Actually your two equivalents are not so equivalent, although in most contexts they would imply the same thing.
There is an interesting file in the root directory.
This is an existential statement that asserts the existence of an entity that can be described as "interesting file in the root directory".
An interesting file is in the root directory.
This does not really have the same connotation, but instead asserts first the existence of an instance of an "interesting file", via the indefinite article "An", and then asserts something more about that entity, namely that it is "in the root directory".
You may still think there is no difference. If so, consider the following possible wider contexts:
There is an interesting file in the root directory of each computer in this network.
An interesting file is in the root directory of every computer in this network.
The first means that each computer has an interesting file, possibly different for different computers. The second means that there is a single interesting file that is on every computer.
There lives an amazing fish in my pond.
An amazing fish lives in my pond.
Similarly your fish-pond example has the same fine distinctions that show up only in certain contexts.
So I am trying to figure out, is there some grammatical basis for usage of the expression "there + verb"?
Well there is a grammatical basis, as shown above by the fine distinctions between such constructions and the apparently equivalent ones without the "there". This also explains why all bare existential statements of the form "There is [a[n]] X." cannot be rephrased except as "[A[n]] X exists.". Some other usages include:
There comes a truck loaded with stones.
A truck comes, loaded with stones.
There flew in a dozen birds through the window.
A dozen birds flew in through the window.
There stood a lone pillar in the courtyard.
A lone pillar stood in the courtyard.
There arose a dispute about money.
A dispute arose about money.
In most cases, it is of the form "There V X [A]." where V is an intransitive verb (no object), X is a noun phrase that is the subject of V, and A is an optional adverbial phrase that modifies X if possible or V otherwise.
4
The construction is called "an existential clause". It's used in English to indicate the presence of something.
– CowperKettle – 2015-11-24T18:57:22.850Thus I should construct my sentences using only "there + be" and "there + exist". Am I right? – Anton Marinin – 2015-11-24T19:14:05.173
4"There's an amazing fish living in my pond" is probably how most native speakers would tell you about it, at least in the American dialect I speak. You are more likely to find "An amazing fish lives in my pond" in a written work. For a long time, it was taught that to begin a sentence with existential-there was flabby style. – Tᴚoɯɐuo – 2015-11-24T19:14:09.073
1There is a difference in emphasis between the two constructions I think. And also some slight gramaticality issues. The first pair of sentences works because the verb is "be" in both parts. So "There is an interesting..." and "An interesting file is..." both work fine. But in general the change has to be made as @TRomano pointed out. "There lives an amazing fish in my pond." is at the very least clumsy but I'd guess probably ungramatical. Even though "An amazing fish lives in my pond" is quite fine. – DRF – 2015-11-24T19:23:06.483
2"Once upon a time there lived a piece of wood."(The Adventures of Pinoccio) Is it correct? – V.V. – 2015-11-24T19:38:34.030
1Hmm having looked into CGEL the situation seems to be somewhat more complex. The construction of "There is/was ..." is apparently something called a dummy there. While in some cases you can change the sentence as you have indicated it is not always the case. An example where you cannot get rid of the there in a simple way is "There was an accident." As @CopperKettle points out the example you give is the case of an existential construction, which usually indicates the presence or existence of something though not always, ("There is also me to consider"). – DRF – 2015-11-24T19:40:47.070
1@V.V. Yes that sentence is perfectly fine and is the second case of the use of there in a "presentational clause". – DRF – 2015-11-24T19:41:46.140
There seems to be lots of verbs used after "there". – V.V. – 2015-11-24T19:50:51.713
1In response to your question in comments ("there+be" and "there +exist") the answer is no. It depends what you are saying consider "There still remain problems." or V.V's example. – DRF – 2015-11-24T19:56:38.407
@DRF: I'd say that "there lives a fish" is perfectly grammatical. Since you agree that "there lived a fish in the pond" is grammatical, you should also agree that "now there lives many fish in the pond" is. – user21820 – 2015-11-25T14:21:28.527
By the way, grammatical not grammatic, and semantically not semanticaly, and am not sure rather than haven't made sure. =) – user21820 – 2015-11-25T14:33:27.540