Explorable Proofs: Making Written Proofs Explorable by Grounding Them in Formal Representations
Hita Kambhamettu, Will Crichton, Sean Welleck, Harrison Goldstein, Andrew Head
cs.HC
Apr 3, 2026 · v3
cs.AI cs.PL
TL;DR
Uses LLMs to translate theorems and written proofs into Lean, then executes the Lean proofs to extract intermediate states for interactive proof exploration.
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.
Problem
LLM-generated explanations of technical content are static text, so readers cannot execute them or step through them. That limits interactive support for understanding mathematical proofs.
Approach
The system, called explorable theorems, uses LLMs to translate a theorem and its written proof into Lean and links the prose proof to the Lean code. Readers can step through the proof, test custom examples or counterexamples, and trace logical dependencies between steps. Each worked-out step is produced by running the Lean proof on the chosen example and extracting its intermediate state.
Results
In a user study with 16 participants on a proof-reading task, those with the explorability features gave better, more correct, and more detailed answers to comprehension questions. This indicates stronger understanding of the underlying mathematics.
