CCG is governed by a set of meta-rules which are commonly called "Principles". E.g.
the Combinatory Projection Principle (CPP)
the Projective Dependency Principle (PDP)
I have found most descriptions of these principles somewhat lacking in accessibility, something I can also say about discussions of why they are a good choice or trade-off in the limitations they impose.
Can you propose a very self-contained explanation of these principles, drawing as little as possible from earlier terminology?