I just stumbled upon the term monoidal parsing from a slide named "Introduction to Monoids" by Edward Kmett. The slide uses haskell throughout.
Now when searching for the term I found nothing but a very few mentions of it and the most from the same author. So I think this term could be explained here.
So, is monoidal parsing something that is interesting and new? Is it appearing anywhere except for in the slide I linked to? And most importantly what is it? The slide itself didn't seem to give a definition nor highlight it that much.