A ‘division’ transformation for program and data structures and the structure clash problem

Abstract

Motivated by the structure clash problem, this study examines certain formal transformations of data and program structures and relates them to the structure clash problem. It defines a division and a decomposition transformation of program and data structures with respect to one of its structure blocks. The latter allows a formal derivation of a new structure where this block appears at the beginning. The transformation is intuitively introduced for program and data structures. At the same time, it is mathematically treated in terms of regular algebra and is shown to be reflexive, symmetric and transitive. Thus, equivalence classes of regular expressions that are decompositions of each other may be defined. A formal realization of these is constructed as a type of circuitless graph.