Explorable Proofs: Making Written Proofs Explorable by Grounding Them in Formal Representations
TL;DR
It is argued that grounding explanations in a formalized representation enables interactive affordances beyond what static text supports, and is instantiated 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.
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.
