TLA-Verus: Generating and Solving Temporal Proof Obligations with LLM Agents

TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-check. We present TLA-Prover, a 20-billion-parameter model for TLA+ specification synthesis. Training combines supervised fine-tuning (SFT) on verified examples with repair-based group-relative policy optimization (GRPO). In the GRPO stage, the model learns to fix its own rejected specifications. We also train a direct preference optimization (DPO) variant from the same SFT checkpoint as an ablation. TLC provides the reward signal directly, with no learned reward model. Four tiers grade each output: Bronze (parses), Silver (no warnings), Gold (passes TLC), and Diamond. To reach Diamond, the model's correctness property is automatically altered in a small way; TLC must then detect a violation. If TLC still passes, the property was always-true and contributes nothing; the output fails Diamond. TLA-Prover reaches 9/30 (i.e. pass@1 = 30%) at both Gold and Diamond on a held-out 30-problem benchmark. This is roughly 3.5x the 8.6% untuned baseline. The DPO variant reaches 20% at Diamond. Gold and Diamond coincide at every checkpoint; this prevents the trivial-property failure mode.

TLA+ has supported industrial verification at companies such as Amazon and Microsoft, yet writing correct TLA+ specifications from natural language still requires time and expertise, which limits adoption. LLMs show promise, but no prior study measures whether they produce semantically correct TLA+ specifications from natural language. This paper presents the first systematic evaluation of LLM-based TLA+ specification synthesis from natural language. Our study evaluates 30 LLMs across eight families on a curated dataset of 205 TLA+ specifications: 25 open-weight models across four prompting strategies (2,600 runs) and 5 proprietary models under few-shot prompting (130 runs), all validated by the SANY parser and TLC model checker. LLMs achieve up to 26.6% syntactic correctness but only 8.6% semantic correctness, with successes exclusive to progressive prompting. Results show that model size does not predict quality, e.g., DeepSeek r1:8b outperforms its 70B variant across all strategies, which suggests the importance of reasoning alignment for formal languages. Code-specialized models consistently underperform due to negative transfer from mainstream language training. We identify five recurring hallucination categories, all traceable to specific training data biases. These results suggest that current LLMs do not generate reliable TLA+ specifications without expert oversight. We release the evaluation framework, code, and dataset to support reproducibility and future research.

LLM-assisted Verus verification is a less tedious method to verify Rust implementations, but paired with self-referential structures, e.g., Doubly Linked Lists (DLLs)—notoriously difficult to formalise for verification—it becomes a substantially more demanding verification task. Moreover, a specification weakness can arise when verification relies on unproven or invalidated assumptions, such as axiomatic lemmas and assume statements. We investigate whether LLM agents can synthesize strong DLL specifications while minimizing these trusted base. The analysis follows three different approaches: manual verification, property-specific verification, and a defined skill for the specific case of DLLs and certain properties of this type of data structure. The skill encodes domain knowledge and a task-decomposition strategy. We show that an LLM agent equipped with a carefully designed verification skill can generate strong, low-trust specifications for DLLs in Verus.