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 …

The theory of program modules is of interest to language designers not only for its practical
importance to programming, but also because it lies at the nexus of three fundamental …

Dependent type theory allows us to write programs and to prove properties about those
programs in the same language. However, some properties do not require much proof, as …

A classical result of topos theory holds that the category of coalgebras for a Cartesian
comonad on a topos is again a topos (Kock and Wraith, 1971). It is natural to refine this …

Presheaf models of dependent type theory have been successfully applied to model HoTT,
parametricity, and directed, guarded and nominal type theory. There has been considerable …

The purpose of these notes is to give a categorical semantics for the transpension type
(Nuyts and Devriese, Transpension: The Right Adjoint to the Pi-type, pre-print, 2023), which …

Dependable Atomicity in Type Theory Page 1 Dependable Atomicity in Type Theory Andreas
Nuyts1, Dominique Devriese2 1KU Leuven, Belgium 2Vrije Universiteit Brussel, Belgium TYPES …

Recently, a number of extensions to dependent type theory have been proposed or refined
that are not easily added to pre-existing proof assistants as they severely impact the nature …

In this chapter, we establish the object part of the mode theory for naturality pretype theory
and its model. Modes will be anpolarity masks ⃗a (section 1. 1) which will be modelled in …

Abstract is note describes and discusses my PhD dissertation 'Contributions to Multimode
and Presheaf Type eory'. e PhD project was motivated by the quest for a higher-dimensional …