Functorial Data Migration

In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three "data migration functors", which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language. We begin the paper with a multitude of examples to motivate the definitions, and near the end we provide a dictionary whereby one can translate database concepts into category-theoretic concepts and vice-versa.Comment: 30 page

The Prefix of Prefixes: Francis Ponge's 'Le Pre' and La Fabrique du 'Pre'

1996-01-01

An Algorithm for Clustered Data Generalized Additive Modelling with S-PLUS

We present a set of functions in S-PLUS to implement the clustered data generalized additive marginal modelling (CDGAM) strategy proposed by Berhane and Tibshirani (1998). A variety of working correlation structures are supported, and the regression basis may include components from the family of smoothing splines.