Bidirectional Type Class Instances (Extended Version)

TL;DR

This paper introduces Bidirectional Type Class Instances for Haskell, enabling more flexible and expressive interactions between GADTs and type classes by interpreting instances as logical bi-implications.

Contribution

It proposes a conservative extension to Haskell's type classes, including a formal design, type inference algorithm, and proof-of-concept implementation.

Findings

Enhanced ability to define instances for GADTs

Formalization of bidirectional type class semantics

Implementation demonstrating practical feasibility

Abstract

GADTs were introduced in Haskell's eco-system more than a decade ago, but their interaction with several mainstream features such as type classes and functional dependencies has a lot of room for improvement. More specifically, for some GADTs it can be surprisingly difficult to provide an instance for even the simplest of type classes. In this paper we identify the source of this shortcoming and address it by introducing a conservative extension to Haskell's type classes: Bidirectional Type Class Instances. In essence, under our interpretation class instances correspond to logical bi-implications, in contrast to their traditional unidirectional interpretation. We present a fully-fledged design of bidirectional instances, covering the specification of typing and elaboration into System FC, as well as an algorithm for type inference and elaboration. We provide a proof-of-concept implementation of our algorithm, and revisit the meta-theory of type classes in the presence of our extension.