A notation for manipulating arrays of operations

Abstract

Much has been written on the-possibility of incorporating arrays of functions and arrays of operators into APL. Various methods have been proposed for creating and restructuring such arrays. This paper proposes the introduction of arrays of operations in general into APL2. Vector notation is extended, as suggested by Brown and Benkard, to allow easy creation of vectors of operations. A new object, called an ELEVATOR, is introduced in order to create operations for manipulating arrays of operations. The semantics of the jot is extended, as per Benkard, to provide a means of extracting structural information from operation arrays. An analysis of the meaning behind the new notation is undertaken. Definitions are given which not only satisfy the notational requirements but also provide insights into the nature of structural operations on function arrays. The information retained in an empty function array is explained, and the relationship between the primitive ENCLOSE function and the EACH operator becomes clear.