Quantomatic: A Proof Assistant for Diagrammatic Reasoning

  • Aleks Kissinger
  • Vladimir ZamdzhievEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)


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.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of OxfordOxfordUK

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