Understanding functional dependencies via constraint handling rules

TLDR

Functional dependencies extend Haskell type classes, but existing sufficient conditions are restrictive, and prior work used CHRs to describe type extensions. The paper reformulates functional dependencies using Constraint Handling Rules. The authors relax the restrictive conditions and propose sound extensions of functional dependencies via CHRs. These extensions enable sound, complete, and decidable type inference and broaden the applicability of functional dependencies.

Abstract

Abstract Functional dependencies are a popular and useful extension to Haskell style type classes. We give a reformulation of functional dependencies in terms of Constraint Handling Rules (CHRs). In previous work, CHRs have been employed for describing user-programmable type extensions in the context of Haskell style type classes. Here, we make use of CHRs to provide for the first time a concise result that under some sufficient conditions, functional dependencies allow for sound, complete and decidable type inference. The sufficient conditions imposed on functional dependencies can be very limiting. We show how to safely relax these conditions and suggest several sound extensions of functional dependencies. Our results allow for a better understanding of functional dependencies and open up the opportunity for new applications.