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All programming languages provide abstractions. It can be argued that the complexity of the problems you can solve is directly related to the kind and quality of abstraction. By “kind” I mean: what is it that you are abstracting? Assembly language is a small abstraction of the underlying machine. Many so-called “imperative” languages that followed (such as FORTRAN, BASIC, and C) were abstractions of assembly language. These languages are big improvements over assembly language, but their primary abstraction still requires you to think in terms of the structure of the computer rather than the structure of the problem you are trying to solve. The programmer must establish the association between the machine model (in the “solution space”) and the model of the problem that is actually being solved (in the “problem space”). The effort required to perform this mapping, and the fact that it is extrinsic to the programming language, produces programs that are difficult to write and expensive to maintain, and as a side effect created the entire “programming methods” industry.
The alternative to modeling the machine is to model the problem you’re trying to solve. Early languages such as LISP and APL chose particular views of the world (“all problems are ultimately lists” or “all problems are algorithmic”). PROLOG casts all problems into chains of decisions. Languages have been created for constraint-based programming and for programming exclusively by manipulating graphical symbols. (The latter proved to be too restrictive.) Each of these approaches is a good solution to the particular class of problem they’re designed to solve, but when you step outside of that domain they become awkward.
The object-oriented approach takes a step farther by providing tools for the programmer to represent elements in the problem space. This representation is general enough that the programmer is not constrained to any particular type of problem. We refer to the elements in the problem space and their representations in the solution space as “objects.” (Of course, you will also need other objects that don’t have problem-space analogs.) The idea is that the program is allowed to adapt itself to the lingo of the problem by adding new types of objects, so when you read the code describing the solution, you’re reading words that also express the problem. This is a more flexible and powerful language abstraction than what we’ve had before. Thus OOP allows you to describe the problem in terms of the problem, rather than in the terms of the solution. There’s still a connection back to the computer, though. Each object looks quite a bit like a little computer; it has a state, and it has operations you can ask it to perform. However, this doesn’t seem like such a bad analogy to objects in the real world; they all have characteristics and behaviors.
Alan Kay summarized five basic characteristics of Smalltalk, the first successful object-oriented language and one of the languages upon which Java is based. These characteristics represent a pure approach to object-oriented programming:
- Everything is an object. Think of an object as a fancy variable; it stores data, but you can also ask it to perform operations on itself by making requests. In theory, you can take any conceptual component in the problem you’re trying to solve (dogs, buildings, services, etc.) and represent it as an object in your program.
- A program is a bunch of objects telling each other what to do by sending messages . To make a request of an object, you “send a message” to that object. More concretely, you can think of a message as a request to call a function that belongs to a particular object.
- Each object has its own memory made up of other objects . Or, you make a new kind of object by making a package containing existing objects. Thus, you can build up complexity in a program while hiding it behind the simplicity of objects.
- Every object has a type . Using the parlance, each object is an instance of a class, where “class” is synonymous with “type.” The most important distinguishing characteristic of a class is “what messages can you send to it?”
- All objects of a particular type can receive the same messages . This is actually a very loaded statement, as you will see later. Because an object of type circle is also an object of type shape, a circle is guaranteed to receive shape messages. This means you can write code that talks to shapes and automatically handle anything that fits the description of a shape. This substitutability is one of the most powerful concepts in OOP.
Some language designers have decided that object-oriented programming itself is not adequate to easily solve all programming problems, and advocate the combination of various approaches into multiparadigm programming languages. 
 See Multiparadigm Programming in Leda by Timothy Budd (Addison-Wesley 1995).