Recursive data structures in APL
Communications of the ACM
The nested rectangular array as a model of data
APL '79 Proceedings of the international conference on APL: part 1
Polyvalent functions, operators, strand notation and their precedence
APL '84 Proceedings of the international conference on APL
Rectangularly arranged collections of collections
APL '82 Proceedings of the international conference on APL
APL '82 Proceedings of the international conference on APL
The nested rectangular array as a model of data
APL '79 Proceedings of the international conference on APL: part 1
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The left argument of the reshaping function in APL is an ordinal number or list of ordinals, called a shape, that measures the rectangularity of an array. Shapes are the simplest measures. A natural extension of the index-generator function shows how an array of any valence (rank), depth of nesting, or type can be used as a measure. The method of generalizing shapes to measures also generalizes addresses and paths to arbitrary arrays. Only the leaves of a measure, address, or path matter, the nested rectangular structure does not. These results of array theory for floating arrays are motivated by similar considerations for grounded arrays.