Coq is built around a well-delimited kernel that perfoms typechecking for definitions in a
variant of the Calculus of Inductive Constructions (CIC). Although the metatheory of CIC is …

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 …

We define and develop two-level type theory (2LTT), a version of Martin-Löf type theory
which combines two different type theories. We refer to them as the 'inner'and the 'outer'type …

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 …

In dependent type theory, impredicativity is a powerful logical principle that allows the
definition of propositions that quantify over arbitrarily large types, potentially resulting in self …

Equations is a plugin for the Coq proof assistant which provides a notation for defining
programs by dependent pattern-matching and structural or well-founded recursion. It …

Building on the recent extension of dependent type theory with a universe of definitionally
proof-irrelevant types, we introduce TTobs, a new type theory based on the setoidal …

Dependently typed programming languages and proof assistants such as Agda and Coq
rely on computation to automatically simplify expressions during type checking. To …

Program verification in the large is not only a matter of mechanizing a program logic to
handle the semantics of your programming language. You must reason in the mathematics …

There is a critical tension between substitution, dependent elimination and effects in type
theory. In this paper, we crystallize this tension in the form of a no-go theorem that …