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 combine homotopy type theory with axiomatic cohesion, expressing the latter internally
with a version of 'adjoint logic'in which the discretization and codiscretization modalities are …

We define a general framework that abstracts the common features of many intuitionistic
substructural and modal logics/type theories. The framework is a sequent calculus/normal …

Polymorphic type systems such as System F enjoy the parametricity property: polymorphic
functions cannot inspect their type argument and will therefore apply the same algorithm to …

Dependent type theory allows us to write programs and to prove properties about those
programs in the same language. However, some properties do not require much proof, as …

We present a system of session types based on adjoint logic which generalizes standard
binary session types. Our system allows us to uniformly capture several new behaviors in …

The Fuzz programming language by Reed and Pierce uses an elegant linear type system
combined with a monad-like type to express and reason about probabilistic sensitivity …

Birkedal et al. recently introduced dependent right adjoints as an important class of (non-
fibered) modalities in type theory. We observe that several aspects of their calculus are left …

We present the semi-axiomatic sequent calculus (SAX) that blends features of Gentzen's
sequent calculus with an axiomatic formulation of intuitionistic logic. We develop and prove …

One idiosyncratic framing of type theory is as the study of operations invariant under
substitution. Modal type theory, by contrast, concerns the controlled integration of operations …