Chapter 8. Reference Properties and Unidirectional Associations

Table of Contents

1. References and Reference Properties
2. Referential Integrity
3. Modeling Reference Properties as Unidirectional Associations
4. Representing Unidirectional Associations as Reference Properties
5. Adding Directionality to a Non-Directed Association
6. Our Running Example
7. Eliminating Unidirectional Associations
7.1. The basic elimination procedure restricted to unidirectional associations
7.2. Eliminating associations from the Publisher-Book-Author design model
8. Rendering Reference Properties in the User Interface
9. Collection Types for Multi-Valued Reference Properties

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 8.1 below has a reference property chair, the values of which are references to objects of type ClubMember.

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 8.2 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 Committee.

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 8.1. An example of an association table

Committee-has-ClubMember-as-chair
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 8.2. Different terminologies

Our preferred term(s) UML ER Diagrams Mathematics
object object entity individual
object type (class) class entity type unary relation
relationship link relationship tuple
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.

1. References and Reference Properties

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 IDREF.

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 also call human-readable references ID references and use the suffix IdRef for the names of human-readable reference properties. 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 publisherIdRef. 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 8.1 below has an attribute name with range String, and a reference property chair with range ClubMember.

Figure 8.1. A committee has a club member as chair expressed by the reference property chair

A committee has a club member as chair expressed by the reference property chair

Object-oriented programming languages, such as JavaScript, PHP, Java and C#, directly support the concept of reference properties, which are properties whose range is not a datatype but a reference type, or class, and whose values are object references to instances of that class.

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 8.1. 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 8.1 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 8.10, “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.