Propositional Equality for Gradual Dependently Typed Programming

@article{Eremondi2022PropositionalEF,
  title={Propositional Equality for Gradual Dependently Typed Programming},
  author={Joey Eremondi and Ronald Garcia and {\'E}ric Tanter},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.01241}
}
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types, though, lack a central feature of type theory: propositional equality. Lennon-Bertrand et al. show that, when the reflexive proof refl is the only closed value of an equality type, a gradual extension of CIC with propositional equality violates static… 

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