Multimodal Dependent Type Theory
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 re...
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| Veröffentlicht in: | Logical methods in computer science Jg. 17, Issue 3 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Logical Methods in Computer Science e.V
01.01.2021
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| Schlagworte: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-17(3:11)2021 |