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Column-Wise Extendible Vector Expressions and the Relational Computation of Sets of Sets

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Mathematics of Program Construction (MPC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9129))

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Abstract

We present a technique for the relational computation of sets of sets. It is based on specific vector expressions, which form the syntactical counterparts of B. Kehden’s vector predicates. Compared with the technique that directly solves a posed problem by the development of a vector expression of type \({2^X}\,\leftrightarrow \,{\mathbf{1}\!\!\!\mathbf{1}}\) from a formal logical problem description, we reduce the solution to the development of inclusions between vector expressions of type \({X}\,\leftrightarrow \,{\mathbf{1}\!\!\!\mathbf{1}}\). Frequently, this is a lot simpler. The transition from the inclusions to the desired vector expression of type \({2^X}\,\leftrightarrow \,{\mathbf{1}\!\!\!\mathbf{1}}\) is then immediately possible by means of a general result. We apply the technique to some examples from different areas and show how the solutions behave with regard to running time if implemented and evaluated by the Kiel RelView tool.

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Acknowledgement

I want to thank the reviewers for carefully reading the paper and for their very detailed and valuable comments. They helped to improve the paper.

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Authors and Affiliations

  1. Institut Für Informatik, Universität Kiel, 24098, Kiel, Germany

    Rudolf Berghammer

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  1. Rudolf Berghammer
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Correspondence to Rudolf Berghammer .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Ralf Hinze

  2. University of Bonn, Bonn, Germany

    Janis Voigtländer

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Berghammer, R. (2015). Column-Wise Extendible Vector Expressions and the Relational Computation of Sets of Sets. In: Hinze, R., Voigtländer, J. (eds) Mathematics of Program Construction. MPC 2015. Lecture Notes in Computer Science(), vol 9129. Springer, Cham. https://doi.org/10.1007/978-3-319-19797-5_12

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  • DOI: https://doi.org/10.1007/978-3-319-19797-5_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19796-8

  • Online ISBN: 978-3-319-19797-5

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