To clarify, and to make it easier for anyone who wants to do further reading, I'll note that being in prison is punishment, and the purposes of punishment are variously deemed to be retribution, deterrence, rehabilitation, and incapacitation.

(And prison only as incapacitation doesn't really make any sense given that prison terms differ based on the crime.)

Prisons have a variety of purposes, depending on who you ask.

Are you making a specific distinction between prisons and penitentiaries?