A Derivation in Combinatory Categorial Grammer

Question

I am reading about CCG on page 23 of Speech and Language processing. There is a derivation as follows:

(VP/PP)/NP , VP\((VP/PP)/NP) => VP?

Can anyone example this please? This make sense if

VP\((VP/PP)/NP) is equivalent to (VP\(VP/PP))/NP 

and

(VP/PP)/NP is equivalent to VP/(PP/NP). 

But they seem at least non-trivial from the text!

Any help would be greatly appreciated.

CS

Answer 1

I guess I got it. It is simply:

(X/Y)(Z\(X/Y)) which Z. 

In the example,

X = VP/PP, Y = NP, and Z = VP.