The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue). If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.
The seminar is open to public and does not require any form of registration.
In recent years, proof assistant have reached an impressive level of maturity. They have led to the certification of complex programs such as compilers and operating systems. Yet, using a proof assistant requires highly specialised skills and it remains very different from standard programming. To bridge this gap, we aim at designing an ML-style programming language with support for proofs of programs, combining in a single tool the flexibility of ML and the fine specification features of a proof assistant. In other words, the system should be suitable both for programming (in the strongly-typed, functional sense) and for gradually increasing the level of guarantees met by programs, on a by-need basis.
We thus define and study a call-by-value language whose type system extends higher-order logic with an equality type over untyped programs, a dependent function type, classical logic and subtyping. The combination of call-by-value evaluation, dependent functions and classical logic is known to raise consistency issues. To ensure the correctness of the system (logical consistency and runtime safety), we design a theoretical framework based on Krivine's classical realizability. The construction of the model relies on an essential property linking the different levels of interpretation of types in a novel way.