We introduce System FC, which extends System F with support for non-syntactic type
equality. There are two main extensions:(i) explicit witnesses for type equalities, and (ii) …

We report on an extension of Haskell with open type-level functions and equality constraints
that unifies earlier work on GADTs, functional dependencies, and associated types. The …

The LF logical framework codifies a methodology for representing deductive systems, such
as programming languages and logics, within a dependently typed λ-calculus. In this …

We generalize the adjoint logics of Benton and Wadler [1994, 1996] and Reed [2009] to
allow multiple different adjunctions between the same categories. This provides insight into …

Abstract Types express properties of programs; typechecking is specification checking.
However, the specifications expressed by types in conventional type systems are imprecise …

The Glasgow Haskell Compiler is an optimizing compiler that expresses and manipulates
first-class equality proofs in its intermediate language. We describe a simple, elegant …

Modular languages support generative type abstraction, ensuring that an abstract type is
distinct from its representation, except inside the implementation where the two are …

Operational Type Theory (OpTT) is a type theory allowing possibly diverging programs while
retaining decidability of type checking and a consistent logic. This is done by distinguishing …

We present a full-spectrum dependently typed core language which includes both
nontermination and computational irrelevance (aka erasure), a combination which has not …

We present Stardust, an implementation of a type system for a subset of ML with type
refinements, intersection types, and union types, enabling programmers to legibly specify …