Reading the fourth entry on parenthesis matching made me wonder whether one could store, in the monoid, partials views into the table that is generated by CYK parsing: https://en.wikipedia.org/wiki/CYK_algorithm

I love the idea of using monoids like they're described in the blog series, but the examples suggest that there's a certain amount of non-generalizable cleverness that goes into defining each monoid. Could you do CYK subtables inside the monoid, so that people can define arbitrary CF grammars, as long as they're in Chomsky normal form?