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J is a dialect of APL, a formal imperative language. Because it is imperative, a sentence in J may also be called an instruction, and may be executed to produce a result. Because it is formal and unambiguous it can be executed mechanically by a computer, and is therefore called a programming language. Because it shares the analytic properties of mathematical notation, it is also called an analytic language.

APL originated in an attempt to provide consistent notation for the teaching and analysis of topics related to the application of computers, and developed through its use in a variety of topics, and its implementation in computer systems [1-5].

J is implemented in C (as detailed in Hui [6]), and is ported to a number of different host computer systems. The effect of the specific host is minimal, and communication with it is confined to the single foreign conjunction detailed in Appendix A. See help files for other host facilities such as Windows.

The Introduction in this book provides guidance to beginners. References [7-9] use J in the exposition of various mathematical topics.

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