A Neurosymbolic Approach to Loop Invariant Generation via Weakest Precondition Reasoning

2025/12/17 by King, Daragh, Koutavas, Vasileios, Kovacs, Laura
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Programming Languages (cs.PL) #Software Testing and Debugging Techniques

paper · pdf · doi:10.48550/arxiv.2512.15816

openalex publication_date 2025/12/17 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

Abstract

Loop invariant generation remains a critical bottleneck in automated program verification. Recent work has begun to explore the use of Large Language Models (LLMs) in this area, yet these approaches tend to lack a reliable and structured methodology, with little reference to existing program verification theory. This paper presents NeuroInv, a neurosymbolic approach to loop invariant generation. NeuroInv comprises two key modules: (1) a neural reasoning module that leverages LLMs and Hoare logic to derive and refine candidate invariants via backward-chaining weakest precondition reasoning, and (2) a verification-guided symbolic module that iteratively repairs invariants using counterexamples from OpenJML. We evaluate NeuroInv on a comprehensive benchmark of 150 Java programs, encompassing single and multiple (sequential) loops, multiple arrays, random branching, and noisy code segments. NeuroInv achieves a 99.5% success rate, substantially outperforming the other evaluated approaches. Additionally, we introduce a hard benchmark of 10 larger multi-loop programs (with an average of 7 loops each); NeuroInv's performance in this setting demonstrates that it can scale to more complex verification scenarios.

Citations

• The Prompt Report: A Systematic Survey of Prompt Engineering Techniques
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