Constraint-aware schema transformation

Abstract

Data schema transformations occur in the context of software evolution, refactoring, and cross-paradigm data mappings. When constraints exist on the initial schema, these need to be transformed into constraints on the target schema. Moreover, when high-level data types are refined to lower level structures, additional target schema constraints must be introduced to balance the loss of structure and preserve semantics. We introduce an algebraic approach to schema transformation that is constraint-aware in the sense that constraints are preserved from source to target schemas and that new constraints are introduced where needed. Our approach is based on refinement theory and point-free program transformation. Data refinements are modeled as rewrite rules on types that carry point-free predicates as constraints. At each rewrite step, the predicate on the reduct is computed from the predicate on the redex. An additional rewrite system on point-free functions is used to normalize the predicates that are built up along rewrite chains. We implemented our rewrite systems in a type-safe way in the functional programming language Haskell. We demonstrate their application to constraint-aware hierarchical-relational mappings.