What does set_index(col, compute=True) do in Dask?

This is now a Github issue

What does the parameter compute in Dask dataframe's set index do?

df.set_index(col, compute=True)

The documentation says

compute: bool, default False

• Whether or not to trigger an immediate computation. Defaults to False. Note, that even if you set compute=False, an immediate computation will still be triggered if divisions is None.

This would suggest that if I provide divisions and set compute=True, immediate computation will be triggered. This does not seem to be true, however.

import dask.datasets
df = dask.datasets.timeseries()

# Nothing gets submitted to the scheduler
df.set_index(
    'name', 
    divisions=('Alice', 'Michael', 'Zelda'), 
    compute=True
) 

Going down the stack of functions set_index actually calls, it appears that the only place where compute is actually used in rearrange_by_column_disk. And indeed:

# Still, nothing gets submitted
df.set_index(
    'name', 
    divisions=('Alice', 'Michael', 'Zelda'), 
    shuffle='tasks',
    compute=True
) 

# Something is computed here
df.set_index(
    'name', 
    divisions=('Alice', 'Michael', 'Zelda'), 
    shuffle='disk',
    compute=True
) 

So what happens, exactly?

I suspect that the actual resulting partitions might be computed and saved to disk. If that's the case, then how could I tell this has happened?