Title: Premise Selection for a Lean Hammer
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: premise selection, interactive theorem proving, automated reasoning, contrastive learning

Abstract: Neural methods are transforming automated reasoning for proof assistants, yet integrating these advances into practical verification workflows remains challenging. A $\textit{hammer}$ is a tool that integrates premise selection, translation to external automatic theorem provers, and proof reconstruction into one overarching tool to automate tedious reasoning steps. We present LeanPremise, a novel neural premise selection system, and we combine it with existing translation and proof reconstruction components to create LeanHammer, the first end-to-end domain general hammer for the Lean proof assistant. Unlike existing Lean premise selectors, LeanPremise is specifically trained for use with a hammer in dependent type theory. It also dynamically adapts to user-specific contexts, enabling it to effectively recommend premises from libraries outside LeanPremise's training data as well as lemmas defined by the user locally. With comprehensive evaluations, we show that LeanPremise enables LeanHammer to solve 21\% more goals than existing premise selectors and generalizes well to diverse domains. Our work helps bridge the gap between neural retrieval and symbolic reasoning, making formal verification more accessible to researchers and practitioners.

TL;DR: LeanHammer integrates neural premise selection with symbolic reasoning to automate theorem proving in Lean.