We introduce MTT, a dependent type theory which supports multiple modalities. MTT is
parametrized by a mode theory which specifies a collection of modes, modalities, and …

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 …

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 …

Fitch-style modal lambda calculi enable programming with necessity modalities in a typed
lambda calculus by extending the ty** context with a delimiting operator that is denoted by …

Graded type theories are an emerging paradigm for augmenting the reasoning power of
types with parameterizable, fine-grained analyses of program properties. There have been …

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

We describe the foundation of the metaprogramming language, Mœbius, which supports the
generation of polymorphic code and, more importantly, the analysis of polymorphic code via …

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 …