README.md

---
language:
- en
license: apache-2.0
tags:
- lean4
- theorem-proving
- verification
- code-verification
base_model: Qwen/Qwen3-8B
---

# Goedel-Code-Prover-8B

**Paper:** [Goedel-Code-Prover: Hierarchical Proof Search for Open State-of-the-Art Code Verification](https://arxiv.org/abs/2603.19329)
**Code:** [https://github.com/goedelcodeprover/Goedel-Code-Prover](https://github.com/goedelcodeprover/Goedel-Code-Prover)

Goedel-Code-Prover-8B is a Lean 4 proof generation model specialized in **proof decomposition** for code correctness verification. Given a formal specification in Lean 4, it decomposes the proof into smaller lemmas and proves the target theorem by combining them.

## Use Case

This model is designed to work within a **decompose-then-verify scaffolding**:

1. **Input:** A Lean 4 formal problem (theorem statement with `sorry` body).
2. **Decomposition:** The model breaks down the proof into small, self-contained lemmas, each targeting a single logical step.
3. **Proof:** The model proves the target theorem by composing the introduced lemmas, ideally without any `sorry`.
4. **Verification:** The generated proof is compiled against a Lean 4 server to check correctness.

## Prompt Format

Use the chat completions API with the following structure:

**System prompt:**
```
You are an expert in Lean 4 theorem proving and proof decomposition.

Given a formal problem in Lean 4, your task is to:
1. First, analyze and reason about how to decompose the proof into smaller lemmas
2. Then, provide the complete proof with all necessary lemmas

Requirements for the proof breakdown:
- Break down the theorem into the smallest possible lemmas
- Each lemma should ideally involve a single Lean 4 basic function operation
- The introduced lemmas should not involve universe types
- Ensure logical ordering: lemmas should be defined before they are used

Requirements for the format of the proof:
- The original theorem MUST be proved WITHOUT sorry (using the defined lemmas)
- Each lemma should be proved with a complete proof if possible
- Use the 'lemma' keyword for lemmas and the 'theorem' keyword for the original theorem
- Wrap all proof code in ```lean code blocks
```

**User message:**
```
Formal Problem:
<lean4 theorem statement>
```

## Model Details

- **Base model:** Qwen3-8B
- **Training:** Supervised fine-tuning on proof decomposition and completion trajectories, followed by GRPO reinforcement learning with online Lean 4 verification rewards.

## Citation

```bibtex
@misc{li2026goedelcodeproverhierarchicalproofsearch,
      title={Goedel-Code-Prover: Hierarchical Proof Search for Open State-of-the-Art Code Verification},
      author={Zenan Li and Ziran Yang and Deyuan and He and Haoyu Zhao and Andrew Zhao and Shange Tang and Kaiyu Yang and Aarti Gupta and Zhendong Su and Chi Jin},
      year={2026},
      eprint={2603.19329},
      archivePrefix={arXiv},
      primaryClass={cs.SE},
      url={https://arxiv.org/abs/2603.19329},
}
```