Pantograph: A Machine-to-Machine Interaction Interface for Advanced Theorem Proving, High Level Reasoning, and Data Extraction in Lean 4
Leni Aniva, Chuyue Sun, Brando Miranda, Clark Barrett, Sanmi Koyejo
2024-10-25
Summary
This paper discusses a new method called Pantograph, which enhances machine-assisted theorem proving by providing a better interface for the Lean 4 proof assistant and improving how proofs are generated.
What's the problem?
Machine-assisted theorem proving is a complex process that involves using computers to help prove mathematical theorems. While there has been interest in combining machine learning with proof assistants, existing tools can be inefficient and may not handle the reasoning steps effectively, making it hard to generate proofs quickly and accurately.
What's the solution?
The authors introduce Pantograph, a tool that connects to the Lean 4 proof assistant and uses advanced search algorithms like Monte Carlo Tree Search to improve proof generation. Pantograph also enhances high-level reasoning by better managing inference steps in Lean 4. The paper provides an overview of Pantograph's features and demonstrates its capabilities through a case study where machine learning models are used to assist in proving theorems in Lean 4.
Why it matters?
This research is important because it paves the way for more effective use of machine learning in theorem proving, allowing for more complex proofs to be generated efficiently. By improving the tools available for researchers, Pantograph can help advance the field of automated reasoning and make it easier to tackle challenging mathematical problems.
Abstract
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.