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.
@incollection{Laemmel02-SPS,
author = "Ralf L{\"a}mmel",
title = "{The Sketch of a Polymorphic Symphony}",
booktitle = {Proc.\ of International Workshop on Reduction Strategies
in Rewriting and Programming (WRS 2002)},
editor = {Bernhard Gramlich and Salvador Lucas},
publisher = "Elsevier Science",
series = "ENTCS",
year = 2002,
volume = {70},
issue = {6},
note = "21 pages"
}