Nested rectangular arrays for measures, addresses, and paths
Trenchard More · ACM SIGAPL APL Quote Quad · 1979
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.