Mappings, Maps and Tables: Towards Formal Semantics for Associations in UML2
In fact, UML2 offers two related yet different definitions of associations. One is implicit in several Description and Semantics sections of the specification and belongs to the UML folklore. It simply says that an association is a set of links. The other – official and formal – definition is explicitly fixed by the UML metamodel and shows that there is much more to associations than just being sets of links. Particularly, association ends can be owned by either participating classes or by the very association (with a striking difference between binary and multiary associations), be navigable or not, and have some constraints on combining ownership and navigability.
The paper presents a formal framework, based on sets and mappings, where all notions involved in the both definitions can be accurately explained and formally explicated. Our formal definitions allow us to reconcile the two views of associations, unify ownership for binary and multiary associations and, finally, detect a few flaws in the association part of the UML2 metamodel.
KeywordsStructural Mapping Formal Semantic Structural View Operational View Extension Table
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