# Notions of Anonymous Existence in Martin-Löf Type Theory

@article{Kraus2017NotionsOA, title={Notions of Anonymous Existence in Martin-L{\"o}f Type Theory}, author={Nicolai Kraus and M. Escard{\'o} and T. Coquand and Thorsten Altenkirch}, journal={Log. Methods Comput. Sci.}, year={2017}, volume={13} }

As the groupoid model of Hofmann and Streicher proves, identity proofs in intensional Martin-L\"of type theory cannot generally be shown to be unique. Inspired by a theorem by Hedberg, we give some simple characterizations of types that do have unique identity proofs. A key ingredient in these constructions are weakly constant endofunctions on identity types. We study such endofunctions on arbitrary types and show that they always factor through a propositional type, the truncated or squashed… Expand

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