https://hal-lara.archives-ouvertes.fr/hal-02102422Kervac, RomainRomainKervacLIP - Laboratoire de l'Informatique du Parallélisme - ENS Lyon - École normale supérieure - Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - Inria - Institut National de Recherche en Informatique et en Automatique - Université de Lyon - CNRS - Centre National de la Recherche ScientifiquePure type systems and classical sequentsSystèmes de types purs et séquents classique.HAL CCSD2006Calculus of constructionsBar lambda mu tilde mu-calculusClassical logicHigher order typesLambda-cubeLambda-calculusPure type systemsSequent calculusStrong normalisationSubject reduction[INFO] Computer Science [cs]ORANGE, Colette2019-04-17 11:51:342022-10-26 08:15:032019-04-18 11:20:28frReportsapplication/pdf1The bar lambda mu tilde mu-calculus was designed by P.-L. Curien and H.Herbelin. One of its interest is that its terms can be interpreted asderivations in the classical sequent calculus. One of the its lacks isthe fact that it has only simple types. Our purpose here is to extendthe calculus to higher-order types, and especially those of thecalculus of constructions, a calculus designed by T. Coquand and G.Huet in order to provide a very general typed language for proofassistants based on \lambda-calculus. In order to do this, we placeourselves in the framework of pure type systems, which are a verygeneral formalism allowing to represent many interesting type systems,among which those of Barendregt's lambda-cube, which is a hierarchicalpresentation of the calculus of constructions. We show that our systemssatisfy some fundamental properties, such as subject reduction, andstrong normalisation on the lambda-cube.