The Sketch of a Polymorphic Symphony

TL;DR

This paper presents a detailed Haskell-based model of functional strategies that combine polymorphism, run-time type case, and traversal combinators to enable flexible, parameterized, and typed generic programming schemes.

Contribution

It introduces a novel Haskell model for functional strategies with advanced parameterization and overloading, enhancing typed generic traversal capabilities.

Findings

Captures common traversal schemes in a highly parameterized style

Designs parameters for control-flow, data-flow, and traversal characteristics

Provides a benchmark suite for typed generic programming setups

Abstract

In previous work, we have introduced functional strategies, that is, first-class generic functions that can traverse into terms of any type while mixing uniform and type-specific behaviour. In the present paper, we give a detailed description of one particular Haskell-based model of functional strategies. This model is characterised as follows. Firstly, we employ first-class polymorphism as a form of second-order polymorphism as for the mere types of functional strategies. Secondly, we use an encoding scheme of run-time type case for mixing uniform and type-specific behaviour. Thirdly, we base all traversal on a fundamental combinator for folding over constructor applications. Using this model, we capture common strategic traversal schemes in a highly parameterised style. We study two original forms of parameterisation. Firstly, we design parameters for the specific control-flow, data-flow and traversal characteristics of more concrete traversal schemes. Secondly, we use overloading to postpone commitment to a specific type scheme of traversal. The resulting portfolio of traversal schemes can be regarded as a challenging benchmark for setups for typed generic programming. The way we develop the model and the suite of traversal schemes, it becomes clear that parameterised + typed strategic programming is best viewed as a potent combination of certain bits of parametric, intensional, polytypic, and ad-hoc polymorphism.