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arXiv · 2111.10413

Continuation-Passing Style, Defunctionalization, Accumulations, and Associativity

Jeremy Gibbons
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Abstract

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 techniques.

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Jeremy Gibbons. 2021-11-19. Continuation-Passing Style, Defunctionalization, Accumulations, and Associativity. https://doi.org/10.22152/programming-journal.org%2F2022%2F6%2F7

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