I was happy to have finished everything early
I was watching a video on active and passive infinitive and this example was in the video. I don't understand why the present perfect is used "to have finished" when the rule is to use past perfect for an action that happened earlier to some action in the past. Therefore the sentence should be "I was happy to had finished everything early".
There is no present perfect infinitive. Infinitives don't have tense. They don't mark either the present or the past.
One way to show the difference is to use a verb that has a separate infinitive form. The verb to be happens to have that property:
I was happy to be finished with everything early.
No present-tense form fits. We don't use "to am finished" or "to is finished" or "to are finished". No past tense form fits. You won't find "to was finished" or "to were finished", either. For to be, only "be" fits.
I was happy to have finished everything early.
In the same way, only "have" fits. Sure, "have" is a simple present-tense form, but it is also the infinitive form. Only the infinitive form fits.
It is reasonable to call this a perfect infinitive. However, it is a non-finite phrase, and it is not reasonable to label it as either past or present. It is a tenseless perfect phrase. It works regardless of the tense of the clause:
I was happy to have finished.
I am happy to have finished.
I will be happy to have finished.
[1] I was happy [to have finished everything early].
[2] *I was happy [to had finished everything early].
The perfect is a past tense that is marked by means of the the auxiliary "have", which is inflected for primary tense ("has" or "had"), as in for example, "Ed has been ill" / "Ed had been ill". These constructions thus have compound tense: 'present perfect' and 'past perfect' respectively.
In [1] "have" is in the plain form, so there is no primary tense, no compound tense, though it is still perfectly grammatical. It is usually known as the 'perfect infinitival' (or 'infinitival perfect').
But [2] is ungrammatical since "had" is a tensed form and thus cannot be used with the infinitival marker "to".
It would depend on where your temporal focus would be. as influenced by Colin Fine's answer here:
"I had finished the work on friday" / "I have finished the work".
with the present perfect your focus is on the PRESENT moment:
I was happy to have finished everything early
It means an action that has been completed but with no specification as to when or if it ended.
When you use the past perfect:
I was happy to had finished everything early,
It is describing a time in the past, the distant past but it does not influence the present or future - the action is completed.
Take this example:
Present perfect: The kids have eaten dinner.
[They ate dinner at point A, it is point C now. Note: For the present perfect, point B does not need to exist. A and C are the only points that matter.]
Past perfect: The kids had eaten dinner before the nanny went home.
[The kids ate dinner at point A, the nanny went home at point B, it is point C now.]
The difference is that in the present perfect example, the result of A is that the kids do not need to eat now, at point C, but in the past perfect example, the result of A is that at point B, no one needed to prepare dinner for the kids.
One of the rules of the perfect infinitive - to have finished - is that it can refer to something that will be completed at a point in the future:
We hope to have finished the building by the end of March.
But this is going beyond the timeline of your context, because the question of finishing is not in debate, like in the above i.e when the building will be completed, but rather in your context which is used depends on what temporal point you wish to emphasise - it's a nuance or a slight difference in semantics. It is even more confusing because 'to have finished' is also used to refer to events that will happen at a later date in the future, not simply ones that have already been completed.
