A property defined for an object type, or class, is called a reference property if its values are references that reference an object of another, or of the same, type. For instance, the class
Committee shown in Figure 1.1 below has a reference property
chair, the values of which are references to objects of type
An association between object types classifies relationships between objects of those types. For instance, the association Committee-has-ClubMember-as-chair, which is visualized as a connection line in the class diagram shown in Figure 1.2 below, classifies the relationships FinanceCommittee-has-PeterMiller-as-chair, RecruitmentCommittee-has-SusanSmith-as-chair and AdvisoryCommittee-has-SarahAnderson-as-chair, where the objects PeterMiller, SusanSmith and SarahAnderson are of type
ClubMember, and the objects FinanceCommittee, RecruitmentCommittee and AdvisoryCommittee are of type
Reference properties correspond to a special form of associations, namely to unidirectional binary associations. While a binary association does, in general, not need to be directional, a reference property represents a binary association that is directed from the property's domain class (where it is defined) to its range class.
In general, associations are relationship types with two or more object types participating in them. An association between two object types is called binary. In this book we only discuss binary associations. For simplicity, we just say 'association' when we actually mean 'binary association'.
|Finance Committee||Peter Miller|
|Recruitment Committee||Susan Smith|
|Advisory Committee||Sarah Anderson|
While individual relationships (such as FinanceCommittee-has-PeterMiller-as-chair) are important information items in business communication and in information systems, associations (such as Committee-has-ClubMember-as-chair) are important elements of information models. Consequently, software applications have to implement them in a proper way, typically as part of their model layer within a model-view-controller (MVC) architecture. Unfortunately, many application development frameworks lack the required support for dealing with associations.
In mathematics, associations have been formalized in an abstract way as sets of uniform tuples, called relations. In Entity-Relationship (ER) modeling, which is the classical information modeling approach in information systems and software engineering, objects are called entities, and associations are called relationship types. The Unified Modeling Language (UML) includes the UML Class Diagram language for information modeling. In UML, object types are called classes, relationship types are called associations, and individual relationships are called "links". These three terminologies are summarized in the following table:
|Our preferred term(s)||UML||ER Diagrams||Mathematics|
|object type (class)||class||entity type||unary relation|
|association (relationship type)||association||relationship type||relation|
|functional association||one-to-one, many-to-one or one-to-many relationship type||function|
We first discuss reference properties, which implicitly represent unidirectional binary associations in an "association-free" class model (a model without any explicit association element).