Algebraic data integration

In this paper we present the first truly practical formalism for querying and integrating data using the functorial data model. In our formalism, database schemas and instances are multi-sorted equational theories of a certain form. Schemas denote categories, and instances denote their initial (term) algebras. The instances on a schema S form a category, S–Inst, and a morphism of schemas F : S→ T induces three adjoint data migration functors: ΣF : S–Inst→ T –Inst, defined by substitution along F , which has a right adjoint ∆F : T –Inst→ S–Inst, which in turn has a right adjoint ΠF : S–Inst→ T –Inst. We present a query language based on for/where/return syntax where each query denotes a sequence of data migration functors, a pushout-based design pattern for performing data integration using our formalism, and describe the implementation of the formalism in a tool we call FQL.