2020/01/21 by Bryce Clarke, Derek Elkins, Jeremy Gibbons +6 · 2 voices · 8 citations
Chemistry · Computer Science · Engineering · Mathematics · #Geophysics and Sensor Technology #Homotopy and Cohomology in Algebraic Topology #Molecular spectroscopy and chirality #cs.PL #math.CT
paper · pdf · doi:10.32408/compositionality-6-1
arxiv published 2020/01/21 · arxiv updated 2024/02/20 · rss pubdate 2024/02/23
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choice of representation supporting modularity, meaning that we can construct accessors for complex structures by combining simpler ones. Profunctor optics have previously been studied only in an unenriched and non-mixed setting, in which both directions of access are modelled in the same category. However, functional programming languages are arguably better described by enriched categories; and we have found that some structures in the literature are actually mixed optics, with access directions modelled in different categories. Our work generalizes a classic result by Pastro and Street on Tambara theory and uses it to describe mixed V-enriched profunctor optics and to endow them with V-category structure. We provide some original families of optics and derivations, including an elementary one for traversals. Finally, we discuss a Haskell implementation.