WHEN LIFE GENERATES DEATH (LEGALLY)
The Greek civilization started in the XV-XIV century b.C. with the occupation of the Greece by the Aeolis and the Dorians, and finished in the I century a.D., with the annexation to the Roman Empire.
The Greek tragedy, in its most ancient expressions, often thinks of the justice as a vendict duty of the victim's sons. So, in Aeschylus' Choephori, uselessly Orestes tries to evade this heavy duty, because Apollo's oracle told him about many pains and illnesses if he doesn't vendicate Agamennon's murder.
In the Greek polis death penalty had many attenuations, particulary in political and constitutional vicissitudes in Athens, losing the meaning of vendict, but for long times executions were left to the initiative of the victim's family.
In some of his works, Plato writes about the usefulness of the penalities as a prevention from other crimes, and also the exceptionality of the death penalty that would be applied only in the most serious cases (sacrilege, murder of relatives, crimes against the State) and to the recidives, remembering the law of retaliation.
Here's what Plato says in his Laws:
"...if someone is proved guilty of a murder, having killed any of these peoples, the judges' slaves will kill him and throw him naked in a cross-road, out of the city; all the judges will bring a stone in the name of the whole State throwing it on the head of the corpse, then will bring him out of the State's frontier and will leave him there unburied; this is the law".