Correspondence Between Composite Theories and Distributive Laws

Aloïs Rosset, Maaike Zwart, Helle Hvid Hansen, Jörg Endrullis

Abstract: Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term rewriting methods, we also describe when a minimal set of equations axiomatises the composite theory.