This semester I am teaching a seminar on computational syntax. It’s mostly on subregular syntax, but I started out with a discussion of CCG. CCG is noteworthy because it is a theory-rich approach that has managed to make major inroads into NLP. It would be cool if we could replicate this with MGs, but in order to do that you need a killer app. Subregular complexity might just be that because CCG doesn’t have a regular backbone, so it can’t have a subregular one either (more on that in a future post). CCG’s killer app was flexible constituency and a one-to-one mapping from syntax to semantics. You combine that with a corpus (CCGbank) and an efficient parsing algorithm (e.g. supertagging with A* parsing), and you have something that is both linguistically sophisticated and sufficiently fast and robust for practical applications. Anyways, this post collects some of my thoughts on flexible constituency and how it could be emulated in MGs. Spoiler: shells, lots and lots of shells.