Objects often characterized in different ways that are orthogonal to each other

For example, the instructor is

• North American
• Male
• Professor
• Computer Scientist

Cannot be placed into an inheritance hierarchy

                                 CS Example - complex Numbers

Two abstract classifications:

Magnitude: things that can be compared to each other

Number: things that can  perform arithmetic

Three specific classes:

Integer: comparable and arithmetic

Char: comparable but not arithmetic

Complex: arithmetic but not comparable
 

                                    Solutions
 

1. make number subclass of magnitude, but redefine comparison operators in class complex to print error message
      - subclassing for limitations
2. Don't use inheritance at all - redefine all operators in all classes
      -flattening the inheritance tree
3. Use inheritance for some relationships, but simulate others - use Number, but have each number implement all relational operators

4. Make Number and Magnitude independent, have Integer inherits from both
     -multiple inheritance

                                                 Another example - walking Menus

• A Menu is structure charged with displaying itself  when selected by users

• A Menu  maintains collection o Menuitems

• Each Menuitem knows now to respond when selected

• A cascading menu  is both a Menuitem and Menu

What happens when same name is used to both parent classes?
 

• A CardDeck knows  how to draw ( select ) a Card

• A GraphicalItem knows how to draw (display) an image on screen

• A GraphicalCardDeck should be able to draw - but which

Java supports Multiple inheritance of interfaces (subtypes) but not of classes (subclasses) 

interface A { ... }

interface B { ... }

interface AB extends A, B { ... }

interface C { ... }

class X { ... }

class Y extends X implements AB, C { ... }