A Simple Semantics for Haskell Overloading

TL;DR

This paper introduces a new semantics for Haskell overloading that captures non-parametric behaviors introduced by advanced type class features, aligning formal understanding with practical language behavior.

Contribution

It proposes a semantics interpreting polymorphic expressions through their ground instances, accommodating non-parametric features like overlapping instances and functional dependencies.

Findings

The semantics accurately models non-parametric behaviors.

It aligns formal semantics with practical Haskell language features.

Provides a foundation for reasoning about complex type class extensions.

Abstract

As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional dependencies and equality constraints allow the satisfiability of predicates to refine typing; this means that the interpretations of equivalent qualified types may not be interconvertible. Overlapping instances and instance chains allow predicates to be satisfied without determining the implementations of their associated class methods, introducing truly non-parametric behavior. We propose a new approach to the semantics of type classes, interpreting polymorphic expressions by the behavior of each of their ground instances, but without requiring that those behaviors be parametrically determined. We argue that this approach both matches the intuitive meanings of qualified types and accurately models the behavior of programs