The word "punishment" is used in the criminal law to stand for whatever treatment the state recommends for convicted offenders. That treatment may be either utilitarian or retributive, but it cannot be both.
The treatment is retributive when the punishment fits the crime, not the criminal. Retributive punishment may or may not have a salutary effect upon the criminal, but the severity of the punishment must be measured by the seriousness of the crime. What was once called the lex talionis required a just proportion between the injury done to the victim of the crime and the injury tone suffered by the criminal -- an eye for and eye, a life for a life.
Punishment is utilitarian or pragmatic when its aim is not to do strict justice, but rather to deter or reform criminals. Here the treatment accorded offenders judged guilty of committing the same offense may not be the same. The treatment may vary with the age and the character of the offender.
It is in this context that the question of capital punishment must be considered by those who think the aim of punishment should be to prevent crime, and particularly recidivism, which is the recurrent criminality of offenders who are paroled.
Some states have now abolished capital punishment on the grounds that it is unjust, a violation of the right to life. While the offender is alive, errors that may have occurred in his or her trial can be rectified. The right to life is not violated by the incarceration of the offender for life with no parole allowed. Nor is the right to liberty violated, for the offender incarcerated for life retains his right to liberty, even though his exercise of liberty is severely curtailed.
The offender's right to liberty would be violated only if the warden treated the incarcerated offender as his personal slave. That would be unjust because it would be a violation of the offender's right to be treated as a free human being rather than as a slave.
Current recommendations that criminals found guilty of three offenses should be incarcerated for life with no parole allowed is not a violation of human rights. They do not deprive the repeat offender's life or liberty, but they may be pragmatically sound measures aimed at reducing recidivism and thus preventing crime