Strategic polymorphism requires just two combinators!

TL;DR

This paper simplifies the implementation of functional strategies in programming by showing that just two combinators are sufficient for strategic polymorphism, supported by a generic operational model.

Contribution

It introduces a minimalistic approach to functional strategies using only two primitive combinators, applicable across different functional languages.

Findings

Captured strategic polymorphism with two combinators

Provided an operational reference model in Haskell

Reconstructed parts of the Strafunski library

Abstract

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.