Strongly Typed Rewriting For Coupled Software Transformation

Coupled transformations occur in software evolution when multiple artifacts must be modified in such a way that they remain consistent with each other. An important example involves the coupled transformation of a data type, its instances, and the programs that consume or produce it. Previously, we have provided a formal treatment of transformation of the first two: data types and instances. The treatment involved the construction of type-safe, type-changing strategic rewrite systems. In this paper, we extend our treatment to the transformation of corresponding data processing programs.The key insight underlying the extension is that both data migration functions and data processors can be represented type-safely by a generalized abstract data type (GADT). These representations are then subjected to program calculation rules, harnessed in type-safe, type-preserving strategic rewrite systems. For ease of calculation, we use point-free representations and corresponding calculation rules.Thus, coupled transformations are carried out in two steps. First, a type-changing rewrite system is applied to a source type to obtain a target type together with (representations of) migration functions between source and target. Then, a type-preserving rewrite system is applied to the composition of a migration function and a data processor on the source (or target) type to obtain a data processor on the target (or source) type. All rewrites are type-safe.