# Verus-SpecGym: An Agentic Environment for Evaluating Specification Autoformalization

arXiv: https://arxiv.org/abs/2605.26457 · HTML: https://mlsanity.com/paper/2605.26457/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 15 of 15)

- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [Clover: Closed-Loop Verifiable Code Generation](https://mlsanity.com/paper/2310.17807/) (2023)
- [Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics](https://mlsanity.com/paper/2601.14027/) (2026)
- [AlphaVerus: Bootstrapping Formally Verified Code Generation through Self-Improving Translation and Treefinement](https://mlsanity.com/paper/2412.06176/) (2024)
- [VERINA: Benchmarking Verifiable Code Generation](https://mlsanity.com/paper/2505.23135/) (2025)
- [Propose, Solve, Verify: Self-Play Through Formal Verification](https://mlsanity.com/paper/2512.18160/) (2025)
- [VeruSAGE: A Study of Agent-Based Verification for Rust Systems](https://mlsanity.com/paper/2512.18436/) (2025)
- [AlgoVeri: An Aligned Benchmark for Verified Code Generation on Classical Algorithms](https://mlsanity.com/paper/2602.09464/) (2026)
- [VerifyThisBench: Generating Code, Specifications, and Proofs All at Once](https://mlsanity.com/paper/2505.19271/) (2025)
- [Agentic Specification Generator for Move Programs](https://mlsanity.com/paper/2509.24515/) (2025)
- [Spec-Harness: Assessing and Guiding LLM-Synthesized Formal Specifications Beyond Verifiability](https://mlsanity.com/paper/2604.00280/) (2026)

## Built on by (most cited first, 3 of 3)

- [Analyzing the Narration Gap in LLM-Solver Loops](https://mlsanity.com/paper/2606.19588/) (2026)
- [Towards Assurance Closure in AI-Native Large-Scale Agile Software Development](https://mlsanity.com/paper/2608.07317/) (2026)
- [claimcheck: Measuring and Improving Specification Faithfulness](https://mlsanity.com/paper/2610.17358/) (2026)

## Abstract (arXiv)

AI coding agents are increasingly used to write real-world software, but ensuring that their outputs are correct remains a fundamental challenge. Formal verification offers a promising path: an agent generates code together with a machine-checked proof, guaranteeing that the code satisfies a formal specification. However, there is no guarantee that the formal spec itself matches the user's intent. In this work, we study specification autoformalization: whether LLM agents can translate informal programming problems into faithful formal specifications. We introduce Verus-SpecBench, a benchmark of 581 spec-writing tasks derived from Codeforces problems targeting Verus, a verifier for Rust, and Verus-SpecGym, an agentic environment in which models interact with Verus, bash, & the filesystem to develop these specs. The central challenge is evaluation: expert-written reference specs are expensive to write, & LLM judges can miss subtle mistakes. We address this by (a) extending Verus's exec_spec mechanism so that generated specs can be executed as Rust code, & (b) testing them against official Codeforces tests & adversarial cases extracted from Codeforces "hacks", which are edge cases written by competitors to break incorrect solutions. On Verus-SpecBench, the strongest model, Gemini 3.1 Pro, solves 77.8% of tasks, other frontier models solve 51.1--57.8% & OSS models reach only 21.5--25.5%. Our analysis of failure modes shows that model-generated specs can omit important input assumptions, accept incorrect outputs, & reject valid ones. We also find that LLM-as-a-judge evaluation misses 26% of the failures our evaluator catches. Overall, our results suggest that spec autoformalization is within reach for frontier agents but remains brittle even on problems where they can already generate correct code. The code, data, & logs can be found at https://github.com/formal-verif-is-cool/verus-spec-gym