A new calculus for multidimensional arrays
APL '02 Proceedings of the 2002 conference on APL: array processing languages: lore, problems, and applications
The nested rectangular array as a model of data
APL '79 Proceedings of the international conference on APL: part 1
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Previous work focused on developing a complete yet concise calculus for programming multidimensional arrays that is based mainly on the essential mathematical properties of computations, that permits the expression of mathematical algorithms as in APL, and that balances abstraction and application. Primitives are defined in an architecture-independent way using algebraic notions, mainly constructors, as in the theory of lists, instead of freely defining operations as in APL. Multidimensional arrays are defined so that they possess a single type, which is a primitive concept independent of other data types or an implementation. Traditional notation for arrays is sometimes more of an obstacle than an aid. We review useful formulas and identities that lack many of the indices typically required. We show how the new notation helps to simplify some of the definitions and proofs. We give a couple examples starting from the specification of a problem.