Daniel Gratzer ; G. A. Kavvos ; Andreas Nuyts ; Lars Birkedal - Multimodal Dependent Type Theory

lmcs:7571 - Logical Methods in Computer Science, July 28, 2021, Volume 17, Issue 3 - https://doi.org/10.46298/lmcs-17(3:11)2021
Multimodal Dependent Type Theory

Authors: Daniel Gratzer ; G. A. Kavvos ; Andreas Nuyts ; Lars Birkedal

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, thereby 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.


Volume: Volume 17, Issue 3
Published on: July 28, 2021
Submitted on: June 10, 2021
Keywords: Computer Science - Logic in Computer Science


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