Premise Selection for a Lean Hammer
This work makes formal verification more accessible to researchers and practitioners by bridging neural retrieval and symbolic reasoning, though it is incremental as it adapts existing hammer concepts to a new proof assistant.
The authors tackled the problem of integrating neural methods into practical verification workflows for the Lean proof assistant by developing LeanHammer, the first end-to-end domain-general hammer for Lean. Their novel neural premise selection system enabled LeanHammer to solve 21% more goals than existing premise selectors and generalize well across diverse domains.
Neural methods are transforming automated reasoning for proof assistants, yet integrating these advances into practical verification workflows remains challenging. Hammers are tools that interface with external automatic theorem provers to automate tedious reasoning steps. They have dramatically improved productivity in proof assistants, but the Lean proof assistant still does not have a hammer despite its growing popularity. We present LeanHammer, the first end-to-end domain-general hammer for Lean, built on a novel neural premise selection system for a hammer in dependent type theory. Unlike existing Lean premise selectors, our approach dynamically adapts to user-specific contexts and combines with symbolic proof search and reconstruction to create a practical hammer. With comprehensive evaluations, we show that our premise selector enables LeanHammer to solve 21\% more goals relative to existing premise selectors, and generalize well to diverse domains. Our work bridges the gap between neural retrieval and symbolic reasoning, making formal verification more accessible to researchers and practitioners.