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07/12/2023
Internal parametricity, without an interval
Parametricity is a property of the syntax of type theory implying e.g. t...
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02/10/2023
For the Metatheory of Type Theory, Internal Sconing Is Enough
Metatheorems about type theories are often proven by interpreting the sy...
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02/23/2021
Induction principles for type theories, internally to presheaf categories
We present new induction principles for the syntax of dependent type the...
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06/21/2020
Large and Infinitary Quotient Inductive-Inductive Types
Quotient inductive-inductive types (QIITs) are generalized inductive typ...
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07/17/2019
Shallow Embedding of Type Theory is Morally Correct
There are multiple ways to formalise the metatheory of type theory. For ...
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02/01/2019