Abstract

In this paper we share several experiments trying to automatically translate informal mathematics into formal mathematics. In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal mathematics refers to statements in the Mizar language. We conducted our experiments against three established neural network-based machine translation models that are known to deliver competitive results on translating between natural languages. To train these models we also prepared four informal-to-formal datasets. We compare and analyze our results according to whether the model is supervised or unsupervised. In order to augment the data available for auto-formalization and improve the results, we develop a custom type-elaboration mechanism and integrate it in the supervised translation.

BibTeX

@inproceedings{qwcbckju-cpp20,
  author    = {Qingxiang Wang and
               Chad E. Brown and
               Cezary Kaliszyk and
               Josef Urban},
  editor    = {Jasmin Blanchette and Catalin Hritcu},
  title     = {Exploration of neural machine translation in autoformalization of
               mathematics in {M}izar},
  booktitle = {Proceedings of the 9th {ACM} {SIGPLAN} International Conference on
               Certified Programs and Proofs, {CPP} 2020, New Orleans, LA, USA, January
               20-21, 2020},
  pages     = {85--98},
  publisher = {{ACM}},
  year      = {2020},
  url       = {https://doi.org/10.1145/3372885.3373827},
  doi       = {10.1145/3372885.3373827},
 }