Is Capital Punishment an Act Which Seeks Revenge Rather than One Which Seeks Social Justice

Arguments claiming to support capital punishment in particular revenge social justice.
Argument against capital punishment include:
: It is revengeful barbaric cruel degrading uncivilized
: Does not correlate with a reduction in crime
: Basic violation of human rights ethical and moral values
: Capital punishment is expensive
:Discriminately selective on focus [rich poor black white]
: Law can make mistakes rushed judgement
: The evidence supplyed might not be fair
: Offenders may have the chance to rehabilitation
: The past dosent always equal the future.
…