Let’s work through an example of creating a UML class diagram based on existing code. This is loosely based off a project from an earlier course, so some of the structure may be familiar.

The Project

This project is a number calculator that makes use of object-oriented concepts such as inheritance, interfaces, and polymorphism to represent different types of numbers using different classes. We’ll also follow the Model-View-Controller (MVC) architectural pattern.

Number Interface

We’ll start by looking at the Number interface, which is the basis of all of the number classes. We’re omitting the method code in these examples, since we are only concerned with the overall structure of the classes themselves.

public interface Number {
    Number add(Number n);
    Number subtract(Number n);
    Number multiply(Number n);
    Number divide(Number n);
}

class Number(metaclass=abc.ABCMeta):

    @classmethod
    def __subclasshook__(cls, subclass: type) -> bool:
        
    @abc.abstractmethod
    def add(self, n: Number) -> Number:

    @abc.abstractmethod
    def subtract(self, n: Number) -> Number:

    @abc.abstractmethod
    def multiply(self, n: Number) -> Number:

    @abc.abstractmethod
    def divide(self, n: Number) -> Number:

In UML, we’d represent this interface using the following box. It includes the <<interface>> stereotype, as well as the listed methods shown in italics since they are all abstract. Finally, each method in an interface is assumed to be public, so we’ll include a plus symbol + in front of each method.

Real Number Class

Next is the class for representing real numbers. This class will be a realization of the Number interface, as we can see in the code:

public class RealNumber implements Number {

    private double value;

    public RealNumber(double value){ }

    public Number add(Number n){ }

    public Number subtract(Number n){ }

    public Number multiply(Number n){ }

    public Number divide(Number n){ }

    @Override
    public String toString(){ }

    @Override
    public boolean equals(Object o){ }
}

class RealNumber(Number):

    def __init__(self, value: float) -> None:
        self.__value = value
        
    def add(self, n: Number) -> Number:

    def subtract(self, n: Number) -> Number:

    def multiply(self, n: Number) -> Number:

    def divide(self, n: Number) -> Number:

    def __str__(self) -> str:

    def __eq__(self, o: object) -> bool:

it also includes implementations for a couple of other methods beyond the interface, including a constructor. So, in our UML diagram, we’ll add another box to represent that class, and use the realization association arrow to show the connection between the classes. Remember that the arrow itself points toward the interface or parent class.

Other Number Classes

From here, it’s pretty easy to see how we can use inheritance to create a RationalNumber class and an IntegerNumber class. The only way that they differ from the RealNumber class are the attributes. So, we’ll quickly add those to our UML diagram as well.

Complex Numbers

At this point, we can add a new class to represent complex numbers. A complex number consists of two parts - a real part and an imaginary part. So, it will both implement the Number interface, but it will also be composed of two RealNumber attributes. Notice that we’re using RealNumber as the attribute instead of the Number interface. This is because we don’t want a complex number to contain a complex number, so we’re being careful about our inheritance. In code, this class would look like this:

public class ComplexNumber implements Number {

    private RealNumber real;
    private RealNumber imaginary;

    public ComplexNumber(RealNumber real, RealNumber imaginary){ }

    public Number add(Number n){ }

    public Number subtract(Number n){ }

    public Number multiply(Number n){ }

    public Number divide(Number n){ }

    @Override
    public String toString(){ }

    @Override
    public boolean equals(Object o){ }
}

class ComplexNumber(Number):

    def __init__(self, real: RealNumber, imaginary: RealNumber) -> None:
        self.__real = real
        self.__imaginary = imaginary
        
    def add(self, n: Number) -> Number:

    def subtract(self, n: Number) -> Number:

    def multiply(self, n: Number) -> Number:

    def divide(self, n: Number) -> Number:

    def __str__(self) -> str:

    def __eq__(self, o: object) -> bool:

In our UML diagram, we’ll add a box for this class. We’ll also add both a realization association to the Number interface, but also a composition association to the RealNumber class, complete with the cardinality of the relationship.

MVC Components

Once we’ve created all of our number classes, we can quickly create our View and Controller classes as well. They will handle getting input from the user, performing operations, and displaying the results.

public class View {

    public View(){ }

    public void show(Number n){ }

    public String input(){ }

}

public class Controller {

    private List<Number> numbers;
    private View view;

    public Controller(){ }

    public void build(){ }
    
    public void sum(){ }

    public static void main(String[] args){ }
}

class View:

    def __init__(self) -> None:

    def show(self, n: Number) -> None:

    def input(self) -> str:


class Controller:

    def __init__(self) -> None:
        self.__numbers: List[Number] = list()
        self.__view: View = View()
    
    def build(self) -> None:

    def sum(self) -> None:

    @classmethod
    def main(self, args: List[str]) -> None:

In the code, we see that the Controller class contains an attribute for a single View() instance, and also a list of Number instances. So, we’ll end up using a composition association between Controller and View, and an aggregation association between Controller and the Number interface.

This is a small example, but it demonstrates many of the important object-oriented concepts in a single UML diagram:

• The Number class is an interface and abstract class
• RealNumber implements the Number class through a realization association
• RationalNumber and IntegerNumber show direct inheritance through a generalization association
• ImaginaryNumber contains two RealNumber instances, showing the composition association and a multiplicity of 2.
• The Controller, View and Number classes make up the various parts of an MVC architecture.
• The Controller stores a list of Number instances, demonstrating the aggregation association.
• The Controller also contains a single View instance, which is another composittion association with multiplicity of 1.

Further Reading

UML is a very broad topic to cover in a single module, let alone a single class. For more information on building and reading UML diagrams, refer to these sources:

• UML Class Diagram Tutorial from Visual Paradigm
• UML Class Diagram Tutorial (Video) from Lucidchart

There are also many textbooks devoted to teaching UML concepts, as well as lots of examples online to learn from. The O’Reilly subscription through the K-State Libraries offers several books to choose from that can be accessed for free through this link:

• Unified Modeling Language User Guide
• Learning UML 2.0