| Summary: | Context 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. Inquiry Buried within all those applications there is usually a hidden appeal to the algebraic property of associativity. Approach Our purpose in this paper is to entice associativity out of the shadows and into the limelight. Knowledge 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. Grounding We replay developments of these programs through a series of program transformations and data refinements, justified by equational reasoning. Importance 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 tech-niques. © Jeremy Gibbons.
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