|The importance of use of the concept of refinement for heterogeneous
multidatabase interoperation research and development is emphasized. Using
this concept, the commutative data model mapping method is reconsidered.
The method provides for verifiable design of the data model mappings handling
the models as formal objects in frame of anabstract metamodel. For such
metamodel an abstract machine notation is used combining pure mathematical
notation with an ability to automatically prove important properties of
the data type definitions as well as the subtype property based on the
The concept of data model refinement is introduced. Data model commutative
mapping method is based on this notion. The method is specifically oriented
on extensible data model mapping (such as the object data models). To preserve
information and operations of types of a specific data model while mapping
them into the canonical types the commutativity of two mapping
diagrams (data type state and data type behavior diagrams) should be
established. The required state-based and behavioral properties of the
mappings lead to a proof that a source data model is a refinement of its
mapping into the canonical data model.
The applicability of the method is demonstrated on the mapping of the
ODMG'93 constructs (the relationship type) into canonical data types. The
SYNTHESIS language is used for the canonical data model.