Section: Overall Objectives

Presentation

Mathematics is among the many human activities that have been transformed by the invention of the computer and its broad diffusion in the second half of the 20^th century. Mathematicians could, from then on, use a tool allowing to carry out operations that were too long or too tedious to be executed by hand. Like the use of the telescope in astronomy, the use of the computer opened many new prospects in mathematics. One of these prospects is the use of proof assistants, i.e. computer programs which perform some operations on mathematical proofs. The goal of the research developed in the TypiCal project-team is to develop such proof assistants. The main effort of the project-team is to contribute to the development of proof assistants in general and of the Coq system in particular, which has an important community of users in industry and in academia. However, we believe that the development of a proof assistant cannot be accomplished without a joint reflection about the structure of mathematical proofs and about the use of proof assistants in various applicative domains. We also believe that proof assistants should take benefit of the use of automated deduction tools. Thus, the questions addressed in the team range from questions related to the Coq system, such as “What will be the features of the next version of Coq ?”, to more theoretical questions of logic, such as “What is a proof?” and more applied ones, such as “How can I delegate part of the proof search to automated tools?” or “How can we use a proof assistant to check whether a protocol is free of deadlocks?”.