# Parametricity, Automorphisms of the Universe, and Excluded Middle

LIPICS - Leibniz International Proceedings in Informatics, Oct 2018

It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address the interaction between classical axioms and the existence of automorphisms of a type universe. We work over intensional Martin-L�f dependent type theory, and for some results assume further principles including function extensionality, propositional extensionality, propositional truncation, and the univalence axiom.

This is a preview of a remote PDF: http://drops.dagstuhl.de/opus/volltexte/2018/9855/pdf/LIPIcs-TYPES-2016-7.pdf

Auke B. Booij, Mart\'in H. Escard\'o, Peter LeFanu Lumsdaine, Michael Shulman. Parametricity, Automorphisms of the Universe, and Excluded Middle, LIPICS - Leibniz International Proceedings in Informatics, 2018, 7:1-7:14, DOI: 10.4230/LIPIcs.TYPES.2016.7