Automated Discovery of Tactic Libraries for Interactive Theorem Proving

Abstract: Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial for proof modularity and automation. This paper presents a novel approach to tactic discovery, which leverages Tactic Dependence Graphs (TDGs) to identify reusable proof strategies across multiple proofs. TDGs capture logical dependencies between tactic applications while abstracting away irrelevant syntactic details, allowing for both the discovery of new tactics and the refactoring of existing proofs into more modular forms. We have implemented this technique in a tool called TacMiner and compare it against an anti-unification-based approach Peano to tactic discovery. Our evaluation demonstrates that TacMiner can learn 3x as many tactics as Peano and reduces the size of proofs by 26% across all benchmarks. Furthermore, our evaluation demonstrates the benefits of learning custom tactics for proof automation, allowing a state-of-the-art proof automation tool to achieve a relative increase of 172% in terms of success rate.