BC-Prover: Backward Chaining Prover for Formal Theorem Proving

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.