Dear Raymott,
First and foremost let me say a big 'thank you' to you for your outstanding and thorough answer. :up:
:arrow:
[ I (Mav) in black (as night, black as cole
), Raymott in blue ]
Yep. I take it you are clear enough up to here.
Yes. I only had (and I still have, to some extent...) problems with the understanding and the use of the Perfect Infinitive.
c) "He turned angry enough to have killed."
Did he, or did he NOT kill in the end?
It’s not implicit in the sentence whether he did or not.
If so, then what justifies the use of the Perfect Infinitive? What extra information or tone does it add to the sentence instead of the Present Infinitive?
If it were something like "He was strong enough (let's say it's a narrative) to have beaten up that rascal who had attacked his family a week ago (before the narrative point). Is it correct? Even if it is, it doesn't explain to me why Perf. Inf. is used in the sentence c. I [strike]kind of[/strike] feel it "weird" on its own, without further words, context, etc. like "He turned angry enough to have killed."
In the following example, it’s clear that he didn’t: "He turned angry enough to have killed if he was pushed much further.”
Some people would prefer the past perfect in this sentence.
Do you mean: "He turned angry enough to have killed if he
had been pushed much further.”? Or "He
had turned angry enough to have killed if he
had been pushed much further.”? In this latter example I could imagine something like: "Eventually he calmed down, but it was surprising as he had (sooner) turned angry enough to have killed if he had been pushed much further.” Is it correct? (I tried to put it into some context.) Am I right about this?
The perfect form suggests (to me) that it actually happened, but if I remember correctly, the Perfect Infinitive has something to do with the 'imaginary past', where the actions did NOT complete. (Eg.: 'He was to have come.' implies that he did not come.
That’s right, and “He was to have come, but he was caught up” is even more revealing.
Again, if the context makes it clear, then what extra 'good' does the Perfect Infinitive do? If I say "He was to have been spared, but he was roasted in the electric chair" then I think it's the brute truth that makes things clear, not the infinitive, so to speak.:-|
Or 'I hoped to have asked you out for a dinner one day.' implies that it has never happened.) Am I right?
Yes. But the beauty of sentences is that you can make them longer to add important qualifying information, or put the sentence in a paragraph and reveal all!
My question remains the same in this case, too.

Would it carry some veiled meaning with the Present Infinitive: ''I hoped
to ask you out for a dinner one day."? Would it be less evident what happened or (did not happen) in this case? *confused*
Or I am right, BUT 'imaginary past' is only one usage of the Perfect Infinitive, and in other situation the Perfect Infinitive 'behaves' differently. If so, how? Might I ask you to make these things, you know, crystal clear?
The perfect infinitive behaves differently if the writer chooses to make it do so. To get his/her message across, s/he has a wide choice of tools which can be used in different combinations, and which still get the same job done.
True and true, but in this very thread I'd like to learn
how the use of the Perfect Infinitive can change the meaning of a sentence when it is chosen to be used instead of the Present Infinitive.

Speaking of the writers... I wrote a sentence by Shakespeare in my previous post: "I had thought, Sir, to have held my peace." Does it convey that he couldn't hold his peace? Or would it be correct (without changing the meaning, of course!) to replace it with "I had thought, Sir, to hold my peace."? What's the difference?
d) "He had turned angry enough to kill."
Goodness gracious! I've just realized that I used the wrong sentence here, in my original post. (I used the clipboard, i.e. Ctrl+C/Ctrl+V, and I inserted the wrong sentence after d). Of course I meant to write (or to have written:?: ) d) "He
had turned angry enough
to have killed. I don't want to edit my post, but I'd like to point it out, along with my apologies for overlooking it.
Well, it is c) with one the tenses changed to the past perfect. That would make it the appropriate phrase to use if “he had turned” rather than “he turned” was indicated by the context. Why does this relationship surprise you?
This relationship does NOT surprise me, but I would be a bit surprised if there weren't more behind it.
And last, can the Perfect Infinitive be used after Present Perfect?
Yes. You generally wouldn’t write, “He has turned angry enough to have killed”. But it could be made to work:
A: “Do you think John could have killed this man yesterday?”
B: “Well, over the last week, he has turned angry enough to have killed this man yesterday.”
But he didn't, right? Would it change the meaning if you used Present Infinitive: “Well, over the last week,
he has turned angry enough
to kill this man yesterday.”:?: In this latter case, I'd think he killed that man. Maybe among all the examples given above, this is where I feel the biggest difference in the meaning between the two sentences, given that I'm right about the interpretation.
How do you feel about: “He's had to have been able to have stayed alive”?
In short: :shock: :shock:
. 
) Does it mean something like "He had no other choice but to stay alive, and he succeeded; he is alive."
Please let me know if you still have doubts.
Thank you very much for your helpfulness. :up: As you can see I still have doubts (and maybe it's an understatement:lol: ), and I'll try to summarize what my understanding is. (Aside from the above mentioned examples, of course, on which I'm anxiously waiting for your comment in order to become enlightened.

)
1.) He is believed to be drunk. (= Now they think he is drunk (now.))
2.) He was believed to be drunk. (Once they thought he was drunk then.)
3.) He is believed to have been drunk. (Now they think that once he was drunk.)
4.) He was believed to have been drunk. (Once they believed he had been drunk. Oh, my beloved Past Perfect.

I think it's necessary in this case.)
4.b) I met a guy whom I did not remember to have met
before.
Am I right so far?
5.) Past in the future (I don't know what to call this.)
This time tomorrow I hope to have finished my email. (Assuming I won't use too complicated sentences. <self-sarcasm on>:mrgreen: )
6.) Imaginary Past
I hoped to have visited you in the States. (But it has never happened.)
7.) I would like (now) to have heard Bing Crosby sing. (He died decades ago. I never heard him sing on stage, and alas, nobody will hear him sing again.:-() Though I would say in this case: "I wish/If only I had heard him sing." Are there any differences in the meaning between the two sentences?
I must have forgotten about some cases (as usual

), but I think this post is already long enough, and I don't want to squeeze everything into one post. Just one more question... How often is the Perfect Infinitive used among the native English speakers? I only very seldom come across with it, and maybe (only maybe) because the Present Infinitive holds its sway, and for a reason, I think. That's why I put the emphasis on the question of the difference between these two different infinitives, and I admit (as you can see) that I still have doubts. Thank you very much again, Raymott, for helping me understand this stuff. :up: