Elaborating Intersection and Union Types

ICFP 2012 (Copenhagen, September 2012); arXiv:1206.5386 [cs.PL]

Joshua Dunfield

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.

Reader’s guide

You should probably read the journal version of the paper instead.

Conference slides and video (YouTube)

Final version (June 2012)

BibTeX entry

  @InProceedings{Dunfield12:elaboration,
    author =    {Joshua Dunfield},
    title =     {Elaborating Intersection and Union Types},
    booktitle = {Int'l Conf. Functional Programming},
    month =     sep,
    year =      {2012},
    note =      {\url{arXiv:1206.5386 [cs.PL]}}
  }
  

Note

I submitted this paper to the arXiv, and granted the arXiv a distribution licence. The arXiv is efficiently managed and 100% open-access; the ACM Digital Library is neither. I consider the arXiv version to be canonical.
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