A Duality of Sorts
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Sorting algorithms are one of the key pedagogical foundations of computer science, and their properties have been studied heavily. Perhaps less well known, however, is the fact that many of the basic sorting algorithms exist as a pair, and that these pairs arise naturally out of the duality between folds and unfolds. In this paper, we make this duality explicit, by showing how to define common sorting algorithms as folds of unfolds, or, dually, as unfolds of folds. This duality is preserved even when considering optimised sorting algorithms that require more exotic variations of folds and unfolds, and intermediary data structures. While all this material arises naturally from a categorical modelling of these recursion schemes, we endeavour to keep this presentation accessible to those not versed in abstract nonsense.
KeywordsSorting Algorithm Functional Programming Recursion Scheme Input List Empty List
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- Braun, W., Rem, M.: A logarithmic implementation of flexible arrays. Memorandum MR83/4, Eindhoven University of Technology (1983)Google Scholar
- Gibbons, J., Jones, G.: The Under-Appreciated Unfold. In: Proceedings of the International Conference on Functional Programming, ICFP 1998, pp. 273–279. ACM (1998), doi:10.1145/289423.289455Google Scholar
- van Groningen, J., van Noort, T., Achten, P., Koopman, P., Plasmeijer, R.: Exchanging sources between Clean and Haskell: A double-edged front end for the Clean compiler. In: Proceedings of the Third ACM Haskell Symposium on Haskell, Haskell 2010, pp. 49–60. ACM (2010), doi:10.1145/1863523.1863530Google Scholar
- Hinze, R., James, D.W.H., Harper, T., Wu, N., Magalhães, J.P.: Sorting with bialgebras and distributive laws. In: Proceedings of the 8th ACM SIGPLAN Workshop on Generic Programming, WGP 2012, pp. 69–80. ACM (2012), doi:10.1145/2364394.2364405Google Scholar
- Knuth, D.E.: The Art of Computer Programming, 2nd edn. Sorting and Searching, vol. 3. Addison-Wesley (1998)Google Scholar
- Peyton Jones, S., et al.: Haskell 98, Language and Libraries. The Revised Report. Cambridge University Press (2003), A special issue of JFPGoogle Scholar