Profunctor optics, a categorical update

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

Climatic oscillations stall vegetation recovery from K/Pg event devastation

Sedimentary rocks filling the Boltysh meteorite crater preserve an expanded record of post K/Pg event vegetation destruction and subsequent floral recolonisation. A post-destruction barren zone is succeeded by a fern spore spike recording the initial recovery vegetation. The Boltysh fern spore spike is divisible into two phases. Phase 1 is characterised by low abundances of fern spores of the Polypodicaeae and Pteridaceae, while the overlying Phase 2 has high fern spore abundances and contains common palm pollen. Comparison of the Boltysh Phase 2 fern spore spike to other palynological records show strong similarities with the immediately post K/Pg boundary record of the Western Interior, North America. Variation in the composition of the Boltysh palynofloras has been used to defined four moisture availability cycles between the K/Pg boundary and Dan-C2. Time constraints consequent on these events indicate that early post K/Pg event vegetation community recovery followed a common seral successional pathway at rates seen in Large Igneous Provinces, although enhanced by high moisture availability. Continued succession to the first true swamp community was at a considerably slower tempo. The post K/Pg event vegetation recovery was therefore retarded by lack of moisture availability, extending the apparent period of recovery. Without this moisture availability oscillation, recovery to the first mature communities could have occurred at similar rates to those seen in Large Igneous Provinces