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 …

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 recent years, we have seen several new models of dependent type theory extended with
some form of modal necessity operator, including nominal type theory, guarded and clocked …

Two approaches exist to incorporate parametricity into proof assistants based on dependent
type theory. On the one hand, parametricity translations conveniently compute parametricity …

Functional reactive programming (FRP) is a paradigm for programming with signals and
events, allowing the user to describe reactive programs on a high level of abstraction. For …

In type theory, coinductive types are used to represent processes, and are thus crucial for
the formal verification of non-terminating reactive programs in proof assistants based on type …

We present a new model of guarded dependent type theory (GDTT), a type theory with
guarded recursion and multiple clocks in which one can program with and reason about …

Functional reactive programming (FRP) provides a high-level interface for implementing
reactive systems in a declarative manner. However, this high-level interface has to be …

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming
with coinductive types, allowing productivity to be encoded in types, and for reasoning about …

In type theory, programming and reasoning with possibly non-terminating programs and
potentially infinite objects is achieved using coinductive types. Recursively defined …