
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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Syllepsis in Homotopy Type Theory
It is wellknown that in homotopy type theory (HoTT), one can prove the ...
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Firstorder natural deduction in Agda
Agda is a dependentlytyped functional programming language, based on an...
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Axioms for Modelling Cubical Type Theory in a Topos
The homotopical approach to intensional type theory views proofs of equa...
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Effective Kan fibrations in simplicial sets
We introduce the notion of an effective Kan fibration, a new mathematica...
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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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Towards a Homotopy Domain Theory (HoDT)
A favourable environment is proposed for the achievement of λmodels wit...
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The RedPRL Proof Assistant (Invited Paper)
RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higherdimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish behavioral properties of cubical functional programs embodying the constructive content of proofs. Notably, RedPRL implements a twolevel type theory, allowing an extensional, proofirrelevant notion of exact equality to coexist with a higherdimensional proofrelevant notion of paths.
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