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UML diagrams are independent of any implementing programming language They are used in object-oriented design to specify objects They should be easy to implement in Java, C++, or any other object-oriented programming language They provide a kind of pseudo-code for classes They specify the state (ie, fields) and the behavior (ie, methods) of an object without specifying how that behavior is accomplished UML diagrams include no executable code Specifying what an object can do without specifying how it does it is an abstraction It allows the design stage to be separated from the implementation stage of the software development It also facilitates modification of the software by allowing an implementation to be changed without affecting dependent modules As long as a method s behavior is unchanged, any invoking modules will be unaffected by a change in that method s implementation.

For example, suppose that an airline reservation system uses the Person class specified by the UML diagram in Figure 13 Presumably, that software will invoke that class s isAnAdult() method in various modules of the system The contract specified by the software design only requires that the method return the right answer: xisAnAdult() should be true if and only if x is an adult How it computes that result is irrelevant The implementation probably computes the chronological difference between the value of the private field xdob and the value of the current date But there is nothing in the contract that specifies that Moreover, if the implementation is changed, none of the other code in the reservation system would be affected by that change.

For example, if the market demand for shoes rises and if the rm provides each worker with better but more expensive equipment, the rm s demand for labor will also rise. That is, to produce more shoes requires more labor; better equipment makes labor more productive so the demand for labor increases; an increase in the price of equipment encourages the substitution of labor for capital in production. If a rm uses more than one variable resource, say labor (L) and capital (K), the rm will maximize total pro ts when it uses labor and capital until the marginal revenue product of each resource equals the re-

Such a change might be warranted by the preference of a different algorithm for computing chronological differences, or possibly by a redefinition of the meaning of adult Concealing the implementation of a method from the clients who use the method is called information hiding It is the software designer s version of the spy s principle that says, If you don t need to know it, then you re are not allowed to know it It makes software easier to design, implement, and modify ABSTRACT DATA TYPES Abstractions are used to help understand complex systems Even though they are different, rocks and tennis balls fall at the same rate The physicist uses the abstraction of imagining a single imaginary point mass to understand the physics of falling bodies By ignoring the irrelevancies (diameter, weight), the abstraction allows the analyst to focus on the relevancies (height).

Abstractions are widely used in software development UML diagrams provide abstractions by focusing on the fields (the state) and methods (the behavior) of a class But at some levels, even the fields of a class may be irrelevant An abstract data type (ADT) is a specification of only the behavior of instances of that type Such a specification may be all that is needed to design a module that uses the type Primitive types are like ADTs We know what the int type can do (add, subtract, multiply, etc) But we need not know how it does these operations And we need not even know how an int is actually stored As clients, we can use the int operations without having to know how they are implemented.

In fact, if we had to think about how they are implemented, it would probably be a distraction from designing the software that will use them Likewise, if you had to think about how your car manages to turn its front wheels when you turn the steering wheel, it would probably be more difficult to drive!.

Most programming languages have types for integers and real (decimal) numbers, but not for fractions. Such numbers can be implemented as objects. Here is a design for a fraction type: