ABSTRACT
The simplest arrays are scalars, vectors, and matrices. A programming language (APL) function catenates, designated with a comma, and is used to attach arrays together. It can be used to attach a scalar to a scalar, a scalar to a vector, and a vector to a vector. Catenation is convenient for constructing matrices with certain types of structure. Most modern versions of APL allow a vector to be catenated directly to a matrix, thereby simplifying many array constructions. Entries or blocks of entries of an array can be referenced by using "position" numbers or indices to specify entries. In the discussion of shape it was observed that scalars are arrays with "empty" shape and dimension 0. The shape of a scalar, although empty, is a legitimate APL array that may itself be manipulated. There are two more examples of empty arrays; they are created by reshape and index generator.
