Formalization of mathematics through proof assistants: a study on the state of the art

Resumo

The formalization of mathematics in practice relies heavily on proof assistants and automatic theorem provers, therefore we studied what are the state of the art proof assitants and their limitations to understand what are the main challenges in making formalized mathematics common practice among mathematicians. We found out that curretly the two major dificulties in formalizing mathematics with proof assistants are due to steep learning curves in how to use these tools and due to a wide gap between the notation employed in these proof assistants and the currently used mathematical notation. We also developed a C++ library to develop proof assistants with great notational flexibility.