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 …
parametrized by a mode theory which specifies a collection of modes, modalities, and …
Dual-context calculi for modal logic
GA Kavvos - Logical Methods in Computer Science, 2020 - lmcs.episciences.org
We present natural deduction systems and associated modal lambda calculi for the
necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in …
necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in …
[PDF][PDF] Syntax and semantics of modal type theory
D Gratzer - 2023 - pure.au.dk
One idiosyncratic framing of type theory is as the study of operations invariant under
substitution. Modal type theory, by contrast, concerns the controlled integration of operations …
substitution. Modal type theory, by contrast, concerns the controlled integration of operations …
Semantics of multimodal adjoint type theory
M Shulman - Electronic Notes in Theoretical Informatics and …, 2023 - entics.episciences.org
We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M
can be interpreted in any M-shaped diagram of categories having, and functors preserving …
can be interpreted in any M-shaped diagram of categories having, and functors preserving …
[PDF][PDF] Contributions to Multimode and Presheaf Type Theory
A Nuyts - eng. PhD thesis. KU Leuven, 2020 - anuyts.github.io
Parts of this introduction were taken from a non-public grant renewal application at the
Research Foundation-Flanders (FWO), authored by myself in collaboration with Dominique …
Research Foundation-Flanders (FWO), authored by myself in collaboration with Dominique …
[PDF][PDF] Higher Inductive Types and Internal Parametricity for Cubical Type Theory.
E Cavallo - 2021 - reports-archive.adm.cs.cmu.edu
Recent innovation in the design of type theories—foundational systems of mathematics with
a focus on constructivity—has produced the concept of interval variable, which can be used …
a focus on constructivity—has produced the concept of interval variable, which can be used …
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 …
parametrized by a mode theory which specifies a collection of modes, modalities, and …