Inheritance provides a natural classification for kinds of objects and allows for the commonality of objects to be explicitly taken advantage of in modeling and constructing object systems. Natural means we use concepts, classification, and generalization to understand and deal with the complexities of the real world. See the example below using computers.
Inheritance is a relationship between classes where one class is the parent (base/superclass/ancestor/etc.) class of another. Inheritance provides programming by extension (as opposed to programming by reinvention [LaLonde 90]) and can be used as an is-a-kind-of (or is-a) relationship or for differential programming. Inheritance can also double for assignment compatibility (see section 2.7).
In delegation languages, such as Self, inheritance is delegation where objects refer to other objects to respond to messages (environment) and do not respecify state by default.
Inherited parents can specify various flavors of state. Delegation languages don't specify new state by default (to do so requires cloning), C-based (C++, Objective-C, etc.), lisp-based (CLOS, Flavors, Scheme, etc.), and Pascal-based (Ada95, Modula-3, Object Pascal, etc.) OO languages do, but with multiple- inheritance can also share parents within a class lattice (CLOS and Eiffel provide this as a default at the level of slots and features, respectively).
Inheritance also provides for member lookup, or internal environment. Various schemes exist, for example C++ finds the closest match within a scope but causes an ambiguity error iff more than one parent has match, CLOS creates a linear precedence list, Self provides parent priorities, and Eiffel forces renaming for any parent member conflicts.
Defining inheritance (with a thorough description or denotational semantic definition, or both) can avoid confusion about which inheritance scheme is being used (especially in OOD), because inheritance has many variations and combinations of state and environment (sometimes with complex rules). Inheritance can also be used for typing, where a type or class can be used to specify required attributes of a matching object (see sections 2.1, 2.7 and [Cardelli 85]). It would be more judicious to have discussions on how inheritance should be defined instead of over what it is, since it has many existing uses and semantics.
An example of the is-a-kind-of relationship is shown below. Is-a is often used synonymously, but can be used to show the "object is-a class" instantiation relationship. In classical OO, inheritance is a relationship between classes only. In one-level systems, is-a (object instantiation) and is-a-kind-of (inheritance) are merged into one [Ungar 87, Madsen 93, Sciore 89].
Computer
/ | \
Mainframe Mini Personal
/ \ ... / \
Data Proc Scientific PC Workstation
Class hierarchies are subjective [Booch 91, 4.2; Lakoff 87] and usually drawn with the parent class on top, but more demanding graphs (as is often the case in [Rumbaugh 91]) allow any topology, with the head of an arrow indicating the base class and the tail indicating the derived class.
Differential programming is the use of inheritance to reuse existing classes by making a small change to a class. Creating a subclass to alter a method or to add a method to a parent class is an example.
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