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Laminar extension: An overlooked capability and the search for its proper home

Scalar extension is an implicit conceptual replication of a single-element argument so that it matches the shape of another. Laminar extension is a related extension of an arbitrary array, formed by repeating layers (or laminae) of the array along a new coordinate or along an existing coordinate with a dimension of 1. A restricted form of laminar extension already exists in APL as an implicit conceptual process. This paper identifies needs for an explicit laminar extension, and shows that no adequate implementation is now available in APL. By examining existing primitives, the paper establishes one of them as the natural home for a primitive implementation of explicit laminar extension. Examples illustrate its utility, and an appendix discusses its relationship to the by-slice operator recently proposed by Jenkins and Michel.