The Art, Science, and Engineering of Programming, 2022, Vol. 6, Issue 2, Article 7
Submission date: 2021-05-26
Publication date: 2021-11-15
Full text: PDF
Reynolds showed us how to use continuation-passing style and defunctionalization to transform a recursive interpreter for a language into an abstract machine for programs in that language. The same techniques explain other programming tricks, including zippers and accumulating parameters.
Buried within all those applications there is usually a hidden appeal to the algebraic property of associativity.
Our purpose in this paper is to entice associativity out of the shadows and into the limelight.
We revisit some well-known applications (factorial, fast reverse, tree flattening, and a compiler for a simple expression language) to spotlight their dependence on associativity.
We replay developments of these programs through a series of program transformations and data refinements, justified by equational reasoning.
Understanding the crucial role played by associativity clarifies when continuation-passing style and defunctionalization can help and when they cannot, and may prompt other applications of these techniques.
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