This is only one of the uses of the present prefect.

When I´m asking "How long have you been waiting?", it implies that you are still waiting, unlike with "How long did you wait?". I think this is the use case that Gokuyum is talking about.

Yeah, isn´t it called present perfect continuous which is used to talk about an action or actions that started in the past and continued until recently or that continue into the future?

You caught me there. I don´t even notice anymore when I´m switching to the continuous version of tenses...

Continuous or not, the present perfect denotes an action that has begun in the past and continues until now (or its consequenses are still there). In

                        How long have you studied Turkish?

there is no mark of continuous aspect but the time conditions are the same.

Interestingly, in Turkish present tense with continuous aspect (öğreniyorsunuz) would be used in such expressions.

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But I must confess I have maybe misunderstood something. Yes, Göksel and Kerslake say the past copula ((y)DI < *er + DI) expresses past tense and imperfective aspect. It presents a situation, a state of affairs (i.e. not a perfected action, of course, "being" is seldom perfective) as it was at some time in the past. But definitely in the past. This is what I missed.

ol- is used for changing the time conditions so that the actions reaches the present moment. It reminds me of expressions where olmak is used in nominal sentences also in order to create habitual aspect:

                        Bazı akşamlar film oluyor(du).

I mean if you have to hang another grammatical marker into a verb phrase, where else could you hang it but to olmak?

continues? hmmm...

I will refer to wikipedia definition for present perfect again.

The present perfect is a grammatical combination of the present tense and the perfect aspect, used to express a past event that has present consequences. The term is used particularly in the context of English grammar, where it refers to forms such as "I have left" and "Sue has died".

See it says a past event. This seems appropriate for English (and also for Turkish) but may be different for some other languages.

-di has sometimes perfect aspect but if it is present perfect continuous, -di disappers and we use another suffix for it.

I have been living here since I was a child. = Çocukluktan beri burada yaşamaktayım.

I have lived here since I was a child. = Çocukluktan beri burada yaşadım.

"I´ve lived here" indicates that you may not be living here presently. You may still be living here but that doesn´t give a clue if you are still living here.

I´ve been living here indicates that you have lived here and continue to do so.