nodejs/sequelize/raw/parallel_create_delete_empty_tag.js is an example which experimentally seems to be solved by REAPEATABLE READ, although we are not sure that this is truly the case and why. What is clear is that that example is not solved by the SQL READ COMMITTED isolation level.
In PostgreSQL, this is the first isolation level which can lead to postgreSQL serialization failures, this does not happen to SQL READ COMMITTED isolation level in that DBMS. You then have to retry the transaction.
../../../nodejs/sequelize/raw/parallel_update_worker_threads.js contains a base example that can be used to test what can happen when queries are being run in parallel. But it is broken due to a sqlite3 Node.js package bug: github.com/mapbox/node-sqlite3/issues/1381...
../../../nodejs/sequelize/raw/parallel_update_async.js is an async version of it. It should be just parallel enough to allow observing the same effects.
This is an example of a transaction where the SQL READ COMMITTED isolation level if sufficient.
These examples run queries of type:
UPDATE "MyInt" SET i = i + 1
Sample execution:
node --unhandled-rejections=strict ./parallel_update_async.js p 10 100
which does:
The fear then is that of a classic read-modify-write failure.
But as www.postgresql.org/docs/14/transaction-iso.html page makes very clear, including with an explicit example of type UPDATE accounts SET balance = balance + 100.00 WHERE acctnum = 12345;, that the default isolation level, SQL READ COMMITTED isolation level, already prevents any problems with this, as the update always re-reads selected rows in case they were previously modified.
If the first updater commits, the second updater will ignore the row if the first updater deleted it, otherwise it will attempt to apply its operation to the updated version of the row
Since in PostgreSQL "Read uncommitted" appears to be effectively the same as "Read committed", we won't be able to observe any failures on that database system for this example.
nodejs/sequelize/raw/parallel_create_delete_empty_tag.js contains an example where things can actually blow up in read committed.
This example is similar to nodejs/sequelize/raw/parallel_update_async.js, but now we are doing a separate SELECT, later followed by an update:
  • SELECT FROM to get i
  • update on Js code newI = i + 1
  • UPDATE SET the newI
Although this specific example is useless in itself, as we could just use UPDATE "MyInt" SET i = i + 1 as in nodejs/sequelize/raw/parallel_update_async.js, which automatically solves any concurrency issue, this kind of code could be required for example if the update was a complex function not suitably implemented in SQL, or if the update depends on some external data source.
Sample execution:
node --unhandled-rejections=strict ./parallel_select_and_update.js p 2 10 'READ COMMITTED'
which does:
Another one:
node --unhandled-rejections=strict ./parallel_select_and_update.js p 2 10 'READ COMMITTED' 'FOR UPDATE'
this will run SELECT FOR UPDATE rather than just SELECT
Observed behaviour under different SQL transaction isolation levels:
  • READ COMMITTED: fails. Nothing in this case prevents:
    • thread 1: SELECT, obtains i = 0
    • thread 2: SELECT, obtains i = 0
    • thread 2: newI = 1
    • thread 2: UPDATE i = 1
    • thread 1: newI = 1
    • thread 1: UPDATE i = 1
  • REPEATABLE READ: works. the manual mentions that if multiple concurrent updates would happen, only the first commit succeeds, and the following ones fail and rollback and retry, therefore preventing the loss of an update.
  • READ COMMITTED + SELECT FOR UPDATE: works. And does not do rollbacks, which probably makes it faster. With p 10 100, REPEATABLE READ was about 4.2s and READ COMMITTED + SELECT FOR UPDATE 3.2s on Lenovo ThinkPad P51 (2017).
    SELECT FOR UPDATE should be enough as mentioned at: www.postgresql.org/docs/13/explicit-locking.html#LOCKING-ROWS
    FOR UPDATE causes the rows retrieved by the SELECT statement to be locked as though for update. This prevents them from being locked, modified or deleted by other transactions until the current transaction ends. That is, other transactions that attempt UPDATE, DELETE, SELECT FOR UPDATE, SELECT FOR NO KEY UPDATE, SELECT FOR SHARE or SELECT FOR KEY SHARE of these rows will be blocked until the current transaction ends; conversely, SELECT FOR UPDATE will wait for a concurrent transaction that has run any of those commands on the same row, and will then lock and return the updated row (or no row, if the row was deleted). Within a REPEATABLE READ or SERIALIZABLE transaction, however, an error will be thrown if a row to be locked has changed since the transaction started. For further discussion see Section 13.4.
A non-raw version of this example can be seen at: nodejs/sequelize/parallel_select_and_update.js.
In this example, posts have tags. When a post is deleted, we check to see if there are now any empty tags, and now we want to delete any empty tags that the post deletion may have created.
If we are creating and deleting posts concurrently, a naive implementation might wrongly delete the tags of a newly created post.
This could be due to a concurrency issue of the following types.
Failure case 1:
  • thread 2: delete old post
  • thread 2: find all tags with 0 posts. Finds tag0 from the deleted old post which is now empty.
  • thread 1: create new post, which we want to have tag tag0
  • thread 1: try to create a new tag tag0, but don't because it already exists, this is done using SQLite's INSERT OR IGNORE INTO or PostgreSQL's INSERT ... ON CONFLICT DO NOTHING
  • thread 1: assign tag0 to the new post by adding an entry to the join table
  • thread 2: delete all tags with 0 posts. It still sees from its previous search that tag0 is empty, and deletes it, which then cascades into the join table
which would result in the new post incorrectly not having the tag0.
Failure case 2:
  • thread 2: delete old post
  • thread 2: find all tags with 0 posts
  • thread 1: create new post
  • thread 1: try to create a new tag tag0, but don't because it already exists
  • thread 2: delete all tags with 0 posts. It still sees from its previous search that tag0 is empty, and deletes it
  • thread 1: assign tag0 to the new post
which leads to a foreign key failure, because the tag does not exist anymore when the assignment happens.
Failure case 3:
  • thread 2: delete old post
  • thread 1: create new post, which we want to have tag tag0
  • thread 1: try to create a new tag tag0, and succeed because it wasn't present
  • thread 2: find all tags with 0 posts, finds the tag that was just created
  • thread 2: delete all tags with 0 posts, deleting the new tag
  • thread 1: assign tag0 to the new post
which leads to a foreign key failure, because the tag does not exist anymore when the assignment happens.
Sample executions:
  • node --unhandled-rejections=strict ./parallel_create_delete_empty_tag.js p 9 1000 'READ COMMITTED': PostgreSQL, 9 tags, DELETE/CREATE the tag0 test tag 1000 times, use READ COMMITTED
    Execution often fails, although not always. The failure is always:
    error: insert or update on table "PostTag" violates foreign key constraint "PostTag_tagId_fkey"
    because the:
    INSERT INTO "PostTag"
    tries to insert a tag that was deleted in the other thread, as it didn't have any corresponding posts, so this is the foreign key failure.
    TODO: we've never managed to observe the failure case in which tag0 is deleted. Is it truly possible? And if not, by which guarantee?
  • node --unhandled-rejections=strict ./parallel_create_delete_empty_tag.js p 9 1000 'READ COMMITTED' 'FOR UPDATE': do a SELECT ... FOR UPDATE before trying to INSERT.
    This is likely correct and the fastest correct method according to our quick benchmarking, about 20% faster than REPEATABLE READ.
    We are just now 100% sure it is corret becase we can't find out if the SELECT in the DELETE subquery could first select some rows, which are then locked by the tag creator, and only then locked by DELETE after selection. Or does it re-evaludate the SELECT even though it is in a subquery?
  • node --unhandled-rejections=strict ./parallel_create_delete_empty_tag.js p 9 1000 'REPEATABLE READ': repeatable read
    We've never observed any failures with this level. This should likely fix the foreign key issue according to the PostgreSQL docs, since:
    • the DELETE "Post" commit cannot start to be seen only in the middle of the thread 1 transaction
    • and then if DELETE happened, the thread 1 transaction will detect it, ROLLBACK, and re-run. TODO how does it detect the need rollback? Is it because of the foreign key? It is very hard to be sure about this kind of thing, just can't find the information. Related: postgreSQL serialization failure.
  • node --unhandled-rejections=strict ./parallel_create_delete_empty_tag.js p 9 1000 'SERIALIZABLE': serializable
  • node --unhandled-rejections=strict ./parallel_create_delete_empty_tag.js p 9 1000 'NONE': magic value, don't use any transaction. Can blow up of course, since even less restrictions than READ COMMITTED
All executions use 2 threads.
Some theoretical notes:
  • Failure case 3 is averted by a READ COMMITTED transaction, because thread 2 won't see the uncommitted tag that thread 1 created, and therefore won't be able to delete it
stackoverflow.com/questions/10935850/when-to-use-select-for-update from SELECT FOR UPDATE also talks about a similar example, and has relevant answers.
ROW_NUMBER by Ciro Santilli 37 Updated 2025-07-16
sqlite3 ':memory:'  'WITH t (i) AS (VALUES (-1), (-1), (-2)) SELECT *, row_number() over () FROM t'
Possible output:
-1|1
-1|2
-2|3
Gives them unique IDs.
With a partition by:
sqlite3 ':memory:'  'WITH t (i) AS (VALUES (-1), (-1), (-2)) SELECT *, row_number() over ( partition by i ) FROM t'
possible output:
-2|1
-1|1
-1|2
SQL window RANGE by Ciro Santilli 37 Updated 2025-07-16
rm -f tmp.sqlite
sqlite3 tmp.sqlite "create table t (id integer, val integer)"
sqlite3 tmp.sqlite <<EOF
insert into t values
  (0, 0),
  (1, 5),
  (2, 10),
  (3, 14),
  (4, 15),
  (5, 16),
  (6, 20),
  (7, 25),
  (8, 29),
  (9, 30),
  (10, 30),
  (11, 31),
  (12, 35),
  (13, 40)
EOF
Show how many neighbours each column has with val between val - 2 and val + 2 inclusive:
sqlite3 tmp.sqlite <<EOF
SELECT id, val, COUNT(*) OVER (
  ORDER BY val RANGE BETWEEN 2 PRECEDING AND 2 FOLLOWING
) FROM t;
EOF
Output:
0|0|1
1|5|1
2|10|1
3|14|3
4|15|3
5|16|3
6|20|1
7|25|1
8|29|4
9|30|4
10|30|4
11|31|4
12|35|1
13|40|1
val - 1 and val + 1 inclusive instead:
sqlite3 tmp.sqlite <<EOF
SELECT id, val, COUNT(*) OVER (
  ORDER BY val RANGE BETWEEN 1 PRECEDING AND 1 FOLLOWING
) FROM t;
EOF
Output:
0|0|1
1|5|1
2|10|1
3|14|2
4|15|3
5|16|2
6|20|1
7|25|1
8|29|3
9|30|4
10|30|4
11|31|3
12|35|1
13|40|1
There seems to be no analogue to HAVING for window functions, so we can just settle for a subquery for once, e.g.:
sqlite3 tmp.sqlite <<EOF
SELECT * FROM (
  SELECT id, val, COUNT(*) OVER (
    ORDER BY val RANGE BETWEEN 1 PRECEDING AND 1 FOLLOWING
  ) as c FROM t
) WHERE c > 2
EOF
which outputs:
4|15|3
8|29|3
9|30|4
10|30|4
11|31|3
SQL contiguous ranges by Ciro Santilli 37 Updated 2025-07-16
stackoverflow.com/questions/17046204/how-to-find-the-boundaries-of-groups-of-contiguous-sequential-numbers/17046749#17046749 just works, even in SQLite which supports all quoting types known to man including [] for compatibility with insane RDBMSs!
Here's a slightly saner version:
rm -f tmp.sqlite
sqlite3 tmp.sqlite "create table mytable (id integer primary key autoincrement, number integer, status integer)"
sqlite3 tmp.sqlite <<EOF
insert into mytable(number, status) values
  (100,0),
  (101,0),
  (102,0),
  (103,0),
  (104,1),
  (105,1),
  (106,0),
  (107,0),
  (1014,0),
  (1015,0),
  (1016,1),
  (1017,0)
EOF
sqlite3 tmp.sqlite <<EOF
SELECT
  MIN(id) AS "id",
  MIN(number) AS "from",
  MAX(number) AS "to"
FROM (
  SELECT ROW_NUMBER() OVER (ORDER BY number) - number AS grp, id, number
  FROM mytable
  WHERE status = 0
)
GROUP BY grp
ORDER BY MIN(number)
EOF
output:
1|100|103
7|106|107
9|1014|1015
12|1017|1017
To get only groups of length greater than 1:
sqlite3 tmp.sqlite <<EOF
SELECT "id", "from", "to", "to" - "from" + 1 as "len" FROM (
  SELECT
    MIN("id") AS "id",
    MIN(number) AS "from",
    MAX(number) AS "to"
  FROM (
    SELECT ROW_NUMBER() OVER (ORDER BY "number") - "number" AS "grp", "id", "number"
    FROM "mytable"
    WHERE "status" = 0
  )
  GROUP BY "grp"
  ORDER BY MIN("number")
) WHERE "len" > 1
EOF
Output:
1|100|103|4
7|106|107|2
9|1014|1015|2
Hamilton's equations by Ciro Santilli 37 Updated 2025-07-16
Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:
So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.
This means that e.g. if you do an UPDATE query on multiple rows, and power goes out half way, either all update, or none update.
This is different from isolation, which considers instead what can or cannot happen when multiple queries are running in parallel.
Determines what can or cannot happen when multiple queries are running in parallel.
See Section "SQL transaction isolation level" for the most common context under which this is discussed: SQL.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact