In this paper, we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (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: Σ _F : S – Inst → T – Inst , defined by substitution along F , which has a right adjoint Δ _F : T – Inst → S – Inst , which in turn has a right adjoint Π _F : 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 our formalism in a tool we call AQL (Algebraic Query Language).

The goal of this paper is to illustrate the use of category theory (CT) as a basis for the integration of manufacturing service databases. In this paper, we use as our reference prior work by Kulvatunyou et al. (2013, “An Analysis of OWL-Based Semantic Mediation Approaches to Enhance Manufacturing Service Capability Models,” Int. J. Comput. Integr. Manuf., 27(9), pp. 803–823) on the use of web ontology language (OWL)-based semantic web tools to study the integration of different manufacturing service capability (MSC) databases using a generic-model approach that they propose in their paper. We approach the same task using a different set of tools, specifically CT and FQL, a functorial query language based on categorical mathematics. This work demonstrates the potential utility of category-theoretic information management tools and illustrates some advantages of categorical techniques for the integration and evolution of databases. We conclude by making the case that a category-theoretic approach can provide a more flexible and robust approach to integration of existing and evolving information.

We survey the field of model management and describe a new model management approach based on algebraic specification.

We describe an alternative solution to the impedance-mismatch problem between programming and query languages: rather than embed queries in a programming language, as done in LINQ systems, we embed programs in a query language, and dub the result QINL.