English Daily Workout: When do we Use Present Perfect?

We use Present Perfect to talk about things that took place:

during a period of time that includes past and present:

They have been singing for an hour. (They started singing some time ago in the past and are still singing now.)

in the past, but we are not specifying exactly when the action took place:

I think Mary has talked to him already. (Mary talked to him in the past, and since we don't know when, we use Present Perfect.

in the past with an effect or result in the present:

Oh, I've left my books at home! Can you share yours with me? (I left my book at home. I need the book for, let's say, the Literature Class. As I don't have the book with me right now, because I left it at home, I need a classmate of mine to share his/her book with me. => My forgetting to bring the book has consequences now)