Encoding !-tensors as !-graphs with neighbourhood orders
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 !-grap...
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| Published in: | Electronic proceedings in theoretical computer science Vol. 195; no. Proc. QPL 2015; pp. 307 - 320 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Open Publishing Association
04-11-2015
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| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 2075-2180 2075-2180 |
| DOI: | 10.4204/EPTCS.195.23 |