Understanding Haskell-style Overloading via Open Data and Open Functions

TL;DR

This paper introduces System F_D, a new core language with open data types and functions, providing a uniform semantics for Haskell-style overloading and encoding advanced type class features more expressively.

Contribution

It presents a novel semantics for overloading using open data and functions, mechanized in Lean4, surpassing existing semantics in expressiveness without extra axioms.

Findings

System F_D can encode advanced Haskell type class features.

The semantics is mechanized in Lean4, ensuring formal correctness.

It offers a more expressive framework than current semantics.

Abstract

We present a new, uniform semantics for Haskell-style overloading. We realize our approach in a new core language, System F$_\mathrm{D}$, whose metatheory we mechanize in the Lean4 interactive theorem prover. System F$_\mathrm{D}$ is distinguished by its open data types and open functions, each given by a collection of instances rather than by a single definition. We show that System F$_\mathrm{D}$ can encode advanced features of Haskell's of type class systems, more expressively than current semantics of these features, and without assuming additional type equality axioms.