Encoding !-tensors as !-graphs with neighbourhood orders

David Quick

Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated structure inside a diagram. This led to !-graphs being implemented in the diagrammatic proof assistant Quantomatic. Having a partially automated program for rewriting diagrams has proven very useful, but being based on !-graphs, only commutative theories are allowed. An enriched abstract tensor notation, called !-tensors, has been used to formalise the notion of !-boxes in non-commutative structures. This work-in-progress paper presents a method to encode !-tensors as !-graphs with some additional structure. This will allow us to leverage the existing code from Quantomatic and quickly provide various tools for non-commutative diagrammatic reasoning.

In Chris Heunen, Peter Selinger and Jamie Vicary: Proceedings of the 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, U.K., July 15-17, 2015, Electronic Proceedings in Theoretical Computer Science 195, pp. 307–320.
Published: 4th November 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.195.23 bibtex PDF
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