A more thorough explanation:

Halifax law refers to an ancient form of private justice that was practiced in the parish of Halifax, England. It involved the summary and unauthorized trial and execution of a person accused of a crime, usually by decapitation. This punishment was carried out after a summary trial and was irrevocable.

The practice of Halifax law was carried out by the free burghers against people accused of stealing. Thieves could be condemned to death by beheading on market day. The last known case of Halifax law occurred in 1650.

Halifax law is also known as gibbet law or Halifax inquest.

For example, if someone was accused of stealing in the parish of Halifax, they could be subjected to Halifax law. They would be given a summary trial and, if found guilty, would be executed by decapitation on market day. This punishment was carried out by the free burghers and was considered an irrevocable punishment.