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I have seen some sentences that include "perfect progressive tenses" and I am absolutely puzzled.
Please help me.
In advance thank you for your replies.

Part one:
I saw the sentence below in an English book:
"Since that unfortunate accident last week, I haven't been sleeping at all well."
According to the grammar of English, the "haven't been sleeping" in the sentence is "present perfect progressive tense".
I guess that there are two explanations for the "I haven't been sleeping at all well" in the sentence:

The first explanation:
The situation of the sleeping well is not at ANY time points in the period from the time of "unfortunate accident" to the time of speaking.
It means that SURELY the whole period from the time of "unfortunate accident" to the time of speaking is the time of the "NOT to sleep well".
The second explanation:
In the period from the time of "unfortunate accident" to the time of speaking, the time points at which the situation of the sleeping well is are not ALL.
It means that MAYBE the whole period from the time of "unfortunate accident" to the time of speaking is the time of the "NOT to sleep well".

Which one of the two explanations above is right?

Part two:
I saw the sentence below in another English book:
"I had not been reading for half an hour when I heard steps outside."
According to the grammar of English, the "had not been reading" in the sentence is "past perfect progressive tense".
I guess that there are two explanations for the "I had not been reading for half an hour" in the sentence.

The first explanation:
The action of the reading is not at ANY time points in the period from a past time to the past time of the "heard steps outside". (The period is the half hour)
It means that SURELY the whole period from a past time to the past time of the "heard steps outside" is the time of the "NOT to read".

The second explanation:
In the period from a past time to the past time of the "heard steps outside", the time points at which the action of the reading is are not ALL.
It means that MAYBE the whole period from a past time to the past time of the "heard steps outside" is the time of the "NOT to read".

Which one of the two explanations above is right?
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Comments  
1. From the time of the incident through the present time it is not customary for me to sleep well .

2. I heard the steps outside before I had finished reading for half an hour.

I hope these simple explanations help.
This is my interpretation of your post. Based on the sentence in question, I have this funny feeling that the "English books" you were reading may not be published nor written by people whose native language is English. Perhaps some of your confusion came from how they explained it.
There are some issues with your sentence, but I presumed this is the one that matches to my explanation below:

In the period from the time of "unfortunate accident" to the time of speaking, the time points at which the situation of the sleeping well is are not ALL.

For the present perfect progressive, I believe "well "should be better put after "sleeping". With " ....at all well. ", it sounds odd to me. We can either say:

"Since that unfortunate accident last week, I haven't been sleeping well at all . Or, " I haven't been sleeping well at all since that unfortunate accident last week."
We can swap the main clause with the subordinate clause while using conjunction such as "since" and "when".

To me, The PPC tense is not that commonly used as the continous structure emphasizes the action or the lack thereof from further past point in time to the most recent past. But that is not to say it is not possible but it will take a convincing context to make it sound reasonable. Your example:
"I had not been reading for half an hour when I heard steps outside." is grammatically fine. But PPC is not necessary if you were describing something happened last nigh. it is an overkill. But that's my opinion. Emotion: rofl
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Thanks a lot.

About the second question:

2. I heard the steps outside before I had finished reading for half an hour.

Can I use the sentence "I had not read for half an hour when I heard steps outside." to express the same meaning?
eagleflychCan I use the sentence "I had not read for half an hour when I heard steps outside." to express the same meaning?
Yes. "had not read" will automatically be understood as "had not been reading" because of the context, namely, the use of "for half an hour".

Similarly,

I [had not been speaking / had not spoken] with him for more than a minute [when / before] we were interrupted by a loud blast.

Laura [had not been been playing / had not played] chess for three years [when / before] she won the regional chess tournament.

In all of these cases, the progressive form is preferable because it emphasizes an on-going activity interrupted by an event.

CJ
CalifJim
eagleflychCan I use the sentence "I had not read for half an hour when I heard steps outside." to express the same meaning?
Yes. "had not read" will automatically be understood as "had not been reading" because of the context, namely, the use of "for half an hour".Similarly,I [had not been speaking / had not spoken] with him for more than a minute [when / before] we were interrupted by a loud blast.Laura [had not been been playing / had not played] chess for three years [when / before] she won the regional chess tournament.In all of these cases, the progressive form is preferable because it emphasizes an on-going activity interrupted by an event.CJ
Thank you very much.

But I saw a conversation in a book about English grammar:

Beggar: Madam, I had not seen a piece of meat for weeks when I met you.

Lady: Mary, please show this poor man the ham we bought just now.

In the conversation, I feel that the meaning of the "I had not seen a piece of meat for weeks when I met you." is not the "I met you before I had finished seeing a piece of meat for weeks."

Why? What is the meaning of it?

I am puzzled.
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eagleflychI had not seen a piece of meat for weeks when I met you.
...

In the conversation, I feel that the meaning of the "I had not seen a piece of meat for weeks when I met you." is not the "I met you before I had finished seeing a piece of meat for weeks."True. That is an awkward paraphrase. I would illustrate the meaning like this:

Weeks had gone by during which I had not seen a piece of meat. At that point in time, I met you.
Or
At the end of a period of weeks during which I had not seen a piece of meat, I met you.

CJ

CalifJimTrue. That is an awkward paraphrase. I would illustrate the meaning like this:Weeks had gone by during which I had not seen a piece of meat. At that point in time, I met you.OrAt the end of a period of weeks during which I had not seen a piece of meat, I met you.CJ
Many thanks.

So does the negative form of the "Perfect Progressive" tense have at least TWO meanings?

and

Does the negative form of the "Perfect " tense also have at least TWO meanings?

Besides, I have seen another explanation for the sentence "I had not been reading for half an hour when I heard steps outside.":

It means that the writer had been reading for less than half an hour when he or she heard the steps.

Is the explanation the same as "I heard the steps outside before I had finished reading for half an hour."?
eagleflychSo does the negative form of the "Perfect Progressive" tense have at least TWO meanings?
...
Does the negative form of the "Perfect " tense also have at least TWO meanings?No. Not that I know of. Maybe I'm not following what you're trying to say.
eagleflychBesides, I have seen another explanation for the sentence "I had not been reading for half an hour when I heard steps outside.":
It means that the writer had been reading for less than half an hour when he or she heard the steps.
Is the explanation the same as "I heard the steps outside before I had finished reading for half an hour."?
I do not see those explanations as exactly the same, and I would certainly not paraphrase it either way, but maybe I should make a general comment before addressing this issue.

It seems to me that you are asking language to have a mathematical precision that it does not have. In the case of reading and being interrupted by the sound of footsteps, for example, we are to take the statement as saying that the reading activity took place for approximately a half hour, and 'approximately' indicates that the time period could have been a little less or a little more than a half hour if not exactly a half hour.

The grammatical pattern we're dealing with here does not convey any sort of exact meaning in terms of time. No one in the situation, and certainly not the speaker who is reporting it, used a stop watch to determine to the second how much time was spent reading. The main point of this grammatical pattern is to show that an event interrupted an activity. The activity would have continued if the event had not occurred, so this kind of pattern indicates a sort of surprise at the interruption. It doesn't matter whether the connecting word is "when" or "before". For all practical purposes, the meaning is the same.
________________

I had not been reading for half an hour [when / before] I heard steps outside.
=
I had been reading for only half an hour [when / before] I heard steps outside.

The reading activity continued for [approximately / almost / about / more or less / perhaps] half an hour. At the end of that approximate time period, the footsteps were heard. This interrupted the activity of reading. The interruption was somewhat surprising because I would have continued to read if I had not heard the footsteps. I expected to be reading longer than just (approximately) half an hour.

_________________

Try not to expect ordinary language to convey mathematically precise ideas! Emotion: smile

CJ
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