From the point of view of grammatical theory, however, frameworks based on categorial grammar have usually been problematic either by being too restricted in their expressive power or by not being restricted enough.
for example, we are told that CCGs can be parsed in polynomial time with a worst-case complexity of O(n6), but this depends on results for linear indexed grammars by Weir (1990, 1994) and an assumed equivalence between CCG and linear indexed grammars, which in turn depends on a certain way of interpreting the rule schemata for type raising in CCG.