Goedel-Code-Prover-8B

Paper: Goedel-Code-Prover: Hierarchical Proof Search for Open State-of-the-Art Code Verification Code: 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

@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},
}