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Symbol manipulation is a valuable set of techniques currently available to computer users. Because many of these techniques are relatively new and have been used in a wide variety of applications, the terminology and utility of symbol manipulation are poorly understood by a large portion of the computing community. This paper presents some definitions of the basic concepts in symbol manipulation, and some examples of the applications of these concepts. These examples have been selected to illustrate the importance of the computational techniques used. They may also suggest valuable new applications for the techniques of symbol manipulation.