Automated Strategy Invention for Confluence of Term Rewrite Systems

TL;DR

This paper introduces a machine learning-based approach to automatically invent strategies for proving confluence in term rewrite systems, significantly enhancing existing automated tools and solving previously unproven cases.

Contribution

It presents the first learning-guided automatic confluence prover and a large dataset for analyzing confluence, advancing automation in term rewriting verification.

Findings

Our strategies outperform human-designed strategies in confluence proving.

The approach successfully proves or disproves confluence for previously unresolved systems.

Enhanced prover surpasses state-of-the-art tools on multiple datasets.

Abstract

Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive parameter space. This complexity exceeds human capacity for parameter selection, motivating an investigation into automated strategy invention. In this paper, we focus on confluence, an important property of term rewrite systems, and apply machine learning to develop the first learning-guided automatic confluence prover. Moreover, we randomly generate a large dataset to analyze confluence for term rewrite systems. Our results focus on improving the state-of-the-art automatic confluence prover CSI: When equipped with our invented strategies, it surpasses its human-designed strategies both on the augmented dataset and on the original human-created benchmark dataset Cops, proving/disproving the confluence of several term rewrite systems for which no automated proofs were known before.