Collection Principles in Dependent Type Theory [chapter]

Peter Aczel, Nicola Gambino
2002 Lecture Notes in Computer Science  
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation
more » ... ion. This paper was written while visiting the Mittag-Leffler Institute, The Royal Swedish Academy of Sciences. Both authors wish to express their gratitude for the invitation to visit the Institute. The first author is also grateful to his two departments for supporting his visit. The second author is grateful to his department and to the "Fondazione Ing. A. Gini" for supporting his visit.
doi:10.1007/3-540-45842-5_1 fatcat:kvqbc2pgbjgyxf54io5hfsmxyy