mathematics

Has-a

Has-a is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Has-a rather than just read about it. In short: In database design, object-oriented programming and design, has-a (has_a or has a) is a composition relationship where one object (often called the constituted object, or part/constituent/member object) "belongs to" (is part or member of) another object (called the composite type), and behaves according to the rules of ownership. In simple words, has-a relationship in an object is called a member field of an object.

Key takeaways

Has-a belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Has-a to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Has-a from memory before moving on to harder problems.

Reference excerpt

In database design, object-oriented programming and design, has-a (has_a or has a) is a composition relationship where one object (often called the constituted object, or part/constituent/member object) "belongs to" (is part or member of) another object (called the composite type), and behaves according to the rules of ownership. In simple words, has-a relationship in an object is called a member field of an object. Multiple has-a relationships will combine to form a possessive hierarchy.

Related concepts "Has-a" is to be contrasted with an is-a (is_a or is a) relationship which constitutes a taxonomic hierarchy (subtyping). The decision whether the most logical relationship for an object and its subordinate is not always clearly has-a or is-a. Confusion over such decisions have necessitated the creation of these metalinguistic terms. A good example of the has-a relationship is containers in the C++ STL. To summarize the relations, we have

hypernym-hyponym (supertype-subtype) relations between types (classes) defining a taxonomic hierarchy, where for an inheritance relation: a hyponym (subtype, subclass) has a type-of (is-a) relationship with its hypernym (supertype, superclass); holonym-meronym (whole/entity/container-part/constituent/member) relations between types (classes) defining a possessive hierarchy, where for an aggregation (i.e. without ownership) relation: a holonym (whole) has a has-a relationship with its meronym (part), for a composition (i.e. with ownership) relation: a meronym (constituent) has a part-of relationship with its holonym (entity), for a containment relation: a meronym (member) has a member-of relationship with its holonym (container); concept-object (type-token) relations between types (classes) and objects (instances), where a token (object) has an instance-of relationship with its type (class).

Examples

Entity–relationship model In databases has-a relationships are usually represented in an Entity–relationship model. As you can see by the diagram on the right an account can have multiple characters. This shows that account has a "has-a" relationship with character.

UML class diagram

In object-oriented programming this relationship can be represented with a Unified Modeling Language Class diagram. This has-a relationship is also known as composition. As you can see from the Class Diagram on the right a car "has-a" carburetor, or a car is "composed of" a carburetor. When the diamond is coloured black it signifies composition, i.e. the object on the side closest to the diamond is made up of or contains the other object. While the white diamond signifies aggregation, which means that the object closest to the diamond can have or possess the other object.

C++

Another way to distinguish between composition and aggregation in modeling the real world, is to consider the relative lifetime of the contained object. For example, if a Car object contains a Chassis object, a Chassis will most likely not be replaced during the lifetime of the Car. It will have the same lifetime as the car itself; so the relationship is one of composition. On the other hand, if the Car object contains a set of Tire objects, these Tire objects may wear out and get replaced several times. Or if the Car becomes unusable, some Tires may be salvaged and assigned to another Car. At any rate, the Tire objects have different lifetimes than the Car object; therefore the relationship is one of aggregation. If one were to make a C++ software Class to implement the relationships described above, the Car object would contain a complete Chassis object in a data member. This Chassis object would be instantiated in the constructor of the Car class (or defined as the data type of the data member and its properties assigned in the constructor.) And since it would be a wholly contained data member of the Car class, the Chassis object would no longer exist if a Car class object was to be deleted. On the other hand, the Car class data members that point to Tire objects would most likely be C++ pointers. Tire objects could be instantiated and deleted externally, or even assigned to data members of a different Car object. Tire objects would have an independent lifetime separate from when the Car object was deleted.

See also Object composition Has-a Holonymy Meronymy Is-a Hypernymy (and supertype) Hyponymy (and subtype)

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Has-a

Start with the simplest possible case. Write down what Has-a claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Has-a before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Has-a ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Has-a

In research: Has-a appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Has-a in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Has-a is common in secondary-school and first-year university syllabi. It links to neighbouring topics Object-oriented programming, Relational algebra, so understanding it makes those chapters shorter.
In everyday life: Look for Has-a outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Has-a in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Has-a means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Has-a out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Has-a in simple terms?

Why does Has-a matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Has-a?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Has-a.