We have built the first family of tagless interpretations for a higher-order typed object
language in a typed metalanguage (Haskell or ML) that require no dependent types …

We introduce a generalization of monads, called relative monads, allowing for underlying
functors between different categories. Examples include finite-dimensional vector spaces …

We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major
open problem in the syntactic metatheory of cubical type theory. Our normalization result is …

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 …

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

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 …

The nominal approach to abstract syntax deals with the issues of bound names and α-
equivalence by considering constructions and properties that are invariant with respect to …

The relationship between categorical gluing and proofs using the logical relation technique
is folklore. In this paper we work out this relationship for Martin-Löf type theory and show that …

We extend universal algebra and its equational logic from first to second order as follows. 1
We consider second-order equational presentations as specified by identities between …