
Modal Dependent Type Theory and Dependent Right Adjoints
In recent years we have seen several new models of dependent type theory...
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Presheaf Models of Relational Modalities in Dependent Type Theory
This report is an extension of 'A Model of Parametric Dependent Type The...
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Normalization for multimodal type theory
We consider the conversion problem for multimodal type theory (MTT) by c...
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Graded Modal Dependent Type Theory
Graded type theories are an emerging paradigm for augmenting the reasoni...
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Cocon: Computation in Contextual Type Theory
We describe a MartinLöf style dependent type theory, called Cocon, that...
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A Type Theory for Defining Logics and Proofs
We describe a MartinLöfstyle dependent type theory, called Cocon, that...
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Computational Aspects of Characteristic Mode Decomposition – An Overview
Nearly all practical applications of the theory of characteristic modes ...
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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 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 typetheoretic 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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