Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908534659088384 |
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| author | Hattori, Seiji Matsuzaki, Takuya Fujiwara, Makoto |
| author_facet | Hattori, Seiji Matsuzaki, Takuya Fujiwara, Makoto |
| contents | This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was applied to formal proof data created in accordance with natural language proofs taken from an undergraduate-level textbook, and the quality of the generated natural language proofs was analyzed in comparison with the original natural language proofs. Furthermore, we will demonstrate that this method can output highly readable and accurate natural language proofs by applying it to existing formal proof library of the Lean proof assistant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Hattori, Seiji Matsuzaki, Takuya Fujiwara, Makoto Computation and Language This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was applied to formal proof data created in accordance with natural language proofs taken from an undergraduate-level textbook, and the quality of the generated natural language proofs was analyzed in comparison with the original natural language proofs. Furthermore, we will demonstrate that this method can output highly readable and accurate natural language proofs by applying it to existing formal proof library of the Lean proof assistant. |
| title | Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2509.09726 |