Lemma Discovery in Agentic Program Verification

2026-03-23

AI Summary

This work addresses the challenge that existing large language model (LLM) agents struggle to automatically discover auxiliary lemmas, thereby failing to effectively prove complex verification conditions. To overcome this limitation, we propose LemmaNet, the first approach that integrates program semantic understanding into the lemma discovery process. LemmaNet synthesizes lemmas offline from source code and specifications and dynamically refines them during online verification to adapt to evolving proof states. By synergistically combining LLM-based agents, program semantic analysis, and verification condition generation, our method establishes a novel framework for both synthesizing and adaptively refining lemmas. Experimental results demonstrate that LemmaNet significantly outperforms state-of-the-art techniques on benchmarks including SV-COMP and real-world system modules from the Linux kernel and Contiki OS, substantially enhancing the automatic provability of complex verification conditions.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Deductive verification provides strong correctness guarantees for code by extracting verification conditions (VCs) and writing formal proofs for them. The expertise-intensive task of VC proving is the main bottleneck in this process, and has been partly automated owing to recent advances in Large Language Model (LLM) agents. However, existing proof agents are not able to discover helper lemmas - auxiliary lemmas that aid in proving - and thus fall short as programs grow in size and complexity. In this paper, we argue that VC proving for program verification is more than a purely mathematical task, and benefits considerably from program comprehension. Our key insight is that human-proof engineers often discover and apply helper lemmas based on their understanding of the program semantics, which are not directly reflected in the VCs produced by VC generators. Inspired by this insight, we propose an LLM agent, LemmaNet, that discovers helper lemmas in two ways. Specifically, the agent first synthesizes lemmas offline by directly analyzing the source code and specifications, and then relating this semantic understanding to the mechanical, verbose encoding produced by VC generators. As the proof unfolds, LemmaNet then adapts existing helper lemmas online to accommodate evolving proof states, enabling the agent to effectively discharge complex VCs on-the-fly. We evaluate LemmaNet on SV-COMP and established real-world subjects, including modules of the Linux kernel, Contiki OS, standard C++ library, and X.509 parser. Our experimental results demonstrate that LemmaNet significantly outperforms state-of-the-art approaches, highlighting the importance of program comprehension-aided lemma discovery in agentic program verification.

Problem

• lemma discovery
• program verification
• verification conditions
• helper lemmas
• agentic reasoning

Innovation

• lemma discovery
• program verification
• large language model agents
• program comprehension
• verification conditions