Kimina Lean Server: A High-Performance Lean Server for Large-Scale Verification

Marco Dos Santos, Hugues de Saxcé, Haiming Wang, Mantas Baksys, Mert Unsal, Junqi Liu, Zhengying Liu, Jia LI

Keywords: formal mathematics, Lean, formal verification, reinforcement learning

TL;DR: We introduce an open-source server for fast and scalable interaction with Lean 4, specifically designed as a high-performance verifier for reinforcement learning pipelines.

Abstract:

Recent progress in neural theorem proving has been driven by the training of large language models on Lean 4 problems via reinforcement learning, a process that requires fast and scalable verification of proofs.
We introduce the Kimina Lean Server, an open-source project designed as a high-performance verifier for reinforcement learning pipelines Built on top of the Lean REPL (Read-Eval-Print Loop) maintained by the Lean Focused Research Organization (FRO), our server combines server-side parallelism by managing multiple Lean processes in parallel with an LRU (Least Recently Used) caching mechanism that reuses Lean imports across requests. On the client side, a lightweight Python package enables submitting proof batches and receiving Lean feedback, including extracted tactics and tactic states.
Together, these features enable a scalable workflow for large-scale verification and data extraction. In our experiments, the Kimina Lean Server outperforms previous Lean interaction tools, achieving a 1.5 to 2 times speedup in verification time. Moreover, its improved efficiency has enabled its use in the large-scale training of state-of-the-art models.
We hope that our open-source project will support the neural theorem proving community and accelerate future progress by enabling efficient large-scale verification and proof data extraction.

Submission Number: 133