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International Conference on Automated Deduction

CADE 2015: Automated Deduction - CADE-25 pp 326–336Cite as

Quantomatic: A Proof Assistant for Diagrammatic Reasoning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

Abstract

Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory, algebraic quantum information, and quantum groups. String diagrams provide a convenient graphical syntax for reasoning formally about such structures, while avoiding many of the technical challenges of a term-based approach. Quantomatic is a tool that supports the (semi-)automatic construction of equational proofs using string diagrams. We briefly outline the theoretical basis of Quantomatic’s rewriting engine, then give an overview of the core features and architecture and give a simple example project that computes normal forms for commutative bialgebras.

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Notes

  1. 1.

    Non-linear term rewriting can be encoded by introducing special ‘copy’ and ‘delete’ nodes which obey certain naturality conditions. However, when \(\otimes \ne \times \), these don’t exist in general.

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Acknowledgements

In addition to the two authors, Quantomatic has received major contributions from Alex Merry, Lucas Dixon, and Ross Duncan. We would also like to thank David Quick, Benjamin Frot, Fabio Zennaro, Krzysztof Bar, Gudmund Grov, Yuhui Lin, Matvey Soloviev, Song Zhang, and Michael Bradley for their contributions and gratefully acknowledge financial support from EPSRC, the Scatcherd European Scholarship, and the John Templeton Foundation.

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Authors and Affiliations

  1. University of Oxford, Oxford, UK

    Aleks Kissinger & Vladimir Zamdzhiev

Authors
  1. Aleks Kissinger
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  2. Vladimir Zamdzhiev
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Correspondence to Vladimir Zamdzhiev .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Kissinger, A., Zamdzhiev, V. (2015). Quantomatic: A Proof Assistant for Diagrammatic Reasoning. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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