Section: Scientific Foundations

Logical formalisms

A proof system implements a logical formalism in the way a compiler implements a programming language. Similarly, the choice of the formalism is crucial for the success of the proof system. One of the main line of research of the team is to study or invent type theories that are well-adapted to the formalization of mathematics. For instance a crucial property of a proof system is its correctness, hence the importance of the study of the models of the meta-theory of the Coq proof assistant. An other issue is the interoperability of the various proof systems used to formalize mathematics in the world-wide community of users of proof assistants, and the design of a system which could serve as a back-end to front-end implementing various formalisms and proof languages.