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The computer virus (having been detected/having detected), the programmers managed to save all necessary data. What's the right version? My guess is that the programmers detected the virus which is the active form as it should have the relationship with the programmers.

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Let's imagine this in a purely active form. I'll write a separate sentence for each of the two ideas.

The computer programmers detected the computer virus.
The computer programmers managed to save all necessary data.

Clearly, the programmers are doing everything. These sentences are written in the active voice, so the programmers are also the grammatical subjects.

In your version, the virus is the grammatical subject, indicating a passive relationship. So let's take the next step and make the first sentence passive:

The computer virus was detected by the programmers.
The computer programmers managed to save all necessary data.

I'll repeat that, but this time I'll remove the programmers from the first sentence.

The computer virus was detected.
The computer programmers managed to save all necessary data.

To combine the sentences, we must use one of the options that you have presented:

  1. The computer virus having detected, the computer programmers managed to save all necessary data.
  2. The computer virus having been detected, the computer programmers managed to save all necessary data.

#1 is not correct because it changes the voice from passive to active, but continues to use the computer virus as the grammatical subject. So now it seems as if the virus is detecting something. That is of course possible in the digital world, but it's not the story you're trying to tell.

#2 is correct, because it retains the passive relationship. That's the function of been.

(Note that in my version, the computer programmers detected the virus. I added the detail for the sake of the example. By the end, they've been eliminated from that part of the sentence, so it does not matter if they are the detectives or not.)

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  • Thank you very much, Jeffrey. What confused me is that using the passive form two sentences seem to be connected only logically and not grammatically. But what if we start with the verb: Having detected the computer virus, the programmers managed to save all necessary data. Is it correct?
    – frussian
    Commented Mar 22, 2022 at 9:10
  • That version also makes perfect sense. And the form is more common. Commented Mar 22, 2022 at 9:36

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