An eye for an eye, a tooth for a tooth "Lex talionis"
EXPIATION OR ATONEMENT
group vengeance
it is punishment in the form of group vengeance where the purpose is to appease the offended public or group.
DETERRENCE - punishment gives lesson to the offender by showing to other what would happen to them if they violate the law.
PROTECTION - by placing the offender in prison, the society is protected from further criminal depredation.
REFORMATION - society interest can be better serve by helping the prisoner become law abiding citizen and productive upon undergoing to an intensive program of rehabilitation in prison.