We prove normalization for MTT, a general multimodal dependent type theory capable of
expressing modal type theories for guarded recursion, internalized parametricity, and …

Reasoning about weak higher categorical structures constitutes a challenging task, even to
the experts. One principal reason is that the language of set theory is not invariant under the …

Birkedal et al. recently introduced dependent right adjoints as an important class of (non-
fibered) modalities in type theory. We observe that several aspects of their calculus are left …

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 …

Shulman's spatial type theory internalizes the modalities of Lawvere's axiomatic cohesion in
a homotopy type theory, enabling many of the constructions from Schreiber's modal …

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 …

We present new induction principles for the syntax of dependent type theories, which we call
relative induction principles. The result of the induction principle relative to a functor F into …

Multimode Type Theory (MTT) is a generic type theory that can be instantiated with an
arbitrary mode theory to model features like parametricity, cohesion and guarded recursion …

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 …

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 …