Perfect infinitives – (to) have done – are sometimes used unnecessarily after a past tense:
? I expected to have met you here at 6 o’clock.
The ‘pastness’ is already expressed in the word expected. So the likely meaning would be conveyed by I expected to meet you here at 6 o’clock. (The problem is that, out of context, such a sentence may be ambiguous. Does it mean that I was here at 6 o’ clock waiting for you but you failed to turn up? Or does it mean that we did indeed meet here at 6 o’ clock as arranged?)
At times, however, a perfect infinitive is not merely justifiable but even necessary – to convey something that is hypothetical or incorrect. Here are two examples:
I was very worried, because I was hoping to have heard my results by then (but I still hadn’t).
I believed the Brazilian to have won (but he didn’t).
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