Robert Nozick [a Havard philosopher, famous for his book "Anarchy, State and Utopia"] defined revenge as delivering the message that you know what someone has done, and it doesn't involve hurting them or doing anything to them beyond that. It's just delivering the message that their crime has been noted not just by its victims, because the victim might be dead, but by another who has a different moral view and will challenge the perpetrator's view.