For many decades the term “correctional institutions” has been applied to prisons. I think that should literally true. People emerging from a prison should be “corrected” in the sense of being better people who are unlikely to commit further crimes.
Today, people who have been in prison are seen as undesirable employees and have trouble getting a job. I believe that people who emerge from a correctional institution should be more desirable employees than when they went in. Someone who has spent a significant amount of time in such an institution should be highly sought after.
Is this possible? If so, is prison really a punishment?
For almost all people, prison would be a punishment because it deprives them of choice, which most of us consider important. Prisoners would not have the choice to live by themselves in a single-person cell, nor would they be able to choose their roommates. More generally, prisoners would not have the ability to choose their own social environments. Their set of of possible friends would be limited to those chosen by the system.
Prisoners would also be force-fed academic and vocational education. Those who do not cooperate would be receive humane but immediate punishment through further restrictions on their freedom and lifestyle — detailed elsewhere on this site.
Because prisoners would be force-fed academic and vocational education, they will emerge from prison better educated individuals, with useful skills. The longer they have spent in prison, the more productive members of society they will be on their release.
On the other hand, prison should not necessarily be a punishment for all individuals. There should be one overall choice, to go to prison or not. People who have not committed crimes should be allowed that choice. It should be possible for a person to enter the prison system voluntarily without having committed a crime to do so. A person who needs more support than society can give them in the outside world should be able to enter the prison system at will and leave it at will. This applies especially to the homeless and those who cannot hold down a job outside of the prison system.
For this reason, the prison system should not require more than a small amount of government support. A prison should also be an industrial institution.
Because of the need to work in an industrial setting to support the prison and the need to get an academic and vocational education, a prisoner should have very little free time. In that sense prison will also be a punishment. Only those who enter the system voluntarily without having committed any offense should be allowed a significant amount of leisure time.
Briefly, a prison should be a place where a rigorous deprivation of choice and leisure both supports the institution and teaches the inmates new skills, so they emerge as productive members of society.