I want to know the difference between present perfect continuous and present perfect in negative sentences. My textbook says (namely, English Grammar In Use, 2nd edition) 'use simple for negative sentences'. Surprisingly, it does not explain the reason. After some googling I found that continuous forms are also used, but I couldn't get the precise distinction. Please help.
Your textbook is oversimplifying things at best or just plain wrong at worst. To understand which to use in a negative sentence, you need to understand the difference between them in a positive sentence.
The point here is that the action I'm speaking of is completed. At some unspecified point in the past, the woman I'm speaking of traveled to various opera houses and sang at all of them. Though she may no longer be singing, or no longer singing at multiple venues, this statement doesn't rule out those possibilities. Either fact is simply not relevant to my statement, I'm only talking about the performances she's previously given. Even though the actions I'm referring to are in the past, it is different from using the past tense in that regard.
This sentence has a similar meaning to the one above, but with some added implications. The singer may no longer be singing at opera houses (preferring other venues), may not be singing at all, or may even be dead. Regardless, that part of her life is behind her.
Again, the meaning is similar to the first example I gave, but the implications are the opposite of the example above. Just as the name implies, present perfect continuous indicates that the activity is continuous, starting at some point in the past (either specified or unspecified) and continuing up until now. In my example, she has been moving between opera houses and giving performances, and is still in the process of touring around.
So now let me actually answer your question about negative sentences. In short, the differences in the meanings conveyed are the same.
Again, this is referring to an action that is complete and the future of her singing career is not the focus of discussion. This would be suitable in a statement such as: "She has not sung at many opera houses, but I always buy tickets when she does." My actions (buying tickets) are in the present tense. Using the future tense would not be natural here, since I am not making any comment on what she may or may not be doing in the future.
(Actually, you could use the future tense for buying, which would give a slightly different implied meaning to the first half of the sentence but I'm employing a little simplification of my own to avoid getting overly confusing. The future tense of 'buy' would only be wrong paired with the past tense example below.)
For the sake of completion, here's the negative example in past tense:
Again, her singing career (at least in opera houses) is over. In "She did not sing at many opera houses, but I always bought tickets when she did" my actions are unsurprisingly in the past tense as well, since I'm referring to a time grounded in the past.
The number of performances she has been giving of late has been fairly low, and that is still the case.
"She has not been singing at many opera houses, but I always buy tickets when she does." "She has not been singing at many opera houses, but I will always buy tickets when she does."
My actions don't sound awkward in either the present tense or the future tense, since this a situation being continued. That allows you to speak of it in the present or project it into the future without sounding bizarre.
[You could also say that you have been buying tickets to either the present perfect or present perfect continuous examples, but that didn't sound like it would help to highlight the differences between them.]
Murphy actually says in the book (page 22):
No further explanation is given, but it is important to understand the context in which he makes the above claim. The page title is How long have you (been) ... ? Murphy gives examples of when the simple or continuous forms are 'more usual', and when both are equally acceptable. He then finishes the page with the above text.
What he means is this: When the verb refers to the last occurrence of a single completed action rather than to an action that extends in time to the present (such as, in his examples, working at a place, learning a language, waiting, etc.), then the present perfect continuous is not used:
The implied "How long ... ?" question in Murphy's examples above is : How long is it since ... you last saw him / she last phoned you? Compare this to the other "How long ... ?" questions on the page: How long have you been living there / waiting / learning English / ... etc.
The caption on the front cover of the book states that it is "A reference and practice book for intermediate students" and the advice on the page in question seems just about right for that level. Admittedly, though, a little more explanation from Murphy would have been helpful.
*Note that it is in fact possible to say:
In this case, however, the verb to see is equivalent to dating or going out with, which is an extended action, and hence permits the negative. But this is an explanation for Advanced students!