Invariants of a database schema are a property of the schema that must be preserved consistently (before and after the schema change). There are four types of invariants: invariants of class hierarchy, name, inheritance and consistency.
- Invariant of class hierarchy has a single root and defines a class hierarchy as a Directed Acyclic Graph (DAG) where all connected classes have a single direction. That is, all classes except the root have one or more super classes, and cannot become their own super classes. The root of DAG is "object," a system-defined class.
- Invariant of name means that all classes in the class hierarchy and all attributes in a class must have unique names. That is, attempts to create classes with the same name or to create attributes or methods with the same name in a single class are not allowed. Invariant of name is redefined by the 'rename' qualifier. The 'rename' qualifier allows the name of an attribute or method to be changed.
- Invariant of inheritance means that a class must inherit all attributes and methods from all super classes. This invariant can be distinguished with three qualifiers: source, conflict and domain. The names of inherited attributes and methods can be modified. For default or shared value attributes, the default or shared value can be modified. Invariant of inheritance means that such changes will be propagated to all classes that inherit these attributes and methods.
- A source qualifier means that if class C inherits sub classes of class S, only one of the sub class attributes (methods) inherited from class S can be inherited to class C. That is, if an attribute (method) defined in class S is inherited by other classes, it is in effect a single attribute (method), even though it exists in many sub classes. Therefore, if a class multiply inherits from classes that have attributes (methods) of the same source, only one appearance of the attribute (method) is inherited.
- A conflict qualifier means that if class C inherits from two or more classes that have attributes (methods) with the same name but of different sources, it can inherit more than one class. To inherit attributes (methods) with the same name, you must change their names so as not to violate the invariant of name.
- A domain qualifier means that a domain of an inherited attribute can be converted to the domain's sub class.
- Invariant of consistency means that the database schema must always follow the invariants of a schema and all rules (Rules for Schema Changes) except when it is being changed.