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Unifying Correctness Statements

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Mathematics of Program Construction (MPC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7342))

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Abstract

Partial, total and general correctness and further models of sequential computations differ in their treatment of finite, infinite and aborting executions. Algebras structure this diversity of models to avoid the repeated development of similar theories and to clarify their range of application. We introduce algebras that uniformly describe correctness statements, correctness calculi, pre-post specifications and loop refinement rules in five kinds of computation models. This extends previous work that unifies iteration, recursion and program transformations for some of these models. Our new description includes a relativised domain operation, which ignores parts of a computation, and represents bound functions for claims of termination by sequences of tests. We verify all results in Isabelle heavily using its automated theorem provers.

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Author information

Authors and Affiliations

  1. Institut für Programmiermethodik und Compilerbau, Universität Ulm, Germany

    Walter Guttmann

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  1. Walter Guttmann
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Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, 28660, Boadilla del Monte, Madrid, Spain

    Pablo Nogueira

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Guttmann, W. (2012). Unifying Correctness Statements. In: Gibbons, J., Nogueira, P. (eds) Mathematics of Program Construction. MPC 2012. Lecture Notes in Computer Science, vol 7342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31113-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-31113-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31112-3

  • Online ISBN: 978-3-642-31113-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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