Verus-SpecGym: An Agentic Environment for Evaluating Specification Autoformalization

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

VeruSAGE: A Study of Agent-Based Verification for Rust Systems

Large language models (LLMs) have shown impressive capability to understand and develop code. However, their capability to rigorously reason about and prove code correctness remains in question. This paper offers a comprehensive study of LLMs' capability to develop correctness proofs for system software written in Rust. We curate a new system-verification benchmark suite, VeruSAGE-Bench, which consists of 849 proof tasks extracted from eight open-source Verus-verified Rust systems. Furthermore, we design different agent systems to match the strengths and weaknesses of different LLMs (o4-mini, GPT-5, Sonnet 4, and Sonnet 4.5). Our study shows that different tools and agent settings are needed to stimulate the system-verification capability of different types of LLMs. The best LLM-agent combination in our study completes over 80% of system-verification tasks in VeruSAGE-Bench. It also completes over 90% of a set of system proof tasks not part of VeruSAGE-Bench because they had not yet been finished by human experts. This result shows the great potential for LLM-assisted development of verified system software.