I have always wondered, if dolphins sleep with one eye opened, do they really sleep at all?
According to this article dolphins indeed shut down their brains.
I already googled it. No help from wikipedia or other articles and publications found.
I'd say that unihemispheric sleep and adaptations like it really are sleep - the brain activity on one side of the brain gives a characteristic sleep pattern. It certainly must satisfy the needs of an aquatic mammal like a dolphin or a whale since they have to be partially conscious to breathe by surfacing regularly.
It does seem to affect the brain physiology, but is there a reason you would not call it sleep?
I suppose that it depends on how sleep is defined. If we define it a a mechanism by which the brain repairs itself in an altered state, then, yes they do indeed sleep. Just not with all of their brain at once.