Papers › Parametricity, automorphisms of the universe, and excluded middle
Parametricity, automorphisms of the universe, and excluded middle
Auke Bart Booij, Martín Hötzel Escardó, Peter LeFanu Lumsdaine, Michael Shulman
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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\"of dependent type theory, and in some results assume further principles including function extensionality, propositional extensionality, propositional truncation, and the univalence axiom.
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