3 ms·
> When they talk about applications to databases it seems quite unrealistic I read a paper that claimed that the category of polynomial-like things ("Poly") wa
by jiggawatts 3y ago
> When they talk about applications to databases it seems quite unrealistic
I read a paper that claimed that the category of polynomial-like things ("Poly") was somehow useful for database migrations! Without a concrete example, that's just an absurd statement to make. If you don't explicitly connect the dots between SQL schemas and polynomials, then you're just hand-waving. It's the equivalent of: "I have a marvellous proof but alas it is too long to fit into this margin."
- solomonb 3y agohere you go: https://arxiv.org/pdf/1009.1166.pdf https://arxiv.org/pdf/1009.1166.pdf
- jiggawatts 3y agoThis paper is actually interesting and talks about real-world schemas. I particularly like the concept of distinguishable nulls that define a sane equality operator, unlike the traditional SQL NULL. The paper I was referring to used the category Poly, and literally just stated that Poly could be used for database migrations without elaborating further.
- matteocapucci 3y agoThat might be a case of the author be really used to a certain crowd and writing for them. The work by Spivak on databases is well-known in ACT so the connection comes pretty easily. Also, in fairness, is pretty easy to Google your way around that claim.
- solomonb 3y agoI don't know the paper you are talking about but the author of this one (David Spivak) does a ton of research on Polynomial Functors and he has a whole book on them: https://topos.site/poly-book.pdf https://topos.site/poly-book.pdf Poly is an incredibly rich category which can be used to describe a ton of stuff such as finite state machines, neural networks, game interactions, wiring diagrams and dynamical systems more generally. I wouldn't be surprised at all if Poly can describe database migrations.
- j2kun 3y ago> can be used to describe a ton of stuff such as One thing that bothers me about applied category theory is that this (being able to describe stuff) always seems to be sufficient for people to claim it is applied. But if the people doing the applying don't find that framing particularly useful, then to me it does not count.
- wisnesky 3y agoWe've used Poly to prove results about functorial data migration.
- solomonb 3y agoHey you might be interested in this work-in-progress type theory for Poly: https://github.com/toposInstitute/polytt https://github.com/toposInstitute/polytt