Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization
While large language models can successfully close proof gaps in interactive theorem provers, a new case study reveals that AI-generated formalizations often fail expert reviews due to poor API design and structural issues. The researchers argue that autoformalization must be evaluated by human standards, not just compiled code.
Computer Science > Artificial Intelligence
Title:Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization
View PDF HTML (experimental)Abstract:Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this distinction through a detailed case study: a semi-autonomous formalization of Grothendieck's vanishing theorem. The initial version compiles with no sorries, but an expert review found serious problems in definitions, theorem generality, file organization, and the API. We then ran a review-driven refactor and compression process and obtained a second expert review. The before-and-after comparison shows a sharp split: agents adapted well to local, mechanically checkable feedback, but remained weak at choosing definitions and designing APIs. We argue that autoformalization should be evaluated not only by closed sorries, but by whether the resulting formalization survives expert review.
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Source: arXiv cs.AI Recent
