Transfinite nesting in array-theoretic figures, changes, rigs, and arms. Part I

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Transfinite nesting in array-theoretic figures, changes, rigs, and arms. Part I

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International Conference on APL archive
Proceedings of the international conference on APL table of contents

Toronto, Ontario, Canada

Pages: 170 - 184

Year of Publication: 1993

ISBN:0-89791-612-3

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Author

Trenchard More, Jr.

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SIGAPL: ACM Special Interest Group on APL Programming Language

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ACM New York, NY, USA

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ABSTRACT

Nesting and stemming (infinite successive singling) of arrays of nestings and stemmings result in forms. Forms of 0th-, 1st-, 2nd-, or 3rd-order, array-theoretic, totally defined functions are again such functions, called, respectively, figures, changes, rigs, and arms. One arms a rig before rigging a change before changing a figure. Part I lays the foundation for a new approach to a theory of arrays. This Part considers the analogy between array-theoretic and Euclidean figures, analyzes form separately from substance, introduces Nth-order functions, presents the beginnings of a syntax for the theory, and constructs a formal system to deduce the first few consequences of the first two primitive operations.

REFERENCES

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