What kind of diet is it that is fruitarian but also involves eating eggs and dairy?

I know vegans don't like dairy or any animal product, although that's really more of a protest of how animals are treated, rather than taking life, seeing how no life is being taken when you milk something or gather eggs. And in fact cows actually go through more problems if they aren't milked and get infections. But there is a fruitarian diet which is the only one I can think of that doesn't involve taking any life whatsoever, like animal or plant life.

But seeing how fruitarian diets aren't really practical and leave you malnourished, I am kind of wondering if it would be possible to eat fruit, without killing any plant life but also get the protein and calcium you need, i.e. eggs and dairy. That would be the only diet that might work that doesn't involve taking any life.