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Correctness of programs over poor signatures

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Book cover Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 560))

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Abstract

A poor signature consists of one (unary) function symbol, a symbol for equality and a number of constant symbols. Due to the lack of internal structure, interpretations of poor signatures differ from interpretations of richer signatures in some respects. One of them is the completeness of Hoare-like systems relative to the first-order theory of the interpretation.

We demonstrate that Hoare-like proof systems for partial correctness are incomplete in any infinite (and not uniformly locally finite) interpretation of a poor signature, even if the systems are supplied with the first-order theory of the interpretation. The reason is that there are always relations which are definable by while-programs but not by formulas. This is shown by an application of a result used in model theory. We also answer the question which enrichments of the signature are necessary and sufficient to allow (nontrivial) infinite interpretations where Hoare-like systems are complete.

The preparation of this article has been supported by the BMFT (ITS 9002 A). The responsibility for the contents lies with the author.

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Authors and Affiliations

  1. Department of Computer Science, University Oldenburg, D-2900, Oldenburg, Germany

    Hardi Hungar

Authors
  1. Hardi Hungar
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Somenath Biswas Kesav V. Nori

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© 1991 Springer-Verlag Berlin Heidelberg

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Hungar, H. (1991). Correctness of programs over poor signatures. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_64

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  • DOI: https://doi.org/10.1007/3-540-54967-6_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54967-3

  • Online ISBN: 978-3-540-46612-3

  • eBook Packages: Springer Book Archive

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