@inproceedings{cao-etal-2025-informal,
title = "From Informal to Formal {--} Incorporating and Evaluating {LLM}s on Natural Language Requirements to Verifiable Formal Proofs",
author = "Cao, Jialun and
Lu, Yaojie and
Li, Meiziniu and
Ma, Haoyang and
Li, Haokun and
He, Mengda and
Wen, Cheng and
Sun, Le and
Zhang, Hongyu and
Qin, Shengchao and
Cheung, Shing-Chi and
Tian, Cong",
editor = "Che, Wanxiang and
Nabende, Joyce and
Shutova, Ekaterina and
Pilehvar, Mohammad Taher",
booktitle = "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
month = jul,
year = "2025",
address = "Vienna, Austria",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.acl-long.1310/",
doi = "10.18653/v1/2025.acl-long.1310",
pages = "26984--27003",
ISBN = "979-8-89176-251-0",
abstract = "The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. However, these studies intertwined multiple skills simultaneously{---}problem-solving, reasoning, and writing formal specifications{---}making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and breaks it down into sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six tasks by distilling gpt-4o and evaluated against ten open-sourced LLMs, including recent popular DeepSeek-R1. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. And interestingly, we observed that fine-tuning with formal data also enhances abilities in mathematics, reasoning, and coding. We hope our findings inspire further research."
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<abstract>The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. However, these studies intertwined multiple skills simultaneously—problem-solving, reasoning, and writing formal specifications—making it hard to precisely identify the LLMs’ strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and breaks it down into sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six tasks by distilling gpt-4o and evaluated against ten open-sourced LLMs, including recent popular DeepSeek-R1. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. And interestingly, we observed that fine-tuning with formal data also enhances abilities in mathematics, reasoning, and coding. We hope our findings inspire further research.</abstract>
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%0 Conference Proceedings
%T From Informal to Formal – Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs
%A Cao, Jialun
%A Lu, Yaojie
%A Li, Meiziniu
%A Ma, Haoyang
%A Li, Haokun
%A He, Mengda
%A Wen, Cheng
%A Sun, Le
%A Zhang, Hongyu
%A Qin, Shengchao
%A Cheung, Shing-Chi
%A Tian, Cong
%Y Che, Wanxiang
%Y Nabende, Joyce
%Y Shutova, Ekaterina
%Y Pilehvar, Mohammad Taher
%S Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2025
%8 July
%I Association for Computational Linguistics
%C Vienna, Austria
%@ 979-8-89176-251-0
%F cao-etal-2025-informal
%X The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. However, these studies intertwined multiple skills simultaneously—problem-solving, reasoning, and writing formal specifications—making it hard to precisely identify the LLMs’ strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and breaks it down into sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six tasks by distilling gpt-4o and evaluated against ten open-sourced LLMs, including recent popular DeepSeek-R1. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. And interestingly, we observed that fine-tuning with formal data also enhances abilities in mathematics, reasoning, and coding. We hope our findings inspire further research.
%R 10.18653/v1/2025.acl-long.1310
%U https://aclanthology.org/2025.acl-long.1310/
%U https://doi.org/10.18653/v1/2025.acl-long.1310
%P 26984-27003
Markdown (Informal)
[From Informal to Formal – Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs](https://aclanthology.org/2025.acl-long.1310/) (Cao et al., ACL 2025)
ACL
- Jialun Cao, Yaojie Lu, Meiziniu Li, Haoyang Ma, Haokun Li, Mengda He, Cheng Wen, Le Sun, Hongyu Zhang, Shengchao Qin, Shing-Chi Cheung, and Cong Tian. 2025. From Informal to Formal – Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 26984–27003, Vienna, Austria. Association for Computational Linguistics.