Abstraction Instability Chart
To provide a flexible and extendable software, it is a good OO practice to reduce the dependencies between implementing classes. This could be achieved by developing against abstractions which means both, abstract classes and interfaces. By using abstractions instead of real implementation in the application you provide some sort of contract, that could be used by others to hook into the application with their own classes that fulfill the contract. Except the extensibility of an application a good abstraction reduces the risk of breaks in multiple subsystems when something was changed in a single package. But how to get rid of all these dependencies, doing this by hand will become an impossible job, at least for larger projects. At this point a tool should be used to assist the development process.
The A-I chart as it is generated by PHP_Depend is based on the whitepaper OO Design Quality Metrics - An Analysis of Dependencies [1] published by Robert C. Martin. It shows you the quality of your design in the terms of extensibility, reusability and maintainability. All these facts are influenced by the inter-package dependencies and the package abstraction that PHP_Depend visualizes in form of an abstract/instability chart.
PHP_Depend calculates the following metrics by counting classes, interfaces and dependencies.
Ca - Afferent Couplings:
The number of other packages that depend upon classes within this package. This value is good indicator how changes to classes in this package would influence other parts of the software.
Ce - Efferent Couplings:
The number of other packages that classes from this package depend upon. This value indicates how sensitive this package is for changes to other packages.
I - Instability:
The ratio between efferent coupling (Ce) and the total package coupling (Ce + Ca) which is based on the following formula (Ce / (Ce + Ca)) and produces results in the range [0,1]. A value I=0 indicates a maximally stable package that depends upon nothing and I=1 indicates a total instable package that has no incoming dependencies but depends upon other packages.
A - Abstractness:
The ratio between abstract classes (ac) and the total of all classes (ac + cc) that is calculated by this formula (ac / (ac + cc)) that results in a value in the range [0,1]. A=0 means that all classes in this package are non-abstract while A=1 shows a package that only consists of abstract classes and interfaces.
With these values we can create a chart that visualizes the relationship between the instability (I) on the y-axis and the abstraction (A) on the x-axis.
Graphical view of PHP_Depend's metricsBecause in a project not each package can achieve the optimal values of A = 1, I = 0 or A = 0, I = 1, we draw a diagonal between the two corners. This line is called the Main sequence and represents an average between abstraction (A) and instability (I). This means that packages near this line have a good mix between abstraction and instability. You can call these packages balanced. Because it is desirable for packages to be close to the Main sequence we have a fifth metric, the package distance (D) from this ideal.
D - Distance:
The normalized distance has a value in the range [0,1] and is calculated by the formula ((A + I) - 1)
- 1
- http://www.objectmentor.com/resources/articles/oodmetrc.pdf
- OO Design Quality Metrics - An Analysis of Dependencies; Robert C. Matrin; 1994
