Byrd’s box model is a fine-grained Prolog execution model that can be the basis of high-level debugging tools. In this article, we provide a formal specification of Byrd’s box model, based on an already existing operational and denotational continuation semantics for Prolog with cut. We show how this specification can be extended to specify richer Prolog trace models. To be able to experiment with trace models, we translate these specifications into ?Prolog. This translation leads to a Prolog interpreter that performs execution traces. We have hence a formal framework to specify, prototype, and validate Prolog trace models.