A New Approach Towards Autoformalization
This addresses the difficulty of verifying mathematical proofs for researchers and developers in automated theorem proving, though it is incremental as it focuses on breaking down the task rather than achieving full autoformalization.
The paper tackles the challenging problem of autoformalizing research-level mathematics by proposing a decomposition into subtasks like unlinked formalization and entity linking, and introduces arXiv2Formal, a benchmark dataset of 50 theorems formalized for Lean from arXiv papers.
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a program. This is a challenging task, and especially for higher-level mathematics found in research papers. Research paper mathematics requires large amounts of background and context. In this paper, we propose an avenue towards tackling autoformalization for research-level mathematics, by breaking the task into easier and more approachable subtasks: unlinked formalization (formalization with unlinked definitions and theorems), entity linking (linking to the proper theorems and definitions), and finally adjusting types so it passes the type checker. In addition, we present arXiv2Formal, a benchmark dataset for unlinked formalization consisting of 50 theorems formalized for the Lean theorem prover sampled from papers on arXiv.org. We welcome any contributions from the community to future versions of this dataset.