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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.
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