VeriBench: An End-to-End Formal Verification Benchmark for AI Coding Agents in Lean 4

Brando Miranda, Srivatsava Daruru, Ethan S Hersch, Zhanke Zhou, Allen Nie, Daneshvar Amrollahi, Leni Aniva, Iddah Mlauzi, Kirill Acharya, Elyas Obbad, Dilara Soylu, Weston Kirk, Zixiao Jolene Wang, Kai Fronsdal, Ying Li, Donald Poindexter Jr, Rakshit Kaushik, Shurui Liu, Yegor Denisov-Blanch, Steven Dillmann et al. (8 additional authors not shown)

Keywords: formal verification, Lean 4, language models, benchmark, code synthesis, correctness proofs, software reliability, generative AI, secure programming, trustworthy AI

TL;DR: VeriBench introduces a benchmark for evaluating language models on end-to-end Lean 4 code verification, showing current models struggle while self-optimizing agents demonstrate meaningful progress toward provably correct software generation.

Abstract:

Test-based coding benchmarks have repeatedly required strengthening passes---HumanEval gave way to HumanEval+, SWE-Bench to SWE-Bench Verified to SWE-Bench+, each release exposing test-invisible bugs in code that passed the prior suite---a structural limitation of finite testing: passing tests routinely leave behaviorally important bugs unobserved.
Existing formal-verification benchmarks (e.g., VERINA, FVAPPS, CLEVER, DafnyBench) provide stronger machine-checkable signals, but many focus on proof completion, scaffolded verified generation, or isolated formal subtasks rather than the full path from developer-written source code to a verified formal artifact.
We argue that trustworthy code-verification benchmarks must be end-to-end and agentic, scoring full Python-to-Lean autoformalization under verifier feedback, and must aggregate verification stages conjunctively ---weakness at any stage penalizing the composite while preserving smooth evaluation signals that retain discriminative power across models still far from the frontier.
We introduce VeriBench, a 452-task end-to-end Python-to-Lean~4 autoformalization benchmark spanning HumanEval-style programs, classical algorithms, Python standard-library functions, security examples, and 282 high-assurance-inspired tasks across 14 domains such as cryptography, aerospace, medical devices, and compilers.
We score agents with the Smooth Conjunctive Score for Code verification (SCSC), a log-domain geometric mean over five per-task factors: $\mathrm{SCSC} = \exp\!\bigl(\tfrac{1}{5}\sum_i \log f_i\bigr)$, combining (i) the agent's Lean file typechecks, (ii) the agent's theorems verify without \textsf{sorry}, (iii) the agent's theorems semantically cover the gold theorems, and (iv,v) gold-side benchmark-validity gates ($D_1, D_2$) ensuring the gold reference itself compiles and proves cleanly before being used to score agents.
Under an agentic verifier-feedback loop, Codex, Claude Code, and Leanstral-v2 reach SCSC of only 0.42, 0.36, and 0.23; iterative self-correction adds 14.3\% over single-shot baselines, yet theorem--gold coverage stalls uniformly at $\leq 0.11$ across all three agents---a specification gap validated by an LLM judge calibrated against five independent human raters (Pearson $r=0.70$, $p<10^{-11}$).
VeriBench reframes code-verification evaluation from isolated proof search to end-to-end conjunctive grounding, surfacing specification synthesis as a bottleneck at least as severe as proof search and offering a measurable target for the next generation of verifiable AI coding agents.

Submission Number: 88