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Model: Goedel-LM/Goedel-Code-Prover-8B
Source: Original Platform

README.md

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+---
+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},
+}
+```