Is it correct? It's the message I see right before the metro/subway train shows up.
Shouldn't it be "train is approaching" or "train approaches"?
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Either way this is just a fragment, so the question is what is the rest of the sentence? Your suggestions read as follows, to me:
The train is approaching
A train approaches
I usually interpret it as the following:
There is a train approaching
There's clearly a lot of flexibility when you're only seeing a fragment of the sentence.
Yes, it's "correct". It is there to carry information, from the metro system to you, namely, that there is a train approaching. And that you should step back ;-)
In all this "proper grammar" and whatever, we (me included, see my rant-with-a-lot-of-comments ;-)) tend to forget that language serves a purpose, to wit, to carry information from A to B (where A to B are very often, but not always, individuals). And as long as it manages this task, to the satifsaction of, well, A and B, all's well.
In this case, I don't see any "failure to inform". So there, job well done, language! Good language, yes, good language! pats language on, uhm, head?
I would say it depends on where you are stood and the information being conveyed. If you are on the platform and you can see or hear a train then the message is providing specific information.
The train approaching platform 5 is the 4:15 to Skegness
This also implies a connection, not always correct, to the next train arriving. To say
There is a train approaching ...
can be confusing, there may be several trains approaching, are you talking about a specific one or all trains?
Whereas if you were on the train the announcement would be
The train is approaching Skegness.
as this is specific to the train you are travelling in.