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Despite the usual passive constructions which use "have been", I've never seen someone have used "to have been". I would really grateful if someone could explain the usage of "to have been" in the following sentence.


Although they don't do a lot of harm, as far as we know up to now, this will probably prove to have been a mistake.

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"prove to ~" is followed by a verb infinitive. "to have been" is the perfect infinitive of the verb "be". It is used here to give a backward-looking sense from the time of "prove" to the time of "been a mistake", like future perfect tense.

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dileepa"to have been"

In terms of meaning it's the past of "to be".

Present or future: to be
Past: to have been

The fugitive is believed to be hiding in the forest. (hiding there now)
The fugitive is believed to have been hiding in the forest for several months. (hiding there in the past)

CJ

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Thank you very much for the answer.

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Thank you very much for the answer. By the way, is there any name related to such usages of "to have been" in terms of grammar. Because if there was such name, I can search related articles to learn more about it.

As GPY said, it's called a perfect infinitive.

Here are all eight "infinitivals", as they're called, for the verb 'take':

to take
to be taking
to have taken
to have been taking
to be taken
to be being taken
to have been taken
to have been being taken

The first four are active; the last four are passive.
Those with auxiliary 'have' are perfect.
Those with 'ing' are continuous.

Not all are equally useful. The 6th and 8th forms are particularly rare.

CJ

Thank you very much for the answer. In actual fact, most of these usages are new to me. So, I started learning this area and at the moment I'm only familiar with "to take" and "to be taken".

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dileepaat the moment I'm only familiar with "to take" and "to be taken".

Those are the most frequently used. Next is "to have taken". After that, it's pretty rare to find them at all. The Google Books corpus can't even find a single example of "to have been being taken", a truly unwieldy form which everyone tends to avoid. You would do well to learn the rare forms only as theoretical curiosities. Emotion: smile

CJ

Ok. Thank you very much for the comment.