Intriguing. The Sudoku puzzle in your last Oracle link from 2009 is exactly the same puzzle used in the SQLite example, doing the same thing.

A prerequisite to understanding is knowing the CTE syntax ("WITH"). That's just a group of SQL queries that can refer to one another. It's extremely useful for making modular SQL queries and has nothing to do with recursion.

Then when you use "WITH RECURSIVE", the queries can now refer back to themselves. This is just a for loop over a queue of SQL results, conceptually. The part before the UNION ALL fills the queue to start, and the part after the UNION ALL runs once for each result in the queue, adding all results back into the queue.

If you understand this, then you can understand the Sudoku or Mandelbrot examples (definitely don't start with trying to understand these two though). For example, the Sudoku example contains one recursive query, "x(s, ind)". As explained on the page, "s" is the puzzle (unsolved spaces shown as ".") and "ind" is the index of the first unsolved space (or 0 for a solved puzzle). It creates an unsolved puzzle in the initial setup. The for loop body finds all valid values for the first unsolved space, and the next index to solve; then puts all these results into the queue. The final (non-recursive) SELECT in the CTE looks over all results in the queue, and returns the one where the index is 0 (the solved puzzles).

SQL recursive queries are just loops. The CTE is a UNION or UNION ALL query (well, never use UNION ALL unless you really want to loop infinitely!) where one side is the query that seeds the CTE and the other is executed and its outputs added to the CTE, and the last part is repeated until the CTE stops growing. There's just one more detail: the "recursive" side of the UNION query needs to do a JOIN to the CTE itself (thus the "recursion"), but this doesn't change the loop nature of the thing.

That's it. It's just a simple loop.

(Yes, recursion is looping. But in this case it's very clear that a stack is not needed, that the recursion is "tail recursion" if know what that is.)

The hard part lies in getting the JOIN in the "recursive" side of the UNION query right. Here's a transitive closure query:

  WITH RECURSIVE closure AS (
    SELECT parent, child FROM relationships
    UNION
    SELECT c.parent AS ancestor, r.child AS descendant
    FROM closure c
    JOIN relationships r ON c.child = r.parent
  )
  SELECT * FROM closure;

An crucial point for me was realizing that "recursive CTEs" are not really recursive but better understood as iterative, in other words a loop. The results of each iteration are fed into the next iteration, until no new result is produced.

“Thinking in sql” is hard because it’s an awkward syntax for the (much simpler) relational algebra.

Learn to think in terms of the relational algebra, and how to translate that to/from SQL, and it starts making sense.

I highly recommend the O'Reilly SQL Pocket Guide (https://www.oreilly.com/library/view/sql-pocket-guide/978149...). Its explanation of CTEs is fantastic, and it does a great job on many other parts of SQL, and it's a short and sweet book you could read in a few hours. And it will server as a reference long after you first absorb it.

Some things that helped me

Every query response in SQL is a rectangular matrix [1]. JOINs add columns sideways. UNIONs add rows vertically[2].

[1] Which is why tree shaped data is awkward to query in SQL in one round-trip.

[2] From this you realize why the column names have to match to apply a UNION, and why recursion is something to do with a UNION.

It's unusual and not a commonly needed tool in SQL. I always need a quick refresher on how to write these after a longer break

For "ordinary" working programmers (some denominator of reasonably common knowledge across the industry without any specific skills that help with CTEs in particular), there are a couple mental models I find helpful:

1. Recursion and iteration are duals of each other. Anywhere a "recursive" CTE is a good tool for the job, there exists a natural for-loop or while-loop you would write in an ordinary programming language to solve the same job. Figure out what that looks like, and then you can translate it to SQL. Optimizing further often isn't necessary. The general form isn't terrible (ellipses hide the extra columns you'd have to manually include in most SQL dialects):

  WITH RECURSIVE t(n, ...) AS (
      SELECT 1 as n, * from base_case
    UNION ALL
      SELECT n+1, f(...) FROM t WHERE not_terminated(n, ...)
  )
  SELECT something_interesting(...) FROM t

2. There exists a concept of "equality saturation" that's exceptionally powerful in a number of domains. Everything in (1) is familiar to an ordinary working programmer, but the database's mental model of a recursive CTE is

  while (not_done(working_set)) {
    working_set.extend(process(working_set));
  }

2a. For each partial potential solution

2b. For all the ways in which the potential solution is viable

2c. Expand into all those new potentialities

2 (continued 1). That ability to describe a monotonically increasing set of things which finitely approaches a boundary is powerful in math, powerful in search, powerful in optimization (the Rust EGG crate (e-graphs good) has reasonable documentation for one particular concrete way in which that idea could manifest, if such concreteness helps you learn -- whether you know/like Rust or not), and so on. Gradient descent is just expanding your information till you don't have much more to learn. Optimizing a program is just expanding the set of optimization-based re-writes till you don't have any more re-writes (and pick the best one). Parsing a document is just adding to the things you know about it till no parsing rules can glean any more information. Since that thinking modality is how the database treats your query, you'll usually have better optimized queries if you can naturally formulate your problem in that language (as opposed to the naive iterative solution I proposed in (1)). Not all problems can be thus phrased, but if you're doing a lot of work in your database with recursive CTEs, it's a good idea to spend a week or three hammering home.

3. Combining (1) and (2) a bit, your database will usually have a cost somewhere around O(all_the_rows_you_produce) when evaluating recursive CTEs. These tasks only get hard when performance is a problem and you have to figure out how to take the naive ideas from (1) and transform them into the expected model of (2) in a way that actually reduces unnecessary work. For the sudoku example, you can do that by adding a bit more internal state to transform the breadth-first-search I described into a depth-first-search (making the solution _more_ iterative, interestingly; the "natural" solution is very slow comparatively), but in general you might have to get very creative or might not actually have a reasonable solution available.

I would also love to take that class!

Sign me up for this class too!

It's just going to be practice, recursion in general is annoying to think about. Start simple, have a loop you want to write instead of a recursive thing, write it step by step instead of trying to do it all at once.

I was implementing newton raphson a few years ago in SQL (so as not to implement it as a straight loop) and iterating over the problem several times really helped.

Get a query. Now think of the next step in the iteration, and you're basically writing a query that connects to that. And now, it runs again and again based on the previous criteria.

If you can isolate each part of the query for each logical step you're going to have a much simpler problem to mentally solve.

12 years ago I wrote a recursive CTE which aggregated a bunch of accounting journal entries from pretty big SAP extracts with intermediate account also needing to be calculated in a way that rolled up to company-level values, with some tagging/indexing in the process. I remember only being able to finish the query after some kind anon helped me in an IRC channel at 4am on a weeknight... to this day I'm immensely grateful to them

I made it into a neat little Django portal with configurable permissions, interactive charts for the data, filtering, etc.

It became a ~10-min async celery task running in the background from what previously used to take the company weeks to create that report in an error prone way with macros written by someone long gone / in another department. I'm still pretty proud of that app even though it never got implemented. I got promoted, moved to a different department and don't think it ever saw the light of day, but I do have the code laying around somewhere

Years ago I came across a Knapsack problem solution written in Oracle SQL, that I adapted to Daily Fantasy Golf.

Here's the source: https://aprogrammerwrites.eu/?p=878

Cheers

Last time it was useful I re-implemented XIRR(https://support.microsoft.com/en-us/office/xirr-function-de1...) using Excel's approach in pure SQL so it would be able to make the finance bros happy, it was something like 50,000x faster than the user defined function/loop approach.

"Something more self-serve" is essentially what graph databases provide.

If you don't have the time to use one of those or build your own (and you probably shouldn't) sort of thing on top of SQL, then you can instead define a bunch of VIEWs using recursive queries and GROUP BY and aggregation functions to provide something simple for your users to query.

If you do want to build something more general purpose... If you begin by modeling your schema in something other than SQL DDLs (like with an AST) and then model FKs as bi-directional relationships (because they are), and if you add a way to group those relationships, and further provide a way to define a subset of like columns from all the tables in a graph defined by a group of those relationships, then suddenly you can also come up with a simple(ish) language for expressing [sub-]graphs that you want to fetch. And there's your ad-hoc query language for dealing with recursive graphs in your relational data.

> can CTE's be used to make time series range queries easier / more performant?

On their own, I'd guess likely not a lot. If a view would help, a CTE will help similarly without needing the external structure, if a correlated subquery would help, then yes similarly, especially if the pattern is repeated in the overall query.

In conjunction with other things (good indexing, materialised sequences ("numbers" tables), etc.), is guess yes.

Though you need to be much more specific about your data and the queries in question before I can do better than these vague guesses.

No. They are a query syntax, they don't change the storage or retrieval performance.

nothing really helps with potato slow Android device / storage media. CTE is not magic sauce that will make sqlite go faster.

Depending on the recursion pattern and the overhead of your sqlite driver, it can be faster to do many ID lookups then try to cram it all into one mega CTE query.

https://www.sqlite.org/np1queryprob.html

source: we have the CTE for loading page data in the notion Android app, and the network regularly beats disk on lower end Android devices using whichever query we pick.

storing the tree as an MPTT/NestedSet would massively simplify this, without any subquery shenanigans.

https://en.m.wikipedia.org/wiki/Nested_set_model

https://imrannazar.com/articles/modified-preorder-tree-trave...

Can you give an example of a query you find offensive, and how you'd format it better?