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An Axiomatization of Arrays for Kleene Algebra with Tests

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Relations and Kleene Algebra in Computer Science (RelMiCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4136))

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Abstract

The formal analysis of programs with arrays is a notoriously difficult problem due largely to aliasing considerations. In this paper we augment the rules of Kleene algebra with tests (KAT) with rules for the equational manipulation of arrays in the style of schematic KAT. These rules capture and make explicit the essence of subscript aliasing, where two array accesses can be to the same element. We prove the soundness of our rules, as well as illustrate their usefulness with several examples, including a complete proof of the correctness of heapsort.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, NY, 14853-7501, USA

    Kamal Aboul-Hosn

Authors
  1. Kamal Aboul-Hosn
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Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Manchester,  

    Renate A. Schmidt

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© 2006 Springer-Verlag Berlin Heidelberg

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Aboul-Hosn, K. (2006). An Axiomatization of Arrays for Kleene Algebra with Tests. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_4

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  • DOI: https://doi.org/10.1007/11828563_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37873-0

  • Online ISBN: 978-3-540-37874-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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