-safe kernel that efficiently checks proofs both concurrently and non-concurrently. This design is implemented in a new proof checker called Kontroli for the lambda-Pi calculus modulo rewriting, which is an established framework to uniformly express a multitude of logical systems. Kontroli is faster than the reference proof checker for this calculus, Dedukti, on all of five evaluated datasets obtained from proof assistants and interactive theorem provers. Furthermore, Kontroli reduces the time of the most time-consuming part of proof checking using eight threads by up to 6.6x.