We propose a type system for functional languages with gradual types and set-theoretic type
connectives and prove its soundness. In particular, we show how to lift the definition of the …

We extend classic union and intersection type systems with a type-case construction and
show that the combination of the union elimination rule of the former and the ty** rules for …

Records are finite functions from keys to values. In this work we focus on two main distinct
usages of records: structs and maps. The former associate different keys to values of …

Programming languages that support multiple dispatch rely on an expressive notion of
subty** to specify method applicability. In these languages, type annotations on method …

Programming languages like P4 enable specifying the behavior of network data planes in
software. However, with increasingly powerful and complex applications running in the …

Erlang is a functional programming language with dynamic ty**. The language offers
great flexibility for destructing values through pattern matching and dynamic type tests …

Polymorphic variants are a useful feature of the OCaml language whose current definition
and implementation rely on kinding constraints to simulate a subty** relation via …

Elixir is a dynamically-typed functional language running on the Erlang Virtual Machine,
designed for building scalable and maintainable applications. Its characteristics have …

This article is the second part of a two articles series about the definition of higher order
polymorphic functions in a type system with recursive types and set-theoretic type …

Union types are nowadays a common feature in many modern programming languages.
This paper investigates a formulation of union types with an elimination construct that …