In the Genki I textbook, they seem to reference the present perfect tense
three times, but each with a different grammar. Here they are, with book-style
English translations:

> 日本に行っています。(Ch 7, 〜ている form)  
>  _I have gone to Japan._
>
> 日本にもう行きました。(Ch 9, simple past form with もう)  
>  _I have already gone to Japan._
>
> 日本に行ったことがあります。(Ch 11, 〜ことがある form)  
>  _I have had the experience of going to Japan._

I'm not really sure about the semantic and grammatical differences between the
three, even in English (although the translations may be imperfect). How can I
understand them in relation to each other?

Also, does it ever make sense to combine the forms? Like,

> 日本に **もう** 行っています。  
>  _I have **already** gone to Japan (?)_
>
> 日本に **もう** 行ったことがあります。  
>  _I have **already** had the experience of going to Japan (?)_
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grammar tense
Present Perfect in Genki I
> 日本に行っています。(Ch 7, 〜ている form)  
>  I have gone to Japan.

ている form indicates an action in progress or something that persists. So when
reading this sentence, you would say "I am going to Japan and I'm still
there." (i.e. you went to Japan and you're still in the state of being there).
Another example would be using the verb 住む（すむ）"To live" 日本に住んでいます。 I am living
(the action persists from the past until now) in Japan.

> 日本にもう行きました。(Ch 9, simple past form with もう) I have already gone to Japan.

Your interpretation of this is already correct. However, this sentence is just
kind of stating a fact with no extra meaning. "Already went to Japan."

> 日本に行ったことがあります。(Ch 11, 〜ことがある form) I have had the experience of going to
> Japan.

This one however conveys the meaning that you have the experience of doing
something rather than just plainly stating a fact of something that happened
in the past.

As for:

> 日本にもう行っています。 I have already gone to Japan (?)
>
> 日本にもう行ったことがあります。 I have already had the experience of going to Japan (?)

I don't think the first one makes sense at all. "I am going to Japan and I am
still there already." As for the second one, I think it could work and does
make sense. I'm no expert though.
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> 日本に行っています。(Ch 7, 〜ている form) I have gone to Japan. Blockquote

This implies that you are currently still in Japan. Otherwise, when you leave
Japan then you would say, 日本に行きました。

> 日本にもう行きました。(Ch 9, simple past form with もう) I have already gone to Japan.

This sentence implies the person you are talking to doesn't know you've
already been to Japan. Like maybe you are doing a tour of Asian countries and
you check off Japan, and say, 日本にもう行きました。

> 日本に行ったことがあります。(Ch 11, 〜ことがある form) I have had the experience of going to
> Japan.

A better translation would be "I have ever been to Japan." Also it would
depend on the context of the conversation, but this would most likely be an
answer to the question, "have you ever been to Japan?"

> 日本にもう行っています。 I have already gone to Japan (?)

I would translate this as "I have already gone to Japan and I'm still here".
～ています implies the action is ongoing.

> 日本にもう行ったことがあります。 I have already had the experience of going to Japan (?)

In English, I would say this as, "I have already been to Japan (before)". It
would also depend on the conversation you are having. For example, someone
might tell you, "oh, you should go to Japan." At which point you would reply,
"oh, I have already been to Japan." In Japanese you would say,
"日本はもう行ったことがあります。"
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> 日本に行っています。  
>  I have gone to Japan.

We don't use this phrase in Japanese. I don't think it corresponds with the
English translation, which may be translated into

> 日本に行きました。

Now there is a big contradiction in this English phrase.  
If you have gone to Japan, you are not here. But you said to me "I have gone
to Japan." Then, where are you now and whom are you talking to?

As a natural Japanese phrase relating to the first one, you can say

> 彼｛かれ｝/彼女｛かのじょ｝は日本に行きました。だから彼｛かれ｝/彼女｛かのじょ｝はここにはいません。  
>  He/She has gone to Japan. So, he/she is not here.

If I hear the phrase "日本に行っています", I image like that you are on a plane flying
to Japan. In this case we say "日本に向｛む｝かっています- We are heading for Japan"
instead.

* * *

> 日本に **もう** 行きました。

Though this sentence has the same contradiction as that of the first one, it
is natural as Japanese.  
You can also say it as " **もう** 日本に行きました" with the same meaning.

* * *

> 日本に行ったことがあります。  
>  I have had the experience of going to Japan.

The third Japanese sentence has no problem at all.  
It could be translated as "I have been to Japan", right?

* * *

> 日本にもう行っています。 I have already gone to Japan (?)  
>  日本にもう行ったことがあります。 I have already had the experience of going to Japan (?)

As you think the former Japanese doesn't make sense, because it has the same
problem as that of the first sentence.  
The latter sentence is a good Japanese.
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