The fact that operators (adverbs and conjunctions) can produce entities of any type (noun, verb, adverb, conjunction) is among the most powerful aspects of J. Here is is most apparent that J facilitates higher orders of abstraction.
K.E. Iverson, writing on the history of APL, noted that the first four operators emerged through independent efforts, and were only later recognized as instances of a common class. It's a huge leap from the initial hand-crafting of those first few operators (embedded in the language) to the freedom, with J, to define custom operators. K.E.I. credited Oliver Heaviside with the innovation of operators. Heaviside was also among the early developers of vectors and vector calculus. His vector solution to Maxwell's equations was a significant advancement. There was a strong emphasis ine Heaviside's work to simplify, to approach mathematics with an exploratory attitude, and to also see it as a tool for practical application. All these strike me as concordant with the spirit of APL. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
