Refinement Kinds: Type-safe Programming with Practical Type-level Computation (Extended Version)

TL;DR

This paper introduces kind refinement, a novel approach to type specifications in a polymorphic language, enabling rich type manipulations and meta-programming with formal safety guarantees.

Contribution

It develops the concept of kind refinement, allowing rich kind specifications and advanced type manipulations in a type-safe, ML-like language.

Findings

Formal proof of type safety

Prototype implementation of kind and type checkers

Enhanced expressiveness for type reflection and meta-programming

Abstract

This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of comprehension principles expressed by predicates over values in the type domain, kind refinements provide rich kind specifications by means of predicates over types in the kind domain. By leveraging our powerful refinement kind discipline, types in our language are not just used to statically classify program expressions and values, but also conveniently manipulated as tree-like data structures, with their kinds refined by logical constraints on such structures. Remarkably, the resulting typing and kinding disciplines allow for powerful forms of type reflection, ad-hoc polymorphism and type meta-programming, which are often found in modern software development, but not typically expressible in a type-safe manner in general purpose languages. We validate our approach both formally and pragmatically by establishing the standard meta-theoretical results of type safety and via a prototype implementation of a kind checker, type checker and interpreter for our language.