New Programs From Old

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh There is often a need in the program-development process to generate a new version of a program that relates to existing versions of the program in some specific way. Program-development tools that assist in the generation of the new version, or possibly even automatically generate the new version from the existing versions, will obviously be of great use in this process. The problems of merging software extensions, program integration, separating consecutive edits, and propagating changes through multiple versions are all instances of situations where such tools would be welcome. These problems give rise to various questions concerning the relationship between these problems and between various strategies that may be used to tackle these problems. The goal of this paper is to address these questions. Previous work has shown how programs may be treated as elements of a double Brouwerian algebra, and how program modifications may be treated as functions from the set of programs to itself. In this paper we study the algebraic properties of program modifications, and use them to establish various results concerning the problem of program integration and the problem of separating consecutive edits. We also show how a particular category can be constructed from programs and program modifications, and address the question of whether integration is a pushout in this category.