
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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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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Failure of Normalization in Impredicative Type Theory with ProofIrrelevant Propositional Equality
In type theory with an impredicative universe of propositions and a proo...
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Homotopy canonicity for cubical type theory
Cubical type theory provides a constructive justification of homotopy ty...
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Canonicity and normalisation for Dependent Type Theory
We show canonicity and normalization for dependent type theory with a cu...
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On Higher Inductive Types in Cubical Type Theory
Cubical type theory provides a constructive justification to certain asp...
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The univalence axiom in cubical sets
In this note we show that Voevodsky's univalence axiom holds in the mode...
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Thierry Coquand
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