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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