  This report describes the parsing problem for Combinatory Categorial Grammar
(CCG), showing how a combination of Transformer-based neural models and a
symbolic CCG grammar can lead to substantial gains over existing approaches.
The report also documents a 20-year research program, showing how NLP methods
have evolved over this time. The staggering accuracy improvements provided by
neural models for CCG parsing can be seen as a reflection of the improvements
seen in NLP more generally. The report provides a minimal introduction to CCG
and CCG parsing, with many pointers to the relevant literature. It then
describes the CCG supertagging problem, and some recent work from Tian et al.
(2020) which applies Transformer-based models to supertagging with great
effect. I use this existing model to develop a CCG multitagger, which can serve
as a front-end to an existing CCG parser. Simply using this new multitagger
provides substantial gains in parsing accuracy. I then show how a
Transformer-based model from the parsing literature can be combined with the
grammar-based CCG parser, setting a new state-of-the-art for the CCGbank
parsing task of almost 93% F-score for labelled dependencies, with complete
sentence accuracies of over 50%.
