Sorts are used: * some are used for data values as in the algebraic approach to data types; and * others are used for states, as in the algebraic approach to abstract machines. The latter give objects. These two uses for sorts are dual: induction is used to establish properties of data types; while coinduction is used to establish (behavioral) properties of objects with states. Similarly, initiality is important for data types, while finality is important for states. However, we do not insist that implementations of abstract machines (or objects) must be final Because we use hidden sorts to specify classes of objects, order sorted algebra provides a very natural way to handle inheritance; it also allows specifying partial recursive functions, partially defined functions, subtypes of various kinds, error definition and recovery, coercions and multiple representations. The module system of parameterized programming gives us other forms of inheritance