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The careful planning and revision clarifies and structures things the writer may think he knows, until he comes to actually write.
Is the usage of 'come to do' the same kind as these? Or is it fundamentally different?
You'll come to like this place.
I came to realize that he didn't love me.
Comments  
Hi,
Yes. It's not fundamentally different.

Clive
I've read somewhere before that 'do' in 'come to do' is stative. You don't think it's always the case, Clive?
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All those usages seem the same to me. to come to ... means that the moment has come when something begins.

... until the moment comes when he actually writes.
The time will come when you'll like this place.
The moment came when I realized that he didn't love me.

CJ
But this doesn't sound right, or does it, Jim?
He will come to swim.
TakaBut this doesn't sound right, or does it, Jim?
He will come to swim.
That particular isolated sentence does sound odd, but in the right context, it could work. come to is so little used that it's hard, even for a native speaker, to get a good feel for it.

CJ
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CalifJim
TakaBut this doesn't sound right, or does it, Jim?
He will come to swim.
That particular isolated sentence does sound odd, but in the right context, it could work. 
I think I have to ask a man of insight, Jim, why it sounds odd whereas the other examples don't, and what context you would come up with which might make it sound right. 
CalifJim come to is so little used that it's hard, even for a native speaker, to get a good feel for it.

CJ

Really!?Emotion: surprise Is it that rare?

Hi,
He sat beside the lake all day in the hot sun, and thought about swimming in its cool, refreshing water.
But when he came to swim, he found the water was freezing.

A phrase like 'But when he came to swim' above is often written as 'But when he actually came to swim', in order to heighten the contrast between the 'thinking' and the 'doing'.

I agree that He will come to swim sounds odd, but I think what makes it odd is the use of 'will'. It's an unlikely tense to need to use here.

More likely is Simple Past, as I have shown above, or possibly Simple Present.
eg He thinks the water is warm but, when he comes to swim, he will find that it is freezing.

Clive