arXiv:1212.5303cs.DB
Relational Foundations For Functorial Data Migration
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Abstract
We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst. A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $Σ_F:S$-inst$\to T$-inst, $Π_F: S$-inst $\to T$-inst, and $Δ_F:T$-inst $\to S$-inst. We present an algebraic query language FQL based on these functors, prove that FQL is closed under composition, prove that FQL can be implemented with the select-project-product-union relational algebra (SPCU) extended with a key-generation operation, and prove that SPCU can be implemented with FQL.
Here you go. It's easy with a bit of Category Theory. Just implement something along the lines of David Spivak's "On The Relational Foundations Of Functorial Data Migration". http://arxiv.org/abs/1212.5303 Original motivation, from v1 of the paper: I asked whether the difficulty…
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