A Topological Relational Algebra in Lisp

From: Norbert_Paul <norbertpauls_spambin_at_yahoo.com>
Date: Sun, 11 Jan 2015 14:25:28 +0100
Message-ID: <m8ttjd$k1$1_at_dont-email.me>

I would like to draw your attention to

   http://pavel.gik.kit.edu/
which contains a result from a project of former times when I used to work as a researcher.

I am mainly interested in comments from practicioners if they see any potential practical application of my results. I am thinking of databases for geo-information, CAD-data, or, in general, applications that must handle topological data with arbitrary topologies.

A brief description:
During my work I have realized that there is an interesting link between Relational Algebra and Topology (in the mathematical sense):
(1) Every finite topological space has a simple and efficient

     relational representation.
(2) Every Relational Algebra operator has a corresponding topological

     construction. This yields a relationally complete query language
     for topological spaces.

So the idea was to extend the relational model in the following way:

   (i) Given a database table $X$ add a relational representation of

       a topology $T_X$ for $X$ such that the pair $(X,T_X)$ becomes
       a topological space. The records in $X$ constitute the pointset
       and a binary relation $R$ on $X$ represents the topology.
  (ii) Provide a version for each database query operator that takes
       /spaces/ as input and produces result spaces:
       First act as usual on the pointsets.
       Then each result set of such query has a uniquely determined
       result topology, (see http://en.wikipedia.org/wiki/Final_topology
       and http://en.wikipedia.org/wiki/Initial_topology) which yields
       a query result space.

(iii) Do this in Lisp because Lisp is fun.
  (iv) I wanted to use (and extend) CLSQL first but then decided to

       change from SQL (after finding the word "madness" in the
       grammar file of PostgreSQL) to Relational Algebra of which I
       defined a Lispy syntax.

The web-page describes everything in more detail, contains the sources, and has a running instance of the experimental database server. The server is just meant as proof-of-concept and, of course, still far far away from parcatical usefullness.

I am interested in a discussion here, because it seemed that reviewers tended to frown on my (any my co-workers) work because, for example:
(1) The applied mathematics is too challenging for the average

     audience at scientific conferences (that was an actual remark)
(2) Why should we need database systems particularly designed for

     mathematicians?
(3) Arbitrary topological dimension leads to an "combinatorial

     explosion of complexity" (another actual remark. Funny, because
     obviously wrong)

Received on Sun Jan 11 2015 - 14:25:28 CET