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LICENSE ADDED
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README.md CHANGED
@@ -1,3 +1,79 @@
1
- ---
2
- license: apache-2.0
3
- ---
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ---
2
+ license: apache-2.0
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+ datasets:
4
+ - purewhite42/DExploration_Dataset
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+ language:
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+ - en
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+ base_model: Goedel-Prover/Goedel-Prover-V2-8B
8
+ pipeline_tag: text-generation
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+ library_name: transformers
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+ tags:
11
+ - formal-mathematics
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+ - lean4
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+ - data-synthesis
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+ - problem-generation
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+ - formal-statement-synthesis
16
+ ---
17
+
18
+ <div align="center">
19
+ <h1 style="font-size: 1.5em;">[ICLR'26] Let's Explore Step by Step: Generating Provable Formal Statements with Deductive Exploration</h1>
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+ <div style="display: flex; justify-content: center; gap: 8px; flex-wrap: wrap;">
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+ <a href="https://choosealicense.com/licenses/apache-2.0/"><img src="https://img.shields.io/badge/License-Apache%202.0-blue.svg" alt="License: Apache 2.0"></a>
22
+ <a href="https://github.com/leanprover-community/mathlib4"><img src="https://img.shields.io/badge/Lean-4-orange" alt="Lean 4"></a>
23
+ <a href="https://github.com/Purewhite2019/dexploration_main"><img src="https://img.shields.io/badge/GitHub-%23121011.svg?logo=github&logoColor=white" alt="GitHub"></a>
24
+ </div>
25
+ <h2>Qi Liu, Kangjie Bao, Yue Yang, Xinhao Zheng, Renqiu Xia, Qinxiang Cao, Junchi Yan* (* indicates corresponding author)</h2>
26
+ <h3>School of Computer Science & School of Artificial Intelligence, Shanghai Jiao Tong University</h3>
27
+ <h3>Shanghai Innovation Institute</h3>
28
+ </div>
29
+
30
+ Please refer to the [📺GitHub repo](https://github.com/Purewhite2019/dexploration_main) and
31
+ [📃Paper](https://openreview.net/pdf?id=Njrkeo3DiJ) for more details.
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+
33
+ ## 🔍 About
34
+
35
+ **DExplorer-8B** is a Lean 4-based agent that generates provable formal mathematical statements through step-by-step **Deductive Exploration (DExploration)**. Instead of directly synthesizing problems in one shot, DExplorer explores the mathematical world step by step — introducing variables/hypotheses, deriving intermediate facts, and submitting conclusions — with each step verified by the Lean 4 kernel. This ensures the **provability** of generated statements while enabling the synthesis of **complex** problems that push the limits of state-of-the-art provers.
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+
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+ This model is fine-tuned from [Goedel-Prover-V2-8B](https://huggingface.co/Goedel-Prover/Goedel-Prover-V2-8B) on [🤗purewhite42/DExploration_Dataset](https://huggingface.co/datasets/purewhite42/DExploration_Dataset) using supervised fine-tuning.
38
+
39
+ ## ⚙️ Usage
40
+
41
+ This model is SFTed for the **DExploration** task: given the current exploration state (introduced variables/hypotheses and Lean 4 context), the model proposes the next exploration step — either introducing a new variable/hypothesis, deriving a new fact, or submitting a conclusion.
42
+
43
+ See the [📺GitHub repo](https://github.com/Purewhite2019/dexploration_main) for prompt templates and detailed usage/
44
+
45
+ ## 📄 Citation
46
+
47
+ If you find our work useful in your research, please cite:
48
+
49
+ ```bibtex
50
+ @inproceedings{
51
+ liu2026lets,
52
+ title={Let's Explore Step by Step: Generating Provable Formal Statements with Deductive Exploration},
53
+ author={Qi Liu and Kangjie Bao and Yue Yang and Xinhao Zheng and Renqiu Xia and Qinxiang Cao and Junchi Yan},
54
+ booktitle={The Fourteenth International Conference on Learning Representations},
55
+ year={2026},
56
+ url={https://openreview.net/forum?id=Njrkeo3DiJ}
57
+ }
58
+ ```
59
+
60
+ ## ©️ License
61
+
62
+ This project is released under the Apache 2.0 license. See [LICENSE](LICENSE) for details.
63
+
64
+ ## 🤝 Contributing
65
+
66
+ We welcome contributions! Please feel free to submit issues or pull requests.
67
+
68
+ ## 📧 Contact
69
+
70
+ For questions about the paper, data, or code:
71
+
72
+ - **Qi Liu**: purewhite@sjtu.edu.cn
73
+ - **Issues**: [GitHub Issues](https://github.com/Purewhite2019/dexploration_main/issues)
74
+
75
+ ## 👍 Acknowledgments
76
+ - [NuminaMath-LEAN](https://huggingface.co/AI-MO/NuminaMath-LEAN) for the high-quality statement-proof data.
77
+ - [Goedel-Prover](https://huggingface.co/Goedel-LM/Goedel-Prover-V2-8B) for the base model.
78
+ - [Pantograph](https://github.com/leanprover/Pantograph) for Lean 4 interaction.
79
+ - And many other open-source projects!
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+ {%- if messages[0].role == 'system' %}
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+ {{- messages[0].content + '\n\n' }}
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+ {%- endif %}
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+ {%- for tool in tools %}
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+ {{- "\n" }}
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+ {{- tool | tojson }}
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+ {%- endfor %}
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+ {{- "\n</tools>\n\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\n<tool_call>\n{\"name\": <function-name>, \"arguments\": <args-json-object>}\n</tool_call><|im_end|>\n" }}
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+ {%- else %}
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+ {%- if messages[0].role == 'system' %}
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+ {{- '<|im_start|>system\n' + messages[0].content + '<|im_end|>\n' }}
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+ {%- endif %}
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+ {%- endif %}
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+ {%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
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+ {%- for message in messages[::-1] %}
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+ {%- set index = (messages|length - 1) - loop.index0 %}
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+ {%- if ns.multi_step_tool and message.role == "user" and message.content is string and not(message.content.startswith('<tool_response>') and message.content.endswith('</tool_response>')) %}
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+ {%- set ns.multi_step_tool = false %}
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+ {%- set ns.last_query_index = index %}
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+ {%- endif %}
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+ {%- endfor %}
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+ {%- for message in messages %}
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+ {%- if message.content is string %}
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+ {%- set content = message.content %}
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+ {%- else %}
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+ {%- set content = '' %}
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+ {%- endif %}
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+ {%- if (message.role == "user") or (message.role == "system" and not loop.first) %}
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+ {{- '<|im_start|>' + message.role + '\n' + content + '<|im_end|>' + '\n' }}
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+ {%- elif message.role == "assistant" %}
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+ {%- set reasoning_content = '' %}
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+ {%- if message.reasoning_content is string %}
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+ {%- set reasoning_content = message.reasoning_content %}
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+ {%- else %}
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+ {%- if '</think>' in content %}
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+ {%- set reasoning_content = content.split('</think>')[0].rstrip('\n').split('<think>')[-1].lstrip('\n') %}
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+ {%- set content = content.split('</think>')[-1].lstrip('\n') %}
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+ {%- endif %}
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+ {%- endif %}
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+ {%- if loop.index0 > ns.last_query_index %}
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+ {%- if loop.last or (not loop.last and reasoning_content) %}
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+ {{- '<|im_start|>' + message.role + '\n<think>\n' + reasoning_content.strip('\n') + '\n</think>\n\n' + content.lstrip('\n') }}
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+ {%- else %}
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+ {{- '<|im_start|>' + message.role + '\n' + content }}
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+ {%- if (loop.first and content) or (not loop.first) %}
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+ {%- set tool_call = tool_call.function %}
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+ {%- endif %}
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+ {{- '<tool_call>\n{"name": "' }}
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+ {{- tool_call.name }}
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+ {{- '", "arguments": ' }}
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+ {%- if tool_call.arguments is string %}
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+ {{- tool_call.arguments }}
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+ {%- else %}
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+ {{- tool_call.arguments | tojson }}
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+ {%- endif %}
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+ {{- '}\n</tool_call>' }}
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+ {{- '<|im_end|>\n' }}
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+ {%- if loop.first or (messages[loop.index0 - 1].role != "tool") %}
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+ {{- '<|im_start|>user' }}
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+ {%- endif %}
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+ {{- '\n<tool_response>\n' }}
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+ {{- content }}
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+ {{- '\n</tool_response>' }}
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+ {%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
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+ {{- '<|im_end|>\n' }}
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+ {%- endif %}
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+ {%- endif %}
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+ {%- if add_generation_prompt %}
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+ {{- '<|im_start|>assistant\n' }}
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+ {%- if enable_thinking is defined and enable_thinking is false %}
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+ {{- '<think>\n\n</think>\n\n' }}
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+ {%- endif %}
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+ {%- endif %}
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