The EPI Gallinette aims at developing a new generation of proof assistants, with the belief that practical experiments must go in pair with foundational investigations:
- The goal is to advance proof assistants both as certified programming languages and mechanised logical systems. Advanced programming and mathematical paradigms must be integrated, notably dependent types and effects. The distinctive approach is to implement new programming and logical paradigms on top of Coq by considering the latter as a target language for compilation.
- The aim of foundational investigations is to extend the boundaries of the Curry-Howard correspondence. It is seen both as providing foundations for programming languages and logic, and as a purveyor of techniques essential to the development of proof assistants. Under this perspective, the development of proof assistants is seen as a total experiment using the correspondence in every aspect: programming languages, type theory, proof theory, rewriting and algebra.