Abstract
Quicksort (Commun. ACM 4(7):321–322, 1961) remains one of the most studied algorithms in computer science. It is important not only as a practical sorting method, but also as a splendid teaching aid for introducing recursion and systematic algorithm development. The algorithm has been studied extensively; so, it is natural to assume that everything that needs to be said about it has already been said. Yet, in attempting to code it using a recent programming language of our design, we discovered that its structure is more clearly expressed as a concurrent program that manipulates a shared mutable store, without any locking or explicit synchronization. In this paper, we describe the essential aspects of our programming language Orc (Proceedings of FMOODS/FORTE, vol. 5522 of LNCS, pp. 1–25. Springer 2009), show a number of examples that combine its features in various forms, and then develop a concise description of Quicksort. We hope to highlight the importance of including concurrency, recursion and mutability within a single theory.
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- 1.
In previous publications, F <x< G was written as F where xG.
- 2.
An implementation can only approximate this guarantee.
- 3.
An implementation can only approximate this guarantee.
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Acknowledgements
Jayadev Misra is deeply grateful to Tony Hoare for research ideas, inspiration,and personal friendship spanning over 3 decades. It is no exaggeration that hewould not have pursued certain research directions, that have ultimately provedquite successful, had it not been for Tony’s encouragement. This paper is a smalltoken of appreciation.
The authors are indebted to Doug McIlroy and Manuel Serrano fortheir careful reading of this manuscript and many perceptive commentsand suggestions. Our long-time collaborators, Albert Benveniste, ClaudeJard, and Jose Meseguer have helped us refine the underlying ideas ofOrc.
This work is partially supported by National Science Foundation grant CCF-0811536.
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Kitchin, D., Quark, A., Misra, J. (2010). Quicksort: Combining Concurrency, Recursion, and Mutable Data Structures. In: Roscoe, A., Jones, C., Wood, K. (eds) Reflections on the Work of C.A.R. Hoare. Springer, London. https://doi.org/10.1007/978-1-84882-912-1_11
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