论文标题
光学的弦图
String Diagrams for Optics
论文作者
论文摘要
光学是用于组成数据访问的数据表示，镜头是流行的特殊情况。树篱已经为镜片提出了图解的演算，但以某种方式不推广到其他类别的光学。我们提出了一个可适用于所有光学元件的演算，而不仅仅是镜头。这是通过将光学嵌入其前膜类别中的，该类别自然具有字符串图。我们将演算应用于镜片的常见情况，将其扩展到有效的镜片，并探索光学定律在这种情况下如何表现出来。
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.
