Elaborating Intersection and Union Types

TL;DR

This paper introduces a foundational approach for compiling unrestricted intersection and union types in programming languages, using an elaboration system with a Forsythe-like merge to preserve type safety during evaluation.

Contribution

It presents a novel elaboration type system that supports unrestricted intersection and union types, enabling encoding of diverse language features with a type-preserving evaluation strategy.

Findings

Prototype implementation demonstrates practical applications

Elaboration system supports encoding of records and operator overloading

Type-preserving evaluation aligns with source program semantics

Abstract

Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide general mechanisms that subsume many different features. In modern type systems, parametric polymorphism is fundamental, but intersection polymorphism has gained little traction in programming languages. Most practical intersection type systems have supported only refinement intersections, which increase the expressiveness of types (more precise properties can be checked) without altering the expressiveness of terms; refinement intersections can simply be erased during compilation. In contrast, unrestricted intersections increase the expressiveness of terms, and can be used to encode diverse language features, promising an economy of both theory and implementation. We describe a foundation for compiling unrestricted intersection and union types: an elaboration type system that generates ordinary lambda-calculus terms. The key feature is a Forsythe-like merge construct. With this construct, not all reductions of the source program preserve types; however, we prove that ordinary call-by-value evaluation of the elaborated program corresponds to a type-preserving evaluation of the source program. We also describe a prototype implementation and applications of unrestricted intersections and unions: records, operator overloading, and simulating dynamic typing.