Abstract
Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web of axioms, definitions, and lemmas before target theorems can even be stated. In this position paper, we argue for theory-level autoformalization: formalizing complete theories, including all their inter-dependencies, as structured libraries.
We examine the significance of this shift, address alternative views, identify open challenges, and propose three promising paths forward. Our survey of autoformalization is available at GitHub.
Blogger's Review: Theory-level autoformalization enhances the efficiency of formalization and provides a more systematic framework for knowledge base construction. By integrating the interdependencies of axioms and definitions, it significantly boosts the ability of machines to understand and reason. Future research should focus on addressing existing challenges to further advance this field.