arXiv subjects

Auke Bart Booij

Publications and source records attributed to Auke Bart Booij.

2 recordsLinked to original sources

arXiv2017

Parametricity, automorphisms of the universe, and excluded middle

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-Löf dependent type theory, and in some results assume further principles including function extensionality, propositional extensionality, propositional truncation, and the univalence axiom.

cs.LO↗

arXiv2017

The HoTT reals coincide with the Euclidean reals

Escard\'o and Simpson defined a notion of interval object by a universal property in any category with binary products. The Homotopy Type Theory book defines a higher inductive-inductive notion of reals, and suggests that the interval in this type may satisfy this universal property. We show that this is indeed the case in the category of sets of any universe. We also show that the type of HoTT reals is the smallest Cauchy complete subset of the Dedekind reals containing the rationals.

cs.LO↗