Vous pouvez vous abonner à nos annonces de séminaires http://gallium.inria.fr/seminaires/ S E M I N A I R E __ / _` _ / / o /| /| __ __ __ __ _ _ / ) __) / / / / / /\/| ----- / |/ | / )(_ / / ) ) ) __) (___/ (_/ (_ (_ / (__/ / | / | (__/ __)(_ (__/ (_/ (_/ I N R I A - Rocquencourt Amphi Turing du bâtiment 1 Lundi 13 mai, 10h30 ---------------- Guillaume Claret ---------------- Université Paris 7 ============================================================= Lightweight proof by reflection using a posteriori simulation of effectful computation ============================================================= Proof-by-reflection is a well-established technique that employs decision procedures to reduce the size of proof-terms. Currently, decision procedures can be written either in Type Theory---in a purely functional way that also ensures termination---or in an effectful programming language, where they are used as oracles for the certified checker. The first option offers strong correctness guarantees, while the second one permits more efficient implementations. We propose a novel technique for proof-by-reflection that marries, in Type Theory, an effectful language with (partial) proofs of correctness. The key to our approach is to use simulable monads, where a monad is simulable if, for all terminating reduction sequences in its equivalent effectful computational model, there exists a witness from which the same reduction may be simulated a posteriori by the monad. We encode several examples using simulable monads and demonstrate the advantages of the technique over previous approaches.