Description
Computers do just one thing: they turn data into other data. Yet the data itself — the substance the entire industry exists to handle — rests on convention rather than on any rigorous foundation. This was not inevitable. The field began, in the early 1970s, with a genuine mathematical ambition; the relational model was meant to put data on a sound footing. It half-succeeded, and the half it left undone has shaped, and quietly distorted, almost everything built since.
Data Algebra is about finishing the work that was begun then and set aside.
Its subject is a single mathematical structure, built in four levels — couplets, relations, clans and hordes — into which all data, of every kind and in every context, can be placed, and through which it can be manipulated with precision. The structure is closed and complete. Every operation a database or a file system performs can be expressed within it, composed from it, and reasoned about in it. No shape of data — table, document, graph, key-value pair, hierarchy — falls outside its reach.
What is new in this edition
The first edition, The Algebra of Data, appeared in 2015. It stood as a mathematical proposition with its proofs in order but little yet built upon it. A decade on, that has changed. The algebra has been put to work.
JabrDB now exists: a native algebraic database for macOS that you can install, load with your own data, and watch the algebra operate on real records. Around it has grown a family of related applications and a connectivity architecture intended to carry the algebra out to the data stores the world already runs on. This edition is the theory and the engineering reality together — which is what the subtitle means. JabrDB has relatives, and they descend from the same root.
How the book proceeds
In three movements.
The algebra itself — from its foundations in set theory up through the four levels of the tower, and across the full operator set: composition, transposition, the Boolean operations, superstriction and substriction and their cross variants, natural join, partitions, the diagonal.
The algebra in practice — principally through JabrDB: how a relational row, an RDF triple, a time-stamped reading and a key-value pair turn out to be the same kind of object underneath, and what follows for a database when paradigm becomes a matter of query surface rather than of storage. This movement includes a candid accounting of where SQL went wrong, and why its failings follow from its founding decision not to be an algebra.
The view outward — connectivity, the wider ecosystem, and the long road still ahead: the SDK, the metadata resource, client-server working, and the algebraic connectors.
Who it is for
Database practitioners who have suspected for years that the relational model was only ever an approximation of something deeper. Architects tired of glue code that exists solely to move data between stores that disagree about what data is. Mathematicians curious about an applied algebra with a large claim attached. And developers who would rather read the mathematics and then run it.
No mathematics is assumed beyond a tolerance for precise definitions. The notation is introduced as it is needed.
A large claim, checkable
We make a large claim in these pages — that the algebra of data is the mathematical foundation the field has lacked since its beginning — but we do not ask you to take it on faith. The mathematics is here to be checked, and the software is here to be used.
Details
| Author | Robin Bloor |
| Publisher | Jabr Data Labs |
| Format | Paperback |
| ISBN | 978-1-957278-19-3 |
| LCCN | 2026916765 |
| Price | $18.99 |
The first nine chapters are published free on this site — start there if you would rather read before you buy.
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