Bidirectional type class instances

Koen Pauwels, Georgios Karachalias, Michiel Derhaeg, Tom Schrijvers
2019 Proceedings of the 12th ACM SIGPLAN International Symposium on Haskell - Haskell 2019  
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
more » ... s 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. CCS Concepts • Theory of computation → Type theory; • Software and its engineering → Functional languages.
doi:10.1145/3331545.3342596 dblp:conf/haskell/PauwelsKDS19 fatcat:2nc3z5itlngozbo3dy2heh66k4