Dependent types allow us to express precisely what a function is intended to do. Recent
work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also …

We present a graded modal type theory, a dependent type theory with grades that can be
used to enforce various properties of the code. The theory has Π-types, weak and strong Σ …

Graded Type Theory provides a mechanism to track and reason about resource usage in
type systems. In this paper, we develop GraD, a novel version of such a graded dependent …

Substructural type systems are growing in popularity because they allow for a resourceful
interpretation of data which can be used to rule out various software bugs. Indeed …

We combine dependent types with linear type systems that soundly and completely capture
polynomial time computation. We explore two systems for capturing polynomial time: one …

Ownership and borrowing systems, designed to enforce safe memory management without
the need for garbage collection, have been brought to the fore by the Rust programming …

Adjoint logic is a general approach to combining multiple logics with different structural
properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each …

In quantitative reasoning one compares objects by distances, instead of equivalence
relations, so that one can measure how much they are similar, rather than just saying …

The modern theory of functional programming languages uses monads for encoding
computational side-effects and side-contexts, beyond bare-bone program logic. Even …

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 …