arXiv:2402.16878v1 Announce Type: new
Abstract: Formal mathematics is the discipline of translating mathematics into a programming language in which any statement can be unequivocally checked by a computer. Mathematicians and computer scientists have spent decades of painstaking formalization efforts developing languages such as Coq, HOL, and Lean. Machine learning research has converged on these formal math corpora and given rise to an assortment of methodologies to aid in interactive and automated theorem proving. However, these papers have primarily focused on one method, for one proof task, in one language. This paper introduces EvoGPT-f: a novel evolutionary framework for the first systematic quantitative analysis of the differential machine learnability of five formal math corpora (Lean 3, Lean 4, Coq, HOL 4, HOL Light) using four tokenization methods (character, word-level, Byte Pair Encoding and StarCoder tokenizer). This paper does not put to rest the question of the “best” or “easiest” language to learn. Rather, this framework and preliminary findings begin to illuminate the differential machine learnability of these languages, offering a foundation to forge more systematic quantitative and qualitative comparative research across communities.
Evolutionary Framework for Analyzing Differential Machine Learnability of Formal Math Corpora
In this paper, the authors introduce a novel evolutionary framework called EvoGPT-f, which aims to investigate the differential machine learnability of five formal math corpora: Lean 3, Lean 4, Coq, HOL 4, and HOL Light. By utilizing four different tokenization methods (character, word-level, Byte Pair Encoding, and StarCoder tokenizer), the authors aim to provide a systematic quantitative analysis of these formal math languages.
Formal mathematics is an essential discipline that enables the translation of mathematical concepts into a programming language, allowing for the verification of mathematical statements by computers. The development of languages such as Coq, HOL, and Lean has been a result of decades of effort by mathematicians and computer scientists.
One of the key aspects of this paper is the multidisciplinary nature of the concepts it explores. It combines elements from formal mathematics, programming languages, and machine learning. By leveraging machine learning techniques, the authors analyze the differential machine learnability of formal math corpora. This multidisciplinary approach allows for a comprehensive investigation into the effectiveness and efficiency of different formal math languages.
The authors emphasize that this paper does not aim to identify the “best” or “easiest” language to learn. Instead, it serves as a foundation for future research that can compare the machine learnability of different formal math languages quantitatively and qualitatively. By shedding light on the differential machine learnability of these languages, the authors hope to encourage further exploration and collaboration across various communities.
The EvoGPT-f framework introduced in this paper opens up new possibilities for studying the effectiveness of formal math languages from a machine learning perspective. By systematically analyzing different tokenization methods and formal math corpora, researchers can gain insights into the strengths and weaknesses of each language. This information can then be used to improve the development and usability of formal math languages in the future.
Conclusion
This paper presents an evolutionary framework, EvoGPT-f, which allows for a systematic quantitative analysis of the differential machine learnability of five formal math corpora. By combining elements from formal mathematics and machine learning, this research provides valuable insights into the effectiveness and efficiency of different formal math languages. The multidisciplinary nature of this work opens up new avenues for collaboration and further research, enabling the improvement of formal math languages in the future.