Linear type systems have a long and storied history, but not a clear path forward to integrate
with existing languages such as OCaml or Haskell. In this paper, we study a linear type …

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 …

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 …

We present PureCake, a mechanically-verified compiler for PureLang, a lazy, purely
functional programming language with monadic effects. PureLang syntax is Haskell-like and …

Despite the great success of inferring and programming with universal types, their dual—
existential types—are much harder to work with. Existential types are useful in building …

We present the design and implementation of the Small Scale Reflection proof methodology
and tactic language (aka SSR) for the Lean 4 proof assistant. Like its Coq predecessor …

Over twenty years ago, Abadi et al. established the Dependency Core Calculus (DCC) as a
general purpose framework for analyzing dependency in typed programming languages …

Some parts of dependently typed programs constitute evidence of their type-correctness
and, once checked, are unnecessary for execution. These parts can easily become …

The expression problem describes how most types can easily be extended with new ways to
produce the type or new ways to consume the type, but not both. When abstract syntax trees …

Type family applications in Haskell must be fully saturated. This means that all type-level
functions have to be first-order, leading to code that is both messy and longwinded. In this …