What is the term for a bill that is enacted retroactively to declare someone guilty of a crime?

The correct term for a bill that is enacted retroactively to declare someone guilty of a crime is "ex post facto." An ex post facto law is one that retroactively changes the legal consequences of actions that were committed before the enactment of the law. This means that if a law is created that makes an action illegal or enhances a punishment for an act committed before the law was enacted, it would be considered an ex post facto law, which is prohibited by the U.S. Constitution under Article I, Sections 9 and 10.

The concept of a bill of attainder refers to legislation that targets a specific individual or group for punishment without a trial, not necessarily retroactively declaring guilt for actions taken in the past. Mandamus is a court order directing a government official to perform a duty, while a writ of prohibition prevents a lower court from exceeding its jurisdiction. All of these serve different functions within legal systems and do not pertain to the retroactive declaration of guilt.