The Sketch of a Polymorphic Symphony

Title: The Sketch of a Polymorphic Symphony

Research Question: How can functional strategies, a form of second-order polymorphism, be used to create a model for parameterized and typed strategic programming?

Methodology: The authors propose a model of functional strategies, a first-class generic function that can traverse into terms of any type while mixing uniform and type-specific behavior. This model is characterized by three key features: first-class polymorphism, run-time type case, and a fundamental combinator for folding over constructor applications.

Results: The authors present two original forms of parameterization. Firstly, they design parameters for the specific control-flow, data-flow, and traversal characteristics of more concrete traversal schemes. Secondly, they use overloading to postpone commitment to a specific type scheme of traversal. This results in a portfolio of traversal schemes that can be viewed as a challenging benchmark for setups for typed generic programming.

Implications: The model and suite of traversal schemes developed in this paper suggest that parameterized + typed strategic programming is a potent combination of parametric, intensional, polytypic, and ad-hoc polymorphism. This could have significant implications for the field of typed generic programming and the development of more flexible and expressive programming languages.

In conclusion, the Sketch of a Polymorphic Symphony presents a model for functional strategies that could potentially revolutionize the field of typed generic programming. By using first-class polymorphism, run-time type case, and a fundamental combinator for folding over constructor applications, the authors create a parameterized and typed strategic programming approach that is both flexible and expressive. This could lead to the development of more powerful and versatile programming languages in the future.

Link to Article: https://arxiv.org/abs/0204013v2 Authors: arXiv ID: 0204013v2