An Extensible User Interface for Lean 4

Authors Wojciech Nawrocki , Edward W. Ayers , Gabriel Ebner

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Wojciech Nawrocki
  • Carnegie Mellon University, Pittsburgh, PA, USA
Edward W. Ayers
  • Carnegie Mellon University, Pittsburgh, PA, USA
Gabriel Ebner
  • Microsoft Research, Redmond, WA, USA


The Lean team at MSR and KIT: Leonardo de Moura and Sebastian Ullrich for extensive discussions, code review, and improvements to the system, Daniel Selsam for suggesting traces, and Daniel Fabian for input on RPC design. The Penrose team: Wode Ni and Sam Estep for considerable help and implementing several features which made our use possible. Jeremy Avigad and Patrick Massot for suggestions, advice, and feedback on a draft of the paper. Tomáš Skřivan, Joachim Breitner, and Sina Hazratpour for trying our systems and suggesting improvements. Chris Lovett and Mariana Alanis for working on vscode-lean4. The Lean Zulip community for technical help and ideas.

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Wojciech Nawrocki, Edward W. Ayers, and Gabriel Ebner. An Extensible User Interface for Lean 4. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Contemporary proof assistants rely on complex automation and process libraries with millions of lines of code. At these scales, understanding the emergent interactions between components can be a serious challenge. One way of managing complexity, long established in informal practice, is through varying external representations. For instance, algebraic notation facilitates term-based reasoning whereas geometric diagrams invoke spatial intuition. Objects viewed one way become much simpler than when viewed differently. In contrast, modern general-purpose ITP systems usually only support limited, textual representations. Treating this as a problem of human-computer interaction, we aim to demonstrate that presentations - UI elements that store references to the objects they are displaying - are a fruitful way of thinking about ITP interface design. They allow us to make headway on two fronts - introspection of prover internals and support for diagrammatic reasoning. To this end we have built an extensible user interface for the Lean 4 prover with an associated ProofWidgets 4 library of presentation-based UI components. We demonstrate the system with several examples including type information popups, structured traces, contextual suggestions, a display for algebraic reasoning, and visualizations of red-black trees. Our interface is already part of the core Lean distribution.

Subject Classification

ACM Subject Classification
  • Human-centered computing → Visualization systems and tools
  • Software and its engineering → Functional languages
  • user interfaces
  • human-computer interaction
  • Lean


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