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A Calculus for Set-Based Program Development

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Formal Methods and Software Engineering (ICFEM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2885))

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Abstract

We propose an algebraic calculus for set-based program development. First, we reconstruct a fragment of set theory via atomic distributive lattices (ADL). Semantically, ADL extends boolean reasoning about sets by element-wise reasoning; it avoids presupposing a universal set. Operationally, ADL yields abstract, concise, elegant proofs from few elementary principles. Second, we develop a focused automated proof-search procedure for ADL with simple deduction and powerful reduction and simplification rules. Proof-search is guided by rewriting techniques. The procedure decides several subclasses. Main application is the proof-support for formal methods like B or Z.

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Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, D-86135, Augsburg, Germany

    Georg Struth

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  1. Georg Struth
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Editor information

Editors and Affiliations

  1. School of Computing, National University of Singapore, Singapore

    Jin Song Dong

  2. University of York,  

    Jim Woodcock

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© 2003 Springer-Verlag Berlin Heidelberg

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Struth, G. (2003). A Calculus for Set-Based Program Development. In: Dong, J.S., Woodcock, J. (eds) Formal Methods and Software Engineering. ICFEM 2003. Lecture Notes in Computer Science, vol 2885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39893-6_31

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  • DOI: https://doi.org/10.1007/978-3-540-39893-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20461-9

  • Online ISBN: 978-3-540-39893-6

  • eBook Packages: Springer Book Archive

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