CQL: Categorical Databases
categoricaldata.net
categoricaldata.net
What Category Theory Teaches Us About DataFrames https://mchav.github.io/what-category-theory-teaches-us-abou...
Discussed on HN at (67 comments)
The same could be said for SQL. How does CQL differ from SQL? If I squint my eyes just a tiny amount, these ideas become really difficult to separate. I was always under the impression that the relational model is based upon many concepts studied in category theory. To my mind, all of the following things are overlapping parts of the exact same monster:
Set theory
Category theory
Graph theory
Type theory
Discrete mathematics
Relational algebra
Relational calculus
Relational modeling
An actual sql schemaSQL is like Java, CQL is like Haskell. SQL has been around and used in production. CQL is a research language, possibly cleaner foundation but YMMV.
The math fields you list are connected, but whether they are the same monster - again it's kinda like claiming all programming languages and implementations are the same (Turing-complete?) monster.
Most of SQL is not imperative, but it certainly also includes some imperative commands.
Inserting a new row into an existing table is an imperative command, which may be the most frequently used of the SQL features, in certain applications concerned with recording transactions.
Only the subset of SQL that is used for queries can be said to not be an imperative programming language.
Imperative SQL is the procedural elements that mostly do not exist at the standard level. Variables, control flow, and cursors.
I always thought this was splitting hairs.
C#,C++, Java seems imperative. You are in control? But you aren't really telling it how to move values between registers, the compiler is making a million decisions for you on how the computer will execute that 'imperative' code. Just like SQL isn't really telling the DB how to do it either..
Contrast that if I create a class/object/field structure/hierarchy in Java, or put a HashMap somewhere with a certain set of keys, I've written something in stone which requires significant refactoring if the data needs to be accessed from a different direction.
What you're really talking about is one of the things Codd wanted to emphasize: representational independence. Which actually was the primary thrust of his famous paper: the user should not need to know how the data is stored in order to use or manipulate it.
The other thing that people are talking about with "declarative" is probably another level up in abstraction. Talking about the business logic or problem in terms that are closer to logic than a sequence of instructions, and then letting the machine sort out what those steps are.
Consider in a Datalog users don't customarily perform DDL type operations; they declare data rules and the system decides the form of the underlying relations. That's a small step up the declarative ladder from SQL, even if it's somewhat analogous to "create view".
So I think there's a blurry definitional line between the two. But I don't think your very blunt "No." is doing much to help clear that up?
printf("Hello world!");
Anyone who claims that an SQL command like insert a row, create a table or destroy a table is not imperative, is just plainly wrong.
Even in real life, when humans communicate commands to each other, from where the term "imperative" comes, the commands normally do not tell anything to the recipient about how to accomplish the order, they just name the action, because it is supposed that whoever receives the command knows how to do it.
After programming languages were invented there was a clear partition between commands a.k.a. imperative statements, expressions and definitions a.k.a. declarations ("definition" and "declaration" were originally synonymous terms, "declaration" being the ALGOL 60 term and "definition" being the CPL term; the use of the 2 words with different meanings, like in C, where it is required by a defect of the compiler, which needs additional declarations besides a definition, is only recent.)
Later the meanings of these terms have become muddled by their careless use by many authors, which usually had political reasons, i.e. because they somehow considered the words "imperative" or "command" as shameful, they attempted to present their pet languages as purely functional or purely declarative, so they twisted the words in various ways, despite the fact that any practical program must contain imperative parts, not only functional or declarative parts.
No. That's more to do with imperative vs functional programming, which is a subset of declarative, but even then you can't simply say "I changed state so it's imperative." That's a drastic oversimplification. That's like saying Haskell can't write to a file, which is plainly false. Declarative (functional) can absolutely change the state of the system. It just doesn't let you do it except by calling fixed commands, which is exactly what `INSERT` is.
When we're talking about imperative vs declarative, state can still be manipulated in both, but it's abstracted away with declarative programming. Like, a `filter()` or a `map()` transform in JavaScript is declarative programming, even in an otherwise imperative language. That's why it returns a new object with an updated state.
Compilers are free to rearrange these accesses if the final result is same as if executed by these ordered microtransactions.
Consider loop fusion, loop splitting and/or loop skewing.
This necessitates some state, most probably, persisted one. Hence, imperativeness.
Full disclosure: I am one of the co-authors of this paper and an associated patch implenting it in PostgreSQL that we have proposed.
I am happy to see more people than us think this is useful.
Most attempts to replace/improve SQL derive from the fact SQL was a poorly conceived and designed interface, that originally was meant to be a very small DSL for end users, but unfortunately, was allowed to become a poor, complicated, confusing mess for app developers:
https://cacm.acm.org/research/50-years-of-queries/
SQL is not an orthogonal language... This is because, in the early days, Ray Boyce and I did not think we were designing a language for programmers. ..
As it turned out, Ray and I were wrong about the predominant usage of SQL...
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So the #1 thing any actual replacement or alternative to SQL is how actually become a good language for development, so it is actually composable, can be actually be used to reason about it, has minimal foot guns, etc.
There is a lot of misunderstanding and pushback, similar to how people in the past fight improvements over JS/C/C++ until typescript, rust comes.
But, oh boy, SQL need their typescript!
(edit: in retrospect, this is just the "getting started" header link, despite the URL)
Unfortunately none that I've followed seems to do much to describe much of anything except the math foundations. They might cover pieces of syntax, but not how to use or think about them, and they seem to be rather excited about the data-generating features that I can't imagine anyone using outside tech demos (unless that's the only insert method? what about update?) :/
(edit 2: you can't even rely on the manual apparently, I'm fairly confident https://categoricaldata.net/help/Demo.html (manual -> examples -> demo) won't work because it has no schema definition for `Animal`. and it like all the others I've checked are little more than syntax and output, no real explanation)
As best as I can tell (but i really dont know much about databases) it's probably a narrow advantage - storage and everyday queries still go to Codd's model - but for stitching schemas together it seems like it could work.
I'm using similar math for automated formal verification, where this approach is what makes it tractable.
Man, it's a rough environment right now marketing-wise. I don't know if they're contractually obligated to say the funny magic words, but the term AI is nearly entirely meaningless at this point. Akin to saying "behold my mighty calculator app: it prevents divisions by zero through artificial intelligence!"
Maybe that's my bias since that's what I'm working on, but it's a big benefit to have stronger compiler guarantees of correctness so that an LLM can't screw things up as much. No BSing that it works when the compiler requires proof.
AI agents fielded by major AI players still fail at the basic task of providing immediate and correct support for use of the current versions of their products. If a programming language is too new to have adequate representation in the training corpus, there isn't an accepted standard way to provide a reference manual targeting AI agents. Even the best way to include documentation in a large project so new AI agents can take over is controversial. A pile of linked markdown files really isn't an answer, less structured than a codebase itself, that AI is good at navigating.
Other HN posts have discussed using SQL as a backbone for the AI "mind mapping" support we need for AI more critically than for ourselves.
I was hoping that CQL could be an answer to this. Perhaps, but not its current primary goal.
1. Easier modelling sum types (inheritance) due to duality.
2. Better handling of null due to labelled null.
3. Better foundation of elementary types (they're just another table ids). (Column stores often do that already, if your question is about storage.)
A general relation exists only between the columns of a table that are included in a multi-column primary key.
All columns that are not part of the primary key are functions of the primary key.
Most tables used in practice use a single column as the primary key, which is frequently just a number or a UUID. Most databases contain only tables that are functions, without any table that contains general relations.
The most frequently used kinds of joins are just function compositions.
The most frequently used kind of join is a general relation.
[1] https://github.com/agirish/tpcds/blob/master/query1.sql
Query 1 from TPC-DS creates a multi-column relation by using GROUP BY. Which relation is then partially constrained by different columns from different tables.
That is quite a claim. I will argue that Categorical Databases most definitely haven't. Any areas where it is true?
The difference is more in theory than in practice.