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Multimodal Dependent Type Theory

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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 to use the same type theory to compute and reason in many modal situations, including guarded recursion, axiomatic cohesion, and parametric quantification. We reproduce examples from prior work in guarded recursion and axiomatic cohesion--demonstrating that MTT constitutes a simple and usable syntax whose instantiations intuitively correspond to previous handcrafted modal type theories. In some cases, instantiating MTT to a particular situation unearths a previously unknown type theory that improves upon prior systems. Finally, we investigate the metatheory of MTT. We prove the consistency of MTT and establish canonicity through an extension of recent type-theoretic gluing techniques. These results hold irrespective of the choice of mode theory, and thus apply to a wide variety of modal situations.

Original languageEnglish
Title of host publicationProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020
Place of publicationS.l.
PublisherAssociation for Computing Machinery
Publication yearJul 2020
Article number3394736
ISBN (Electronic)9781450371049
Publication statusPublished - Jul 2020
Event35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020 - Saarbrucken, Germany
Duration: 8 Jul 202011 Jul 2020


Conference35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020
SponsorACM Special Interest Group on Logic and Computation (SIGLOG), Association for Symbolic Logic, European Association for Theoretical Computer Science (EATCS), IEEE Technical Committee on Mathematical Foundations of Computing
SeriesACM International Conference Proceeding Series

    Research areas

  • categorical semantics, gluing, guarded recursion, Modal types K@dependent types

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