Anothr Definition of Order-Sorted Algebra

In this paper the definition of order-sorted algebra is generalized by introducing transforma-tion functions between subtypes and supertypes. According to our definition, a type needn'tbe a subset of its supertype and a record model may form an order-sorted algebra. A newdefinition of equation is given. It has also been proved that equational theories and describingsingle inheritance have the initial model.