Kind Inference for Datatypes: Technical Supplement

TL;DR

This paper explores kind inference for datatypes in Haskell-like languages, providing new declarative specifications and algorithms, along with proofs of soundness and completeness, to aid language designers and implementors.

Contribution

It introduces novel declarative and algorithmic approaches for kind inference in Haskell, including extensions for modern features like PolyKinds and dependent types.

Findings

Proposes declarative specifications for datatype kind inference

Provides sound and complete algorithms for kind inference

Connects theoretical results with GHC implementation details

Abstract

In recent years, languages like Haskell have seen a dramatic surge of new features that significantly extends the expressive power of their type systems. With these features, the challenge of kind inference for datatype declarations has presented itself and become a worthy research problem on its own. This paper studies kind inference for datatypes. Inspired by previous research on type-inference, we offer declarative specifications for what datatype declarations should be accepted, both for Haskell98 and for a more advanced system we call PolyKinds, based on the extensions in modern Haskell, including a limited form of dependent types. We believe these formulations to be novel and without precedent, even for Haskell98. These specifications are complemented with implementable algorithmic versions. We study soundness, completeness and the existence of principal kinds in these systems, proving the properties where they hold. This work can serve as a guide both to language designers who wish to formalize their datatype declarations and also to implementors keen to have principled inference of principal types. This technical supplement to Kind Inference for Datatypes serves to expand upon the text in the main paper. It contains detailed typing rules, proofs, and connections to the Glasgow Haskell Compiler (GHC).