Paper Detail
Alessandro Sosso, Akhil Arora, Bas Spitters
Agentic systems have recently emerged as state-of-the-art approaches for automated theorem proving in formal mathematics. To assess how far these capabilities extend to program verification, we evaluate Claude Code in an agentic proving framework on CLEVER, a Lean 4 benchmark for verifiable code generation. Our results show that Claude generates arguably valid specifications for 98.8% of problems (with 81.3% also accepted by CLEVER's isomorphism-based scoring on the correct portion of the benchmark), certifies implementations against correct ground-truth specifications for 87.5% of problems, and reaches a 98.1% success rate on the end-to-end program generation and verification pipeline over entries with self-consistent premises. Across all stages, Claude further provides high-quality feedback on its own attempts (as confirmed under manual review), identifying underlying causes of failure and lingering bugs in the dataset. These findings highlight a growing mismatch between the difficulty of existing program verification benchmarks and the capabilities of modern agentic provers, and point to the need for more rigorous, bug-resilient evaluation methodologies, and in particular for alternatives to isomorphism-based scoring of generated specifications. More broadly, our results provide empirical evidence that tight compiler-in-the-loop agentic paradigms are currently the most effective approach for foundational program verification.
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@article{sosso2026agentic,
title = {Agentic Proving for Program Verification},
author = {Alessandro Sosso and Akhil Arora and Bas Spitters},
year = {2026},
abstract = {Agentic systems have recently emerged as state-of-the-art approaches for automated theorem proving in formal mathematics. To assess how far these capabilities extend to program verification, we evaluate Claude Code in an agentic proving framework on CLEVER, a Lean 4 benchmark for verifiable code generation. Our results show that Claude generates arguably valid specifications for 98.8\% of problems (with 81.3\% also accepted by CLEVER's isomorphism-based scoring on the correct portion of the benchm},
url = {https://arxiv.org/abs/2605.23772},
keywords = {cs.AI, cs.LO, cs.PL, cs.SE},
eprint = {2605.23772},
archiveprefix = {arXiv},
}
{}