• Corpus ID: 57373903

Parametric Cubical Type Theory

@article{Cavallo2019ParametricCT,
  title={Parametric Cubical Type Theory},
  author={Evan Cavallo and Robert Harper},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.00489}
}
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions between the two along the way. The combined theory supports both univalence and its relational equivalent, which we call relativity. We demonstrate the use of the theory by analyzing polymorphic types, including functions between higher inductive types, and we… 

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