I'd argue that the purpose of justice is to ensure that a society can be sustainable in the long term. That means justice is combination of deterrence and reha

I'd argue that the purpose of justice is to ensure that a society can be sustainable in the long term. That means justice is combination of deterrence and rehabilitation to a. discourage behaviours that are detrimental to society as a whole and b. to ensure that the offender ceases that behaviour and becomes a productive member of society again. 'Punishment' can play as small or as large a part in point (a) as you want, but the more you make it a large part of (a), the less success you will have with point (b). And failing at point (b) means you effectively fail point (a) - ie offenders coming out of the justice system who can't integrate back into society often reoffend.