BC-Prover: Backward Chaining Prover for Formal Theorem Proving

Yuhang He, Jihai Zhang, Jianzhu Bao, Fangquan Lin, Cheng Yang, Bing Qin, Ruifeng Xu, Wotao Yin


Abstract
Despite the remarkable progress made by large language models in mathematical reasoning, interactive theorem proving in formal logic still remains a prominent challenge. Previous methods resort to neural models for proofstep generation and search. However, they suffer from exploring possible proofsteps empirically in a large search space. Moreover, they directly use a less rigorous informal proof for proofstep generation, neglecting the incomplete reasoning within. In this paper, we propose BC-Prover, a backward chaining framework guided by pseudo steps. Specifically, BC-Prover prioritizes pseudo steps to proofstep generation. The pseudo steps boost the proof construction in two aspects: (1) Backward Chaining that decomposes the proof into sub-goals for goal-oriented exploration. (2) Step Planning that makes a fine-grained planning to bridge the gap between informal and formal proofs. Experiments on the miniF2F benchmark show significant performance gains by our framework over the state-of-the-art approaches. Our framework is also compatible with existing provers and further improves their performance with the backward chaining technique.
Anthology ID:
2024.emnlp-main.180
Volume:
Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing
Month:
November
Year:
2024
Address:
Miami, Florida, USA
Editors:
Yaser Al-Onaizan, Mohit Bansal, Yun-Nung Chen
Venue:
EMNLP
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
3059–3077
Language:
URL:
https://aclanthology.org/2024.emnlp-main.180
DOI:
Bibkey:
Cite (ACL):
Yuhang He, Jihai Zhang, Jianzhu Bao, Fangquan Lin, Cheng Yang, Bing Qin, Ruifeng Xu, and Wotao Yin. 2024. BC-Prover: Backward Chaining Prover for Formal Theorem Proving. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 3059–3077, Miami, Florida, USA. Association for Computational Linguistics.
Cite (Informal):
BC-Prover: Backward Chaining Prover for Formal Theorem Proving (He et al., EMNLP 2024)
Copy Citation:
PDF:
https://aclanthology.org/2024.emnlp-main.180.pdf
Software:
 2024.emnlp-main.180.software.zip
Data:
 2024.emnlp-main.180.data.zip