Ouisch and Mike, thank you very much for the explanation. I was really shocked to see such difficult diagrams, no wonder they are not so popular with the students :). I wonder if diagramming is used in Britain as well.
One more question. All over the world English is taught in accordance with grammar reference books written by Michael Swan, Thomson&Martinet. Did these authors write for foreign students of English only or did they also write books for native speakers?
I only know of Swan. He is British, so I doubt his works are used in American schools.