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

Author:

Trenchard More, Jr.Authors Info & Claims

ACM SIGAPL APL Quote Quad, Volume 24, Issue 1

Pages 170 - 184

https://doi.org/10.1145/166198.166219

Published: 01 September 1993 Publication History

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.

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In discussing some of the background on the nesting of arrays, Part II of this paper places the evolution of the theory in the context of related work by referring to some of the papers in a chronological list.

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Cited By

Franksen O(1996)Invariance under Nesting — An Aspect of Array-Based Logic with Relation to Grassmann and PeirceHermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar10.1007/978-94-015-8753-2_26(303-335)Online publication date: 1996
https://doi.org/10.1007/978-94-015-8753-2_26

Index Terms

Transfinite nesting in array-theoretic figures, changes, rigs, and arms. Part I
1. Information systems
  1. Information storage systems
    1. Record storage systems
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Data types and structures
        Procedures, functions and subroutines
      2. Language types

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Published In

cover image ACM SIGAPL APL Quote Quad

ACM SIGAPL APL Quote Quad Volume 24, Issue 1

Aug. 1993

316 pages

ISSN:0163-6006

DOI:10.1145/166198

Editor:
Elena M. Anzalone

Issue’s Table of Contents

APL '93: Proceedings of the international conference on APL
September 1993
325 pages
ISBN:0897916123
DOI:10.1145/166197
Editor:
Elena M. Anzalone

Copyright © 1993 Author.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 1993

Published in SIGAPL Volume 24, Issue 1

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Cited By

Franksen O(1996)Invariance under Nesting — An Aspect of Array-Based Logic with Relation to Grassmann and PeirceHermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar10.1007/978-94-015-8753-2_26(303-335)Online publication date: 1996
https://doi.org/10.1007/978-94-015-8753-2_26

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