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I've learned my English in the US and I know that I tend to use a simple past in places where Grammar books say I'm supposed to use a Present Perfect (e.g. Did you see the movie?). So, I'm trying to understand if the difference between "but she didn't" and "but she hasn't" in the sentence above is simply one between American usage and British usage, or if there is more to it. From a purely grammatical perspective, if she still hasn't called at the time of speaking then "but she hasn't" should be the right choice, at least in BrE. And yet, for some reason, I cannot bring myself to say it. Maybe I'm hearing it like it was a tag question and I want to follow the tense in the main clause, I dunno. Especially in its negative form, e.g. "I didn't think she would call but she has", it does sound a little bit off to me. Thank you for your help
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In Brit. Eng., there is no context to justify the speaker's use of Present Perfect:

"I didn't think she would call - but she did!"
Thank you for your reply.
The problem is now I'm even more confused. I don't understand anymore the way I've been speaking.
Take a sentence like, she said she wouldn't come to visit but she has. Why is this wrong? The person in question is here now, so it is correct to say that she's come to visit. If I say but she did am I not saying that she came to visit at some point in the past (and may have left by now)?.
Again, thanx a lot.
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He said she wouldn't come to visit but she has. Why is this wrong? It isn't.
The person in question is here now, so it is correct to say that she's come to visit. Exactly. It is not a completed action in the past, it is an ongoing situation still in effect NOW, the moment of speaking. Use the Present Perfect 'has (come to visit)'
......................|<A.........has...come.........NOW...........>|L..................
Where A= she arrived.
The part in black is the projected future, where the visit continues past NOW, to L= she leaves, ends the visit.

If I say "...but she did." Am I not saying that she came to visit at some point in the past and may HAS left by now?.
Yes. A completed done deal, over and out, she visited, she went. Use Past Tense

.........................|V|....................NOW
Where V= She did visit.
Henry74I'm trying to understand if the difference between "but she didn't" and "but she hasn't" in the sentence above is simply one between American usage and British usage, or if there is more to it.
In my opinion, "there is more to it".

She said she would call, but she didn't. The period of time you were willing to wait is "closed", i.e., you are no longer waiting for her to call.
She said she would call, but she hasn't. The period of time you are willing to wait is "open", i.e., you are still waiting for her to call.
Henry74if she still hasn't called at the time of speaking then "but she hasn't" should be the right choice, at least in BrE. And yet, for some reason, I cannot bring myself to say it.
You have to try harder! Emotion: smile
I don't think an American / British contrast has anything to do with this one.
Henry74Especially in its negative form, e.g. "I didn't think she would call but she has", it does sound a little bit off to me.
In this case I can more easily see your point. She did in fact call. Presumably the ensuing conversation is also already finished, so did seems quite natural. I can only imagine the alternate form in the case where you are talking to someone in the room with you, holding up the phone to indicate you are currently speaking with "her", saying (maybe whispering while "she" is talking to you on the phone), "I didn't think she would call, but (See?) she has!" In this scenario you have the current relevance necessary to sanction the present perfect.

CJ
Awesome explanation! Thank you!
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...holding up the phone to indicate you are currently speaking with "her"

The Present Perfect because the 'ringing' is not a completed event in the past...she is on the phone, NOW, as you whisper to this other person in the room!