LIPIcs.FSCD.2020.17.pdf
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String Diagrams for Optics
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Guillaume Boisseau 
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5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Formal Structures for Computation and Deduction (FSCD) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-06-28
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Acknowledgements
I want to thank the reviewers for the SYCO6 workshop for their thorough reviews, and Jeremy Gibbons for his ever helpful comments.
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Guillaume Boisseau. String Diagrams for Optics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSCD.2020.17
Abstract
Optics are a data representation for compositional data access, with lenses as a popular special case. Hedges has presented a diagrammatic calculus for lenses, but in a way that does not generalize to other classes of optic. We present a calculus that works for all optics, not just lenses; this is done by embedding optics into their presheaf category, which naturally features string diagrams. We apply our calculus to the common case of lenses, extend it to effectful lenses, and explore how the laws of optics manifest in this setting.
Subject Classification
ACM Subject Classification
- Software and its engineering → Visual languages
- Software and its engineering → Data types and structures
- Software and its engineering → Specialized application languages
- Software and its engineering → Functional languages
Keywords
- Optic
- string diagram
- lens
- category theory
- Yoneda lemma
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References
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