
Internal Parametricity for Cubical Type Theory
We define a computational type theory combining the contentful equality ...
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Relational Type Theory (All Proofs)
This paper introduces Relational Type Theory (RelTT), a new approach to ...
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A General Framework for Relational Parametricity
Reynolds' original theory of relational parametricity was intended to ca...
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Internalizing Representation Independence with Univalence
In their usual form, representation independence metatheorems provide an...
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Naive cubical type theory
This paper proposes a way of doing type theory informally, assuming a cu...
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Modeling selectional restrictions in a relational type system
Selectional restrictions are semantic constraints on forming certain com...
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The Integers as a Higher Inductive Type
We consider the problem of defining the integers in Homotopy Type Theory...
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Parametric Cubical Type Theory
We exhibit a computational type theory which combines the higherdimensional 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 show by example how relativity can be used to characterize the relational interpretation of inductive types.
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