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08/31/2023
A variation of Reynolds-Hurkens Paradox
We present a variation of Hurkens paradox, which can itself be seen as a...
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12/06/2022
Type Theories with Universe Level Judgements
The aim of this paper is to refine and extend Voevodsky's draft "A unive...
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10/11/2022
Controlling unfolding in type theory
We present a novel mechanism for controlling the unfolding of definition...
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03/07/2021
Reduction Free Normalisation for a proof irrelevant type of propositions
We show normalisation and decidability of convertibility for a type theo...
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12/15/2020
A Note on Generalized Algebraic Theories and Categories with Families
We give a new syntax independent definition of the notion of a generaliz...
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11/19/2019
Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality
In type theory with an impredicative universe of propositions and a proo...
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02/18/2019
Homotopy canonicity for cubical type theory
Cubical type theory provides a constructive justification of homotopy ty...
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10/22/2018
Canonicity and normalisation for Dependent Type Theory
We show canonicity and normalization for dependent type theory with a cu...
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02/04/2018
On Higher Inductive Types in Cubical Type Theory
Cubical type theory provides a constructive justification to certain asp...
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10/30/2017