Lean-auto: An Interface between Lean 4 and Automated Theorem Provers

Abstract: Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and Isabelle, leveraging the power of ATPs. An important component of a hammer is the translation algorithm from the ITP's logical system to the ATP's logical system. In this paper, we propose a novel translation algorithm for ITPs based on dependent type theory. The algorithm is implemented in Lean 4 under the name Lean-auto. When combined with ATPs, Lean-auto provides general-purpose, ATP-based proof automation in Lean 4 for the first time. Soundness of the main translation procedure is guaranteed, and experimental results suggest that our algorithm is sufficiently complete to automate the proof of many problems that arise in practical uses of Lean 4. We also find that Lean-auto solves more problems than existing tools on Lean 4's math library Mathlib4.