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

We present calf, ac ost-a ware l ogical f ramework for studying quantitative aspects of
functional programs. Taking inspiration from recent work that reconstructs traditional aspects …

The aim of staged compilation is to enable metaprogramming in a way such that we have
guarantees about the well-formedness of code output, and we can also mix together object …

Hofmann and Streicher famously showed how to lift Grothendieck universes into presheaf
topoi, and Streicher has extended their result to the case of sheaf topoi by sheafification. In …

We propose a new sheaf semantics for secure information flow over a space of abstract
behaviors, based on synthetic domain theory: security classes are open/closed partitions …

Metatheorems about type theories are often proven by interpreting the syntax into models
constructed using categorical gluing. We propose to use only sconing (gluing along a global …

We present a novel analysis of the fundamental Löb induction principle from guarded
recursion. Taking advantage of recent work in modal type theory and univalent foundations …

We present a cubical type theory based on the Cartesian cube category (faces,
degeneracies, symmetries, diagonals, but no connections or reversal) with univalent …