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What Is a Multilevel Array?

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2 Author(s)
Rosenberg, A.L. ; IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA ; Thatcher, J.W.

In intuitive terms, a multilevel array is either a scalar or an array each of whose elements is a multilevel array. The “semantics” of multilevel arrays can be easily expressed in terms of a notion of selector, which is basically that of the Vienna Definition Language. These selectors provide both a notational device for accessing multilevel arrays and a clean mathematical definition of “multilevel array with data domain D.” However, the definition so obtained lacks the recursive flavor of the intuitive definition. By means of an axiomatic characterization of multilevel arrays, the selector-based definition and the recursive definition are shown to be equivalent.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:19 ,  Issue: 2 )