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Why we use the Present Simple in the sentence:

The train leaves at half past six tomorrow morning.

I think the future progressive also may use there. It is because future progressive can denote events which are expected to happens in the normal course of events. That is, what is differences of the sentence, cited above and the sentence:

The train will be leaving at half past six tomorrow morning.

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    Both sentences express a future action, but in: "The train leaves at half past six tomorrow morning", you imply that it's the next train on the regular schedule. "The train is leaving at half past six tomorrow morning" can imply that it's an exceptional time for tomorrow, and that the train doesn't leave at that time on other days. But of course it all depends on context. – Laure Jul 6 '14 at 10:33
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We use the present simple to talk about events in the future which are 'timetabled'. We can also use the present continuous to talk about these.

My plane leaves at 6 in the morning.
The shop opens at 9.30.
The sun rises a minute earlier tomorrow.
My plane is leaving at 8.30.
The shop is closing at 7.00.
The sun is rising at 6.32 tomorrow.

We also use the present continuous to talk about things that we have already arranged to do in the future.

I've got my ticket. I'm leaving on Thursday.
I'm seeing Julie at 5 and then I'm having dinner with Simon.
He's picking me up at the airport.
The company is giving everyone a bonus for Christmas.

In many situations when we talk about future plans we can use either the present continuous or the 'going to' future. However, when we use the present continuous, there is more of a suggestion that an arrangement has already been made.

I'm going to see him./I'm seeing him.

I'm going to do it./I'm doing it.

Source

The future continuous (will be + ‘ing’ form) can also be used here to talk about events in the future.

Don’t ring at 8 o’clock. I’ll be watching Who Wants to be a Millionaire.
This time tomorrow we’ll be sitting on the beach. I can’t wait!

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    Ah, but what about the future continuous tense that Dmitry was asking about? – Dangph Jul 6 '14 at 13:12
  • @Dangph Yeah, I edited my answer above. – user6200 Jul 6 '14 at 13:18

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