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Dualized Simple Type Theory [PDF]
Logical Methods in Computer Science, 2017 We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus.
Harley Eades III +2 more
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Bulletin of the Section of Logic, 2023 Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a ...
Emma van Dijk +2 more
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Multimodal Dependent Type Theory [PDF]
Logical Methods in Computer Science, 2021 We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode theory allow us
Daniel Gratzer +3 more
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Modalities in homotopy type theory [PDF]
Logical Methods in Computer Science, 2020 Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes.
Egbert Rijke +2 more
doaj +3 more sources
Normalisation by Evaluation for Type Theory, in Type Theory [PDF]
Logical Methods in Computer Science, 2017 We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types.
Thorsten Altenkirch, Ambrus Kaposi
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Idempotents in intensional type theory [PDF]
Logical Methods in Computer Science, 2017 We study idempotents in intensional Martin-L\"of type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky's univalence axiom, there exist idempotents that do not ...
Michael Shulman
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Internal Parametricity for Cubical Type Theory [PDF]
Logical Methods in Computer Science, 2021 We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives.
Evan Cavallo, Robert Harper
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A dependent nominal type theory [PDF]
Logical Methods in Computer Science, 2012 Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and
James Cheney
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W-types in Homotopy Type Theory [PDF]
Mathematical Structures in Computer Science, 2014 We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of simplicial presheaves and an application to models of set theory.Comment:
Benno Van, Den Berg, Ieke Moerdijk
core +12 more sources
Explicit Substitutions for Contextual Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory.
Andreas Abel, Brigitte Pientka
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