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The ever-growing complexity of mathematical proofs makes their manualverification by mathematicians very cognitively demanding. Autoformalizationseeks to address this by translating proofs written in natural language into aformal representation that is computer-verifiable via interactive theoremprovers. In this paper, we introduce a semantic parsing approach, based on theUniversal Transformer architecture, that translates elementary mathematicalproofs into an equivalent formalization in the language of the Coq interactivetheorem prover. The same architecture is also trained to translate simpleimperative code decorated with Hoare triples into formally verifiable proofs ofcorrectness in Coq. Experiments on a limited domain of artificial andhuman-written proofs show that the models generalize well to intermediatelengths not seen during training and variations in natural language.

Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofs