The implementation and semantics of dependent type theories can be studied in a syntax-
independent way: the objective metatheory of dependent type theories exploits the universal …

We present an extensive mechanization of the metatheory of Martin-Löf Type Theory (MLTT)
in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not …

Modalities are everywhere in programming and mathematics! Despite this, however, there
are still significant technical challenges in formulating a core dependent type theory with …

In this paper, we introduce DeLaM, a dependent layered modal type theory which enables
meta-programming in Martin-Löf type theory (MLTT) with recursion principles on open code …

We present the Kripke-style modal type theory, Mint, which combines dependent types and
the necessity modality. It extends the Kripke-style modal lambda-calculus by Pfenning and …

We develop the usage of certain type theories as specification languages for algebraic
theories and inductive types. We observe that the expressive power of dependent type …

There are multiple ways to formalise the metatheory of type theory. For some purposes, it is
enough to consider specific models of a type theory, but sometimes it is necessary to refer to …

In this thesis, I study the interaction between type theory and continuity, a mathematical
concept describing the intuition that a function can only query a finite part of its argument …

Dependently typed proof assistant rely crucially on definitional equality, which relates types
and terms that are automatically identified in the underlying type theory. This paper extends …

Dependently typed languages allow us to state a program's expected properties and
automatically check that they are satisfied at compile time. Yet the implementations of these …