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Unifying Recursion in Partial, Total and General Correctness

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Unifying Theories of Programming (UTP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6445))

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Abstract

We give an algebraic semantics of non-deterministic, sequential programs which is valid for partial, total and general correctness. It covers full recursion based on a unified approximation order. We provide explicit solutions in terms of the refinement order. As an application, we systematically derive a semantics of while-programs common to the three correctness approaches.

UTP’s designs and prescriptions represent programs as pairs of termination and state transition information in total and general correctness, respectively. We show that our unified semantics induces a pair-based representation which is common to the correctness approaches. Operations on the pairs, including finite and infinite iteration, can be derived systematically. We also provide the effect of full recursion on the unified, pair-based representation.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Sheffield, UK

    Walter Guttmann

Authors
  1. Walter Guttmann
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Editor information

Editors and Affiliations

  1. School of Computing, University of Teesside, Borough Road, TS1 3BA, Middlesbrough, UK

    Shengchao Qin

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Guttmann, W. (2010). Unifying Recursion in Partial, Total and General Correctness. In: Qin, S. (eds) Unifying Theories of Programming. UTP 2010. Lecture Notes in Computer Science, vol 6445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16690-7_10

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  • DOI: https://doi.org/10.1007/978-3-642-16690-7_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16689-1

  • Online ISBN: 978-3-642-16690-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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