Not entirely. There are a few different motivations for punishment: one, is to act as a deterrant (people won't do the crime because they fear the punishment. Tends to work best when people think they are likely to be caught), two is to act as a form of correction/rehabilitation: (after one punishment people are less likely to do it again. Tends to have problems when the punishment sets people up to be more likely to commit crime, by either putting them in contact with other criminals or further pushing them into desperate circumstances after the punishment), third is as a sense of justice, to some extent as revenge. The punishment of an offender can help the victims on an emotional level and also foster trust in the system (requires that the punishments are viewed as just and proportional). Lastly, in extreme cases, as a form of protection/prevention: by removing the person from being able to commit any further crimes.