Language researchers and designers have extended a wide variety of type systems to support gradual typing, which enables languages to seamlessly combine dynamic and static checking. These efforts consistently demonstrate ...

Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized ...

Union types allow to capture the possibility of a term to be of several possibly unrelated types. Traditional static approaches to union types are untagged and tagged unions, which present dual advantages in their use. ...

Gradual typing enables a smooth and progressive integration of static and dynamic typing. The semantics of a gradually-typed program is given by translation to an intermediate language with casts: runtime type checks ...

Dynamically-typed languages offer easy interaction with ad hoc data such as JSON and S-expressions; staticallytyped languages offer powerful tools for working with structured data, notably algebraic datatypes, which are a ...

Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual ...

Language researchers and designers have extended a wide variety of type systems to support gradual typing, which enables languages to seamlessly combine dynamic and static checking. These efforts consistently demonstrate ...

Refinement types are an effective language-based verification technique. However, as any expressive typing discipline, its strength is its weakness, imposing sometimes undesired rigidity. Guided by abstract interpretation, ...

Despite their obvious advantages in terms of static reasoning, the adoption of effect systems is still rather limited in practice. Recent advances such as generic effect systems, lightweight effect polymorphism, and gradual ...

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition ...