Table of Contents
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,
Committee shown in Figure 11.1 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 11.2 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 tutorial we only discuss binary associations. For simplicity, we just say 'association' when we actually mean 'binary association'.
Table 11.1. An example of an association table
|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) architecure. 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:
Table 11.2. Different terminologies
|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 represent unidirectional binary associations in a model without any explicit graphical rendering of the association in the model diagram.
A reference can be either human-readable or an internal object reference. Human-readable references refer to identifiers that are used in human communication, such as the unique names of astronomical bodies, the ISBN of books and the employee numbers of the employees of a company. Internal object references refer to the memory addresses of objects, thus providing an efficient mechanism for accessing objects in the main memory of a computer.
Some languages, like SQL and XML, support only human-readable, but not internal
references. Human-readable references are called foreign
keys, and the identifiers they refer to are called primary keys, in SQL. In XML, human-readable references are called ID references and the corresponding attribute type is
Objects can be referenced either with the help of human-readable references (such as integer
codes) or with internal object references, which are preferable for accessing objects efficiently
in main memory. Following the XML terminology, we call human-readable references ID references. We follow the standard naming convention for ID
reference properties where an ID reference property defined in a class
referencing objects of class
B has the name class
b_id using the suffix
_id. When we store persistent objects in the form of records or table rows, we need
to convert internal object references, stored in properties like
publisher, to ID
references, stored in properties like
publisher_id. This conversion is performed as
part of the serialization of the object by assigning the standard identifier value of the
referenced object to the ID reference property of the referencing object.
In object-oriented languages, a property is defined for
an object type, or class, which is its domain. The values of a
property are either data values from some datatype, in which
case the property is called an attribute, or they are object
references referencing an object from some class, in which case the property is
called a reference property.
For instance, the class
Committee shown in Figure 11.1 below has an attribute
name with range
String, and a reference property
By default, the multiplicity of a property is
1, which means that the property
is mandatory and functional (or, in other words,
single-valued), having exactly one value, like the property
chair in class
Committee shown in Figure 11.1. When a functional
property is optional (not
mandatory), it has the multiplicity
0..1, which means that the property's minimum
cardinality is 0 and its maximum cardinality is 1.
A reference property can be either single-valued (functional) or
multi-valued (non-functional). For instance, the reference property
Committee::chair shown in Figure 11.1 is single-valued, since it assigns a unique club member as
chair to a club. An example of a multi-valued reference
property is provided by the property
Book::authors shown in Figure Figure 11.10, “The association-free Publisher-Book-Author design model” below.
Normally, a multi-valued reference property is set-valued, implying that the order of the references does not matter. In certain cases, however, it may be list-valued, such that the references are ordered.