Verified Propagation Redundancy and Compositional UNSAT Checking in CakeML

Abstract

Modern SAT solvers can emit independently-checkable proof certificates to validate their results. The state-of-the-art proof system that allows for compact proof certificates is propagation redundancy (textsf{PR}). However, the only existing method to validate proofs in this system with a formally verified tool requires a transformation to a weaker proof system, which can result in a significant blowup in the size of the proof and increased proof validation time. This article describes the first approach to formally verify textsf{PR} proofs on a succinct representation. We present (i) a new Linear PR (LPR) proof format, (ii) an extension of the DPR-trim tool to efficiently convert textsf{PR} proofs into LPR format, and (iii) cake_lpr, a verified LPR proof checker developed in CakeML. We also enhance these tools with (iv) a new compositional proof format designed to enable separate (parallel) proof checking. The LPR format is backwards compatible with the existing LRAT format, but extends LRAT with support for the addition of textsf{PR} clauses. Moreover, cake_lpr is verified using CakeML ’s binary code extraction toolchain, which yields correctness guarantees for its machine code (binary) implementation. This further distinguishes our clausal proof checker from existing checkers because unverified extraction and compilation tools are removed from its trusted computing base. We experimentally show that: LPR provides efficiency gains over existing proof formats; cake_lpr ’s strong correctness guarantees are obtained without significant sacrifice in its performance; and the compositional proof format enables scalable parallel proof checking for large proofs.