Explorable Proofs: Making Written Proofs Explorable by Grounding Them in Formal Representations

Abstract:LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding explanations in a formalized representation enables interactive affordances beyond what static text supports. We instantiate this idea for mathematical proof comprehension with explorable theorems, a system that uses LLMs to translate a theorem and its written proof into Lean, a programming language for machine-checked proofs, and links the written proof with the Lean code. Readers can work through the proof at a step-level granularity, test custom examples or counterexamples, and trace the logical dependencies bridging each step. Each worked-out step is produced by executing the Lean proof on that example and extracting its intermediate state. A user study ($n = 16$) shows potential advantages of this approach: in a proof-reading task, participants who had access to the provided explorability features gave better, more correct, and more detailed answers to comprehension questions, demonstrating a stronger overall understanding of the underlying mathematics.

Human-Computer Interaction (cs.HC); Artificial Intelligence (cs.AI); Programming Languages (cs.PL)

arXiv:2604.02598 [cs.HC]

(or arXiv:2604.02598v3 [cs.HC] for this version)

https://doi.org/10.48550/arXiv.2604.02598 Focus to learn more arXiv-issued DOI via DataCite

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