Despite the fact that there is a strongly context-free CCG which generates all of the derivations in CCGbank, it is still possible that the grammar learned by the Clark and Curran parser is not a context-free grammar.
these rule systems vary from a small rule set, motivated theoretically (Vijay-Shanker and Weir, 1994), to a larger rule set, motivated linguistically, (Steedman, 2000) to a very large rule set, motivated by practical coverage (Hockenmaier and Steedman, 2007;Clark and Curran, 2007).