Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofs
This work addresses the challenge of verifying complex mathematical proofs and code for mathematicians and programmers, but it is incremental as it focuses on elementary domains and artificial data.
The paper tackles the problem of autoformalizing mathematical proofs and code correctness by introducing a semantic parsing approach based on the Universal Transformer architecture, which translates elementary proofs and simple imperative code into formal representations in Coq, with experiments showing good generalization to unseen lengths and variations in natural language.
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal representation that is computer-verifiable via interactive theorem provers. In this paper, we introduce a semantic parsing approach, based on the Universal Transformer architecture, that translates elementary mathematical proofs into an equivalent formalization in the language of the Coq interactive theorem prover. The same architecture is also trained to translate simple imperative code decorated with Hoare triples into formally verifiable proofs of correctness in Coq. Experiments on a limited domain of artificial and human-written proofs show that the models generalize well to intermediate lengths not seen during training and variations in natural language.