2026-07-24T18:31:35Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12339 2024-03-06T10:50:00Z ddc:004 open_access

String Diagrams for Optics Boisseau, Guillaume Optic string diagram lens category theory Yoneda lemma 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Guillaume Boisseau 2020 Is Part Of LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2020.17 urn:nbn:de:0030-drops-123399 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.17 eng https://creativecommons.org/licenses/by/3.0/legalcode