Computational Higher Type Theory III: Univalent Universes and Exact Equality

5 Dec 2017Carlo AngiuliKuen-Bang HouRobert Harper

This is the third in a series of papers extending Martin-L\"of's meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higher-dimensional types. We extend this framework to include a cumulative hierarchy of univalent Kan universes of Kan types, exact equality and other pretypes lacking Kan structure, and a cumulative hierarchy of pretype universes... (read more)

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