Without function composition, the category of regularly would have to be ((S\NP)/NP)\((S\NP)/NP), but (crossed) composition allows the ordinary category (S\NP)\(S\NP) to also work in this case.
this is crucial to correctly inducing and evaluating grammars and parsers for any expressive formalism, including tAG, GPSG, HPSG, LFG, and MPG.