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Alex Nelson

@pqnelson

Mathematician, software engineer. Obsessed with everything about proof assistants. AMS Subject Class.: 68V15, 68V20, 20Exx.

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20.08.2024
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Latest posts by Alex Nelson @pqnelson

We don’t talk enough about how morally depraved the tech industry turned out to be. Every single ounce of their self-regarding statements of values was an outright lie.

07.03.2026 05:03 πŸ‘ 5435 πŸ” 1158 πŸ’¬ 122 πŸ“Œ 91

Erm, I'm sorry I tried to help answer your question about solving the Einstein field equations...

07.03.2026 19:48 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

I've noticed that people who heavily use AI are way more fragile on the internet (like, when saying, "Hey, you should try working out the following calculation: ..." they interpret it as an "ad hominem").

Weirder, they overreact and start attacking you way more personally.

Just enshittification...

07.03.2026 19:47 πŸ‘ 2 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0
trolley problem diagram, with Sisyhpus pushing his boulder as the trolley car, and text that reads:

Sisyphus is rolling a boluder towards the Grand Hilbert Hotel. The hotel has an infinite number of rooms, but they are all full, so they may not be able to accomodate him or his boulder.

If you choose to divert him, his boulder will destroy the Ship of Theseus.  But the ship has had all of its constituent parts replaced, so it may not actually be the same ship.

Is Sisyphus happy?

trolley problem diagram, with Sisyhpus pushing his boulder as the trolley car, and text that reads: Sisyphus is rolling a boluder towards the Grand Hilbert Hotel. The hotel has an infinite number of rooms, but they are all full, so they may not be able to accomodate him or his boulder. If you choose to divert him, his boulder will destroy the Ship of Theseus. But the ship has had all of its constituent parts replaced, so it may not actually be the same ship. Is Sisyphus happy?

a question for the ages, really.

06.03.2026 07:04 πŸ‘ 342 πŸ” 101 πŸ’¬ 12 πŸ“Œ 6

I don't know why it's so hard for the Democrats to say something like this. Instead they hem and haw, and end up supporting Trump accidentally πŸ™„

02.03.2026 14:35 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

My Mom bought some coffee from some website, and they sent the wrong coffee.

She tried to complain, but the website has an AI customer feedback system which literally cannot register there was a problem.

Welcome to the future.

27.02.2026 00:42 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Is that...Gollum? "Come see my PRECIOUS...bathroom fixtures."

18.02.2026 14:49 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0
Post image

TOON TUESDAY
#ToonTuesday

17.02.2026 17:21 πŸ‘ 1273 πŸ” 377 πŸ’¬ 0 πŸ“Œ 22
Preview
Infinite-Dimensional Lie Groups This is a preliminary version of a book on infinite-dimensional Lie groups. It covers the basics of calculus and manifolds in the context of locally convex spaces, based on Bastiani's notion of a smoo...

Read later (a ~1026 page manuscript)...

arxiv.org/abs/2602.12362

17.02.2026 21:44 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0
Preview
Hilbert's Program and Infinity The primary aim of Hilbert's proof theory was to establish the consistency of classical mathematics using finitary means only. Hilbert's strategy for doing this was to eliminate the infinite (in the f...

Read later

arxiv.org/abs/2602.12131

13.02.2026 14:39 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

I'm hardly the first person to note this, but it's enormously instructive that our President and his followers saw the message "THE ONLY THING MORE POWERFUL THAN HATE IS LOVE" and understood it, correctly, as an attack on them

09.02.2026 02:11 πŸ‘ 25099 πŸ” 5884 πŸ’¬ 104 πŸ“Œ 50

Some people are asking what I want Schumer to do. He should be screaming over medical care and access to facilities. He should be going to detention facilities himself and putting his body on the line, as he did at the border in 2019. He should lean into stories about New Yorkers in detention. [1/4]

04.02.2026 14:25 πŸ‘ 2760 πŸ” 792 πŸ’¬ 54 πŸ“Œ 92

I just wish there were an "Algebraic Geometry for Differential Geometers" book out there :(

31.01.2026 20:59 πŸ‘ 1 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Edward Gibbon was far better with this type of juxtaposition, specifically to maximize irony. But I guess we can't all be a Gibbon...

29.01.2026 01:01 πŸ‘ 1 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

I wish people would use commas.

For example: "While tropical countries will bear the brunt[,] cooler regions will also need to adapt."

You need that comma inserted for the sentence to make grammatical sense.

USE COMMAS, GOSH DARNIT.

27.01.2026 01:05 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

But I don't think I will adequately get a chance to do this for about a month, because my sister and her husband are visiting until the end of February.

24.01.2026 23:49 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

I was thinking about writing a post about the desired qualities ("desiderata") and design choices necessary when implementing a literate programming tool...especially since implementing a proof assistant *as* a literate program requires special concerns.

24.01.2026 23:49 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

Perhaps I should write a meta-"literate program" to document the successes and failures of these explorations?

But to have found me on Bluesky, which is no small task, so I guess someone must be interested in what I have to say about it.

22.01.2026 19:30 πŸ‘ 1 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Ah, well, currently I am working my way through bootstrapping a literate programming toolkit. I feel the Markdown prototype was...inadequate for my needs.

Now that I am thinking about it, I suppose I am experimenting with several prototypes...

22.01.2026 19:30 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

If you are serious about literate programming, I would still recommend building a Pandoc filter: you will save yourself a boat load of trouble.

Trouble is my business, so I'm still bootstrapping a literate toolkit in Standard ML to study implementing proof assistants.

What piqued your interest?

22.01.2026 01:04 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

I'm still working on it (I realized too late that Markdown was inadequate for my purposes because I wanted to state theorems, and that forced *me* to *manually* write the theorem numbers and italicize the theorem statement).

I have a version of the Markdown locally, somewhere...

22.01.2026 01:00 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

Every "Let's build an LSP server" starts off simple, then ends up with extraordinarily convoluted data structures by step 3 🫣

22.01.2026 00:58 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

You know...from that land...from the land of the ice and snow from the midnight sun where the hot springs flow...

21.01.2026 14:50 πŸ‘ 1 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Concurrent POSIX file system operations has been verified in TaDa

www.doc.ic.ac.uk/~pg/publicat...

20.01.2026 20:33 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0
Preview
Executable formal semantics for the POSIX shell The POSIX shell is a widely deployed, powerful tool for managing computer systems. The shell is the expert's control panel, a necessary tool for configuring, compiling, installing, maintaining, and de...

The POSIX shell semantics has been formalized in Lem (which extracts to Coq/Rocq and Isabelle/HOL and other proof assistants).

arxiv.org/abs/1907.05308

20.01.2026 20:33 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

UNIX Path resolution has been formalized in Why3

inria.hal.science/hal-01406848...

20.01.2026 20:33 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

How much of POSIX has been formalized in a proof assistant? I know of a bunch of scattered results, but they seem to be independent disjoint efforts...

And since POSIX is a multi-volume specification, I wouldn't be surprised I don't cover everything here in one thread.

20.01.2026 20:33 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0

After writing a POSIX-compliant shell script, then rewriting as a literate program using Noweb, I realize I might need to use an honest programming language like Standard ML to actually implement the desired program πŸ˜…

18.01.2026 20:08 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Since it's under the 35^4 ~ 1.5e6 threshold, that's the critical thing. I'd only need to pause and re-evaluate things if there were, say, 1.5e5 such identifiers.

18.01.2026 19:57 πŸ‘ 0 πŸ” 0 πŸ’¬ 0 πŸ“Œ 0

Things reduce a little (you get 10,385 at the top-level directory, and 44,969 in subdirectories).

I'm just trying to get a feel for things (specifically if something like Stacks tags could be used for literate programming proof assistants), so over-estimating is better than under-estimating.

18.01.2026 19:57 πŸ‘ 0 πŸ” 0 πŸ’¬ 1 πŸ“Œ 0