Trenchard More
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Abstract
The concepts of collection, rectangular arrangement, and membership for nested arrays are discussed separately and independently of array-theoretic operations. The concepts are illustrated by examples generated in the Nested Interactive Array Language, Nial.
- 1 A. D. Falkoff and K. E. Iverson, APL/360 User's Manual. Thomas J. Watson Research Ctr., IBM Corp., Yorktown, NY, July, 1968.Google Scholar
- 2 T. More, "Nested rectangular arrays for measures, addresses and paths," ACM STAPL/Sigplan APL79, also APL Quote Quad 9, 4 - part 1, June 1979, pp. 156-163. "Each component of a grounded, rectangular, nested array is either another such array or an elementary object, such as a number or character, that is not a grounded array. A basic array is a grounded array in which all components are elementary objects." {p. 158} I prefer the word "basic" to the word "flat" because "flat" has technical meaning in affine spaces and linear algebra. Google ScholarDigital Library
- 3 T. More, "The nested rectangular array as a model of data," invited address, ACM STAPL/Sigplan APL79, also APL Quote Quad 9, 4 - part 1, June 1979, pp. 55-73. I use the word "array" instead of the phrase "general array," as logicians use "set" instead of "general set," to indicate that the general case is the fundamental concept. Special kinds of arrays, such as simple arrays and atomic arrays, are named by qualifying the root word "array." The phrase "general array" suggests that a fundamental concept has been generalized. I have used the terms nested rectangular array and nested array in a descriptive rather than a qualifying sense to mean array: "The purpose of array theory or list theory is to carry the mathematics of nested arrays or nested lists far into the province of algorithms before using programming techniques to bestow the full power of effective computability." {p. 55} Google ScholarDigital Library
- 4 C. M. Cheney, APL*PLUSTM Nested Arrays System Reference Manual. STSC, Inc., Bethesda, MD, 1981.Google Scholar
- 5 R. A. Smith, "Nested arrays, operators, and functions," ACM SIGAPL APL81, also APL Quote Quad 12, 1, Sept. 1981, pp. 286-290. Google ScholarDigital Library
- 6 R. Bernecky and K. E. Iverson, "Operators and enclosed arrays," APL USERS MEETING, I. P. Sharp Associates Limited, Toronto, 1980.Google Scholar
- 7 R. Bernecky, "Representations for enclosed arrays," ACM SIGAPL APL81, also APL Quote Quad 12, 1, Sept. 1981, pp. 42-46. Google ScholarDigital Library
- 8 T. More, "A theory of arrays with applications to databases," Tech. Rep. G320-2106, IBM Scientific Ctr., Cambridge, MA, Sept. 1975.Google Scholar
- 9 T. More, "Types and prototypes in a theory of arrays," Tech. Rep. G320-2112, IBM Scientific Ctr., Cambridge, MA, May 1976.Google Scholar
- 10 T. More, "On the composition of array-theoretic operations," Tech. Rep. G320-2113, IBM Scientific Ctr., Cambridge, MA, May 1976.Google Scholar
- 11 J. A. Brown, "APL language extensions," Proceedings of SEAS 1978 anniversary meeting, Stresa, Italy, vol. 1, pp. 335-353.Google Scholar
- 12 J. A. Brown, "Evaluating extensions to APL," ACM STAPL/Sigplan APL79, also APL Quote Quad 9, 4 - part 1, June 1979, pp. 148-155. Google ScholarDigital Library
- 13 J. A. Brown and M. A. Jenkins, "The APL identity crisis," ACM SIGAPL APL81, also APL Quote Quad 12, 1, Sept. 1981, pp. 62-66. Google ScholarDigital Library
- 14 A. Hassitt and L. E. Lyon, "Array theory in an APL environment," ACM STAPL/Sigplan APL79, also APL Quote Quad 9, 4 - part 1, June 1979, pp. 110-115. Google ScholarDigital Library
- 15 M. A. Jenkins, "A development system for testing array theory concepts," ACM SIGAPL APL81, also APL Quote Quad 12, 1, Sept. 1981, pp. 152-159. Google ScholarDigital Library
- 16 W. G. Bouricius and N. R. Sorensen, "An informal introduction to array theory with applications to a language and a database." Oyvind Bjorke and Ole. I. Franksen (eds.), Structures and Operations in Engineering and Management Systems. Tapir Publishers, Trondheim, Norway, 1981, pp. 447-496.Google Scholar
- 17 T. More, "Notes on the diagrams, logic and operations of array theory." Oyvind Bjorke and Ole. I. Franksen (eds.), Structures and Operations in Engineering and Management Systems. Tapir Publishers, Trondheim, Norway, 1981, pp. 497-666.Google Scholar
- 18 N. Jacobsen, S. W. Poulsen, R. Stockner, and P. H. Thygesen, "Nial applications, an introductory investigation," Electric Power Engineering Department, Technical University of Denmark, Publ. 8202, April 1982.Google Scholar
- 19 M. A. Jenkins, The Q'NialTM Reference Manual, Queen's University, Kingston, Ontario, April 1982.Google Scholar
- 20 W. S. Adams, "Plain programming in Nial," Queen's University Tech. Rep., Kingston, Ontario, June 1982.Google Scholar
- 21 F. Schmidt and M. A. Jenkins, "Systems design and the Nial approach," Queen's University Tech. Rep., Kingston, Ontario, June 1982.Google Scholar
- 22 W. E. Gull and M. A. Jenkins, "Recursive data structures in APL," Comm. ACM 22, Feb. 1979, pp. 79-96. Google ScholarDigital Library
- 23 D. L. Orth, "A comparison of the IPSA and STSC implementations of operators and general arrays," APL Quote Quad 12, 2, Dec. 1981, pp. 11-18. Google ScholarDigital Library
- 24 R. Mercer, "A based system for general arrays," APL Quote Quad 12, 2, Dec. 1981, pp. 18-21. Google ScholarDigital Library
- 25 W. V. Quine, "Unification of universes in set theory," Journal of Symbolic Logic 21, 3, Sept. 1956, pp. 267-279.Google ScholarCross Ref
- 26 J. C. H. Gerretsen, Lectures on Tensor Calculus and Differential Geometry. P. Noordhoff N.V. Groningen, 1962.Google Scholar
Index Terms
- Rectangularly arranged collections of collections
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