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The theory of function arrays

This paper presents a theoretical foundation for objects known as function arrays, which have been widely written about in past conferences. In contrast to the usual constructive approach, where the emphasis is on the method for creating function arrays, this paper follows a deductive approach, where a given function is defined to be a function array if it has certain properties. The principles outlined here are independent of any method for constructing function arrays, but when particular examples are required, they are taken from APL2.