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Hidden Congruent Deduction

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Automated Deduction in Classical and Non-Classical Logics (FTP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1761))

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Abstract

Cleverly designed software often fails to satisfy its requirements strictly, but instead satisfies them behaviorally, in the sense that they appear to be satisfied under every experiment that can be performed on the system. A good example is the traditional implementation of sets by lists, where union as implemented by append fails to strictly satisfy basic laws like commutativity and idempotency, but does satisfy them behaviorally. It is becoming increasingly clear that behavioral specification is more appropriate to software engineering than traditional approaches that rely on strict satisfaction of axioms, and it is therefore becoming increasingly important to develop powerful techniques for behavioral verification. This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8,10,3,12,5] among other places; the most comprehensive survey currently available is [12].

On leave from Fundamentals of Computer Science, Faculty of Mathematics, University of Bucharest, Romania.

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Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, University of California at San Diego, San Diego

    Grigore Roşu & Joseph Goguen

Authors
  1. Grigore Roşu
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  2. Joseph Goguen
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Editors and Affiliations

  1. Leibniz-IMAG, 46 Avenue Felix Viallet, 38031, Grenoble cedex, France

    Ricardo Caferra

  2. Technical University of Vienna, Favoritenstraße 9-11/E185-2, 1040, Vienna, Austria

    Gernot Salzer

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© 2000 Springer-Verlag Berlin Heidelberg

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Roşu, G., Goguen, J. (2000). Hidden Congruent Deduction. In: Caferra, R., Salzer, G. (eds) Automated Deduction in Classical and Non-Classical Logics. FTP 1998. Lecture Notes in Computer Science(), vol 1761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46508-1_17

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  • DOI: https://doi.org/10.1007/3-540-46508-1_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67190-9

  • Online ISBN: 978-3-540-46508-9

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