Adding and using structure in general arrays

Abstract

Examples of pre-APL general arrays suggest uses for APL II. Two structure-creating functions are proposed. Using numerical or logical control arguments, they partition a level of an array regularly or irregularly, with or without reuse of items. The resulting arrays reduce string search to item search in two distinct ways. They can be used on arrays of any rank to simplify search for abstractly defined patterns of relationships between nearby elements or to construct a tessellation by repetition of a given pattern. The relationships between these techniques and programming techniques using operators is noted. Formal identities relate the two proposed functions to APL I functions and to each other.