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International Conference on Theory and Application of Diagrams

Diagrams 2012: Diagrammatic Representation and Inference pp 163–177Cite as

Speedith: A Diagrammatic Reasoner for Spider Diagrams

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7352)

Abstract

In this paper, we introduce Speedith which is a diagrammatic theorem prover for the language of spider diagrams. Spider diagrams are a well-known logic for which there is a sound and complete set of inference rules. Speedith provides a way to input diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. It is designed as a program that plugs into existing general purpose theorem provers. This allows for seamless formal verification of diagrammatic proof steps within established proof assistants such as Isabelle. We describe the general structure of Speedith, the diagrammatic language, the automatic mechanism that draws the diagrams when inference rules are applied on them, and how formal diagrammatic proofs are constructed.

Keywords

  • Inference Rule
  • Abstract Representation
  • Logical Connective
  • Rule Application
  • Proof Assistant

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-31223-6_19
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Author information

Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, UK

    Matej Urbas & Mateja Jamnik

  2. School of Computing, Engineering and Mathematics, University of Brighton, UK

    Gem Stapleton

  3. Autodesk, UK

    Jean Flower

Authors
  1. Matej Urbas
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  2. Mateja Jamnik
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  3. Gem Stapleton
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  4. Jean Flower
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, 6050 University Avenue, B3H 1W4, Halifax, NS, Canada

    Philip Cox

  2. Department of Computer Science, University of Auckland, Private bag 92019, Auckland, New Zealand

    Beryl Plimmer

  3. School of Computing, Unviersity of Kent, CT2 7NF, Canterbury, UK

    Peter Rodgers

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Urbas, M., Jamnik, M., Stapleton, G., Flower, J. (2012). Speedith: A Diagrammatic Reasoner for Spider Diagrams. In: Cox, P., Plimmer, B., Rodgers, P. (eds) Diagrammatic Representation and Inference. Diagrams 2012. Lecture Notes in Computer Science(), vol 7352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31223-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-31223-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31222-9

  • Online ISBN: 978-3-642-31223-6

  • eBook Packages: Computer ScienceComputer Science (R0)