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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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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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Semantics for Combinatory Logic With Intersection Types
Frontiers in Computer Science, 2022 There is a plethora of semantics of computational models, nevertheless, the semantics of combinatory logic are among the less investigated ones. In this paper, we propose semantics for the computational system of combinatory logic with intersection types.
Silvia Ghilezan +2 more
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Dynamic Semiosis: Meaning, Informing, and Conforming in Constructing the Past
Information, 2023 Constructed Past Theory (CPT) is an abstract representation of how information about the past is produced and interpreted. It is grounded in the assertion that whatever we can write or say about anything in the past is the product of cognition ...
Kenneth Thibodeau
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Call-by-name Gradual Type Theory [PDF]
Logical Methods in Computer Science, 2020 We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments
Max S. New, Daniel R. Licata
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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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Al-Lisaniyyat, 2022 The aim of our paper is to present the Constructive Type Theory (CTT) and some related concepts for the Swedish logician Per Martin Löf, who constructed a formal logic system in order to establish a philosophical foundation of constructive mathematics ...
Terkia Mechouet, Farid Zidani
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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
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2-adjoint equivalences in homotopy type theory [PDF]
Logical Methods in Computer Science, 2021 We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
Daniel Carranza +3 more
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