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Autoformalization with Large Language Models

Albert Jiang
Charles Edgar Staats
Christian Szegedy
Markus Rabe
Mateja Jamnik
Wenda Li
Yuhuai Tony Wu
NeurIPS (2022) (to appear)
Google Scholar


Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs --- a task that is similar to software synthesis. Here, we study the ability of large language models to produce correct formalization of informally given statements. These models are trained using a (next-token-prediction) language modeling objective on a large web corpus containing both natural language and formal (including programming) languages. We use few-shot prompting of large language models and find that they can correctly translate a significant portion of mathematical competition problems to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover for Isabelle via training on these autoformalized theorems. Our methodology results in state-of-the-art on the miniF2F theorem proving benchmark, improving the proof rate from $29.6\%$ to $35.2\%$

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