Control of structure and evaluation

Abstract

Scalar conformance controls the structure phase of expression evaluation. Program control of this phase is achieved through insertion and deletion of scalar levels of structure. The basic functions to do this are ENCLOSE and DISCLOSE with axis. Their application in some common cases is made easier with proposed extensions to BRACKET INDEX and INTERVAL. This approach provides the function of a RANK operator with greater flexibility while keeping data structure information with the data. A number of simple expression transformations have proved useful experimentally. Two operators are defined which in their several invocations provide full and partial currying and commutation of left and right arguments; composition, power, and dual of functions; composition, conversion between dyadic and monadic function syntax. The variations in the definitions of partitions have led to suggestions that more than one primitive operation may be needed. Extensions to EACH and ENCLOSE are proposed which provide a wide range of function while satisfying numerous identities. Since these two operations are each used in APL2 to create a level of structure, the extensions are appropriate.