Here is a sentence from The Marvelous Land of Oz:
When sent to the forest Tip often climbed trees for birds' eggs or amused himself chasing the fleet white rabbits or fishing in the brooks with bent pins.
All the things in bold haven't been mentioned before. Why is it birds but the rabbits and trees but the brooks if all these things are in the same forest?
I think the following piece would be relevant:
At Canter's Deli, you should get the corned-beef sandwich.
Here, "the" is appropriate because bringing up the deli implicitly brings up typical items on the menu.
I was in the N.Y. Library. I was reading the books there, and one book interested me.
"Oh, you were reading the books!" As opposed to what, the posters on the wall? Usually when there is grammatical ambiguity, a listener will use common sense to avoid making an absurd interpretation, but in this case, the absurdity is hard to avoid because a listener understands this sentence by analogy with the "…and fixed the sink" and "…get the corned-beef sandwich" sentences.
I don't know if I understand that answer completely. Did the author omit the article because it was obvious that every forest had trees and birds? Did he use the article to point out that in some forests there might not be white rabbits or brooks, but in his forest they were there and were some of its features?