How is the present perfect “connected” with the present?

I usually put it in the form "the speaker is choosing to present the past event as relevant to the present".

But either way, the particular relevance (or connection) can vary. Some examples are:

• a state which continues to the present ("has lived");

• an action which has a continuing effect in the present ("has written");

• an action which is so recent that it seems still relevant (No clear example in the ones you give, though "has finished" might be in this category);

• (especially in the negative), regarded as taking place in a period which extends to the present ("haven't seen him").

In many cases, the speaker can choose the past or the present perfect, depending on whether they want to present this "present relevance": So "he finished his homework" is not relating it to the present - this might indicate that you weren't talking about the recent past, but some earlier day; but it doesn't necessarily do so; whereas "he has finished his homework" almost certainly means that it was recent, probably today, so the homework being in a finished state is still relevant.

"Have been to" is a special case, and I don't think they should have listed it with the others. It is an idiom that means "went to at some time, and came back". The "present relevance" there is that the visit is seen as taking place in a time that stretches up to the present; but it could have been long ago. If you don't use the perfect, you don't get the idiom: "He went to Canada" does not imply that he came back: he might have, but you can't tell. "He has been to Canada" means that he went and he came back.

Edited in response to comments.

Has lived: She has lived here all her life.

• the action of her living here is unfinished because she is still alive, was living here and is still living here; She lived here all her life gives an impression she is dead now.

Have written: They have written three letters already.

• Present Perfect is often used for recent events so it may be this case - they have just finished them; or it may be the case that this action is still going on - they are in the process of writing, they have written three letter already and there are more to come.

Have worked: I have worked here since I graduated school.

• After I finished my graduation I started to work here and I am working here still - so - I have worked here (I was and I am still working here) since I graduated (finished action marking the start of me working here in the past)

Has done: He has finished his homework.

• Either he has finished it recently (just now) or it’s relevant somehow - for example - a friend, John, is asking him, Peter, out telling Peter’s mom Peter has finished his homework - John is emphasising the fact Peter has finished his homework when persuading Peter’s mom - thus it’s relevant in the moment of speaking.

Have been: We have been to Canada.

• We were in Canada and we are still alive - it’s a life experience of a living person. If the persons are dead Past Simple is appropriate - not we (because we are dead now) but they (our friends talking about us to someone after we passed) - they were in Canada.

Has forgotten: She has forgotten her folder.

• It’s somehow relevant to the present - like - She has forgotten her folder where she had her notes so she can’t study now.

Present Perfect - unfinished actions

• they started in the past and are continuing to the present, often with words since and for

since:

• I’ve known him since 2000 - so I got to know him in 2000 and today I still know him
• I’ve worked here since I graduated (or I’ve been working here since I graduated if you want to put the emphasis on the time period - emphasising you’ve been working here for so long) - so I started to work here after my graduation and I am still working here
• I’ve liked swimming since I was a child - I started to like it as a child and I like it still
• the time is fixed - since I graduated, since I was a child

for:

• I’ve been thirsty for hours - I was and I still am thirsty
• She’s had a headache for a week - She had and still has a headache
• I’ve known her for ten years - we are in touch for ten years now - she was and still is my friend (or my acquaintance at least); I knew her for ten years - she was my friend or my acquaintance for ten years in the past but she is not now - she moved, we lost touch...
• this is for a period of time

Present Perfect - finished actions

• We have been to Canada - this action was finished, but our lives are not - it’s our life experience that is still going on so despite the fact our trip to Canada is finished, it must be Present Perfect because it’s about a life experience of a person or persons that are still alive; We have been to Canada but our life experience is not over so we still might go to Canada again so it’s not a finished action

• We have been to Canada - we went and came back and are still alive

• We have gone to Canada - we went to Canada and we are still in Canada and now we are mentionning it to our friends over the phone

• He’s been to the shops - he was there and came back just now, he’s not going to go there again so you should have asked for that chocolate bar earlier

• he’s gone to the shops - he is in those shops right now so I can call him and ask him to get you a chocolate bar

• He has finished his homework - this action has ended but as I stated previously it may be relevant to the present - putting emphasis on the fact he has done his homework so he’s free to go out when persuading his mom to let him for example

• unfinished time word - I haven’t seen her this month - this month is still going on - so this action was finished but this month is not; He has drunk two beers today - he finished drinking those two beers but this day isn’t over so he still might have another beer - it’s still going on so if you’re not mentionning this to someone like 11:59:59 pm it’s Present Perfect

• finished time words are for example yesterday, last month, last year - they are finished - and you cannot use Present Perfect with them - I saw him yesterday

• She’s missed the school bus and now she must go home on foot - her missing the school bus is finished action but is important and relevant to the present - she must go on foot becasue she missed that bus

• She has forgotten her folder - so she can’t be studying her notes now as she intended - it’s relevant to the present

• note - that in these last two cases in US English you can often use Present Simple instead of Present Perfect and it would still be correct - so remember - in US English you can use also Present Simple even in the case when finished action from the past is important and relevant for the present

• and lastly - events that happened recently

• the President has given a speech - it happened earlier that day for example but it is important for you when you start mentionning it to your friends so you can talk about it

• I have just seen her! - Do you know where Emily is? - I’ve just seen her around the corner! - it just happened - recently

• in this case also in US English you can often use Present Simple and it would still be correct

• Present Perfect words - already, ever, just, never, not yet, so far, till now, up to now (emphasising the result)

• Present Perfect Progressive words - all day, for 4 years, since 1993, how long?, the whole week (emphasising the duration)

• use Past Perfect in a Present Perfect sentence to identify what happened earlier - she’s done as she’d been bid - she has done as she had been requested - first she was requested to do something - then she had done it - and it’s relevant and important in the present; remember that the main difference between Present Perfect and Past Perfect is that action described by Past Perfect started and also ENDED in the past, it’s not going on.

• you can also use Past Perfect to identify the action that happened earlier with the other action in the sentence in Past Simple - she failed the test because she hadn’t studied

• when you go by these rules you can use Present Perfect when you want to give relevance to something that is still going on or something that ended but is relevant or in some way important to the present; if there are two actions in the sentence - either in Present Perfect or Past Simple - use Past Perfect for the one that happened earlier - I’d never had (had never had) Italian food before my trip to Italy last month - me never having Italian food happened earlier

• Past Perfect words - already, just, never, not yet, once, until that day, conditional sentence type III (If I had talked, would + have + past participle)

• Past Perfect progressive words - for, since, the whole day, all day

Practical English Usage and the Cambridge Grammar of English say that the present perfect “is connected in some way with the present.”

Neither book explains this, and this is why I’m asking for you to indicate how the present perfect “is connected in some way with the present” in the examples below — by saying, for example, “The past is connected with the present in ‘She has lived here all her life’ ... (your answer).”

1. It is called the present perfect as it uses the present tense of “have” as an auxiliary.

2. It is a form of the present tense that ends as soon as it is spoken or done.

She has lived here all her life. = She is, as I speak, currently in a state of living here (and she has been in that state all her life.) The second main clause is irrelevant to the tense.

If, on turning round to look at her, the speaker find she is dead, he would have to correct the sentence to “She [had] lived here all her life” as the matter is now in the past. - = She was, when I spoke, then in a state of living here.

He has finished his homework. = He is, as I speak, currently in a state of having finished his homework.

We have been to Canada. = We are, as we speak, currently in a state of having travelled to Canada.

She has forgotten her folder. = We are, as we speak, currently in a state of having forgotten her folder.

If you ask “Well why are we using “have”? It is because, at a very base level, the subject is in possession of the state described.

Your problem comes with:

A: “Have you ever worked for that company?”

B: “Yes, I have worked for the firm, but that was 4 years ago.”

This arises because it is normal to answer, where possible, by using the same form of the verb:

A: “Did you ever work for that company?”

B: “Yes, I worked for the firm, but that was 4 years ago.”

So, where is the connection with the present? A was asking about B’s past experience, which is still currently valid, and so, whilst the present perfect is valid, it is not the only option.

“Yes, I have worked for the firm, but that was 4 years ago.” = Yes, I am, as I speak, in a state of having worked for the firm.”

In Old English, in common with other languages, the verb “to be” was used to form the past tense of verb that described motion or change – some forms of this still exist, but are rare.

“The prisoner is not there! He is gone!” “You cannot cross the river, the ice is melted.”

They describe a state and it is hard not to see “gone” and “melted” as adjectives. Adjectives describe attributes – and we see that being in a particular state is an attribute.