A Simple Model Construction for the Calculus of Constructions (1996)
| Venue: | Types for Proofs and Programs, International Workshop TYPES'95 |
| Citations: | 3 - 0 self |
BibTeX
@INPROCEEDINGS{Stefanova96asimple,
author = {M. Stefanova and H. Geuvers},
title = {A Simple Model Construction for the Calculus of Constructions},
booktitle = {Types for Proofs and Programs, International Workshop TYPES'95},
year = {1996},
pages = {5--8},
publisher = {Springer-Verlag}
}
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Abstract
. We present a model construction for the Calculus of Constructions (CC) where all dependencies are carried out in a set-theoretical setting. The Soundness Theorem is proved and as a consequence of it Strong Normalization for CC is obtained. Some other applications of our model constructions are: showing that CC + Classical logic is consistent (by constructing a model for it) and showing that the Axiom of Choice is not derivable in CC (by constructing a model in which the type that represents the Axiom of Choice is empty). 1 Introduction In the literature there are many investigations on the semantics of polymorphic -calculus with dependent types (see for example [12, 11, 10, 1, 5, 13]). Most of the existing models present a semantics for systems in which the inhabitants of the impredicative universe (types) are "lifted" to inhabitants of the predicative universe (kinds) (see [16]). Such systems are convenient to be modeled by locally Cartesian-closed categories having small Cartesia...
