In the grammar formalisms folklore, the generative capacity of CCG is often attributed to generalized composition, and indeed we have seen (in Lemma 4) that even grammars without target restrictions can generate non-context-free languages such as L(G 2 ).
our results show that composition by itself is not enough to achieve weak equivalence with TAG: The yields of the transformed derivations from Section 3.4 form a context-free language despite the fact that these derivations may still contain compositions, including compositions of degree n > 2.