The main Christian aims of punishment are:
Vindication- justice must appear to be done.
Detterence- they want the fear of punishment to put people of from committing crimes.
Protection- they have the duty to protect society from somebody that they may view as dangerous.
Reformation- they believe that they have the responsibility to reform criminals, making sure that they see the errors in their ways; preventing them from reoffending.
In the Old Testament, Moses taught: "an eye for an eye, a tooth for a tooth". Some people may use this is support of capital punishment, so if somebody killed someone else…