Parametricity and Semi-Cubical Types
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes.Our construction works not only for parametricity, but also for similar interpretations of...
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| Vydané v: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 11 |
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| Hlavný autor: | |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
IEEE
29.06.2021
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| Shrnutí: | We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes.Our construction works not only for parametricity, but also for similar interpretations of type theory and in fact similar interpretations of any generalized algebraic theory. To be precise we consider a functor forgetting unary operations and equations defining them recursively in a generalized algebraic theory. We show that it has a right adjoint.We use techniques from locally presentable category theory, as well as from quotient inductive-inductive types. |
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| DOI: | 10.1109/LICS52264.2021.9470728 |