Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

**Multimodal Dependent Type Theory.** / Gratzer, Daniel; Kavvos, G. A.; Nuyts, Andreas; Birkedal, Lars.

Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

Gratzer, D, Kavvos, GA, Nuyts, A & Birkedal, L 2020, Multimodal Dependent Type Theory. in *Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020.*, 3394736, Association for Computing Machinery, S.l., ACM International Conference Proceeding Series, pp. 492-506, 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020, Saarbrucken, Germany, 08/07/2020. https://doi.org/10.1145/3373718.3394736

Gratzer, D., Kavvos, G. A., Nuyts, A., & Birkedal, L. (2020). Multimodal Dependent Type Theory. In *Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020 *(pp. 492-506). [3394736] Association for Computing Machinery. ACM International Conference Proceeding Series https://doi.org/10.1145/3373718.3394736

Gratzer D, Kavvos GA, Nuyts A, Birkedal L. 2020. Multimodal Dependent Type Theory. In Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020. S.l.: Association for Computing Machinery. pp. 492-506. (ACM International Conference Proceeding Series). https://doi.org/10.1145/3373718.3394736

Gratzer, Daniel et al. "Multimodal Dependent Type Theory". *Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020.* S.l.: Association for Computing Machinery. (ACM International Conference Proceeding Series). 2020, 492-506. https://doi.org/10.1145/3373718.3394736

Gratzer D, Kavvos GA, Nuyts A, Birkedal L. Multimodal Dependent Type Theory. In Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020. S.l.: Association for Computing Machinery. 2020. p. 492-506. 3394736. (ACM International Conference Proceeding Series). https://doi.org/10.1145/3373718.3394736

Gratzer, Daniel ; Kavvos, G. A. ; Nuyts, Andreas ; Birkedal, Lars. / **Multimodal Dependent Type Theory**. Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020. S.l. : Association for Computing Machinery, 2020. pp. 492-506 (ACM International Conference Proceeding Series).

@inproceedings{9360dc7680b74411a0d305f6410af82e,

title = "Multimodal Dependent Type Theory",

abstract = "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.",

keywords = "categorical semantics, gluing, guarded recursion, Modal types K@dependent types",

author = "Daniel Gratzer and Kavvos, {G. A.} and Andreas Nuyts and Lars Birkedal",

year = "2020",

month = jul,

doi = "10.1145/3373718.3394736",

language = "English",

series = "ACM International Conference Proceeding Series",

pages = "492--506",

booktitle = "Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020",

publisher = "Association for Computing Machinery",

note = "35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020 ; Conference date: 08-07-2020 Through 11-07-2020",

}

TY - GEN

T1 - Multimodal Dependent Type Theory

AU - Gratzer, Daniel

AU - Kavvos, G. A.

AU - Nuyts, Andreas

AU - Birkedal, Lars

PY - 2020/7

Y1 - 2020/7

N2 - 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.

AB - 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.

KW - categorical semantics

KW - gluing

KW - guarded recursion

KW - Modal types K@dependent types

UR - http://www.scopus.com/inward/record.url?scp=85085942561&partnerID=8YFLogxK

U2 - 10.1145/3373718.3394736

DO - 10.1145/3373718.3394736

M3 - Article in proceedings

AN - SCOPUS:85085942561

T3 - ACM International Conference Proceeding Series

SP - 492

EP - 506

BT - Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020

PB - Association for Computing Machinery

CY - S.l.

T2 - 35th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2020

Y2 - 8 July 2020 through 11 July 2020

ER -