Brent Yorgey

Associate professor of CS at Hendrix College in Conway, AR. Open-source Haskell development, education, competitive programming, type theory, category theory, combinatorics, etc.

Homepage: http://ozark.hendrix.edu/~yorgey/
Blog: https://byorgey.github.io/blog/

Last Notes

2026-06-25 16:11:44 GMT

- reply

Yes, I think so.

2026-06-25 15:52:00 GMT

- reply

Did you see my example from elsewhere in the thread of multisets that allow infinite multiplicity? In that case the star of a multiset is the multiset with the same elements, with each having infinite multiplicity, NOT the multiset with infinite copies of everything.

2026-06-24 22:28:50 GMT

Suppose we have a monoid M with a "star" operation * : M -> M satisfying a* = aa*. I'm not sure if there are other laws we might also want (e.g. perhaps we also want a* = a*a), but the idea is that a* is supposed to represent "combining a with itself infinitely often", i.e. the limit \(\lim_{n \to \infty} a^n\). One simple example would be the natural numbers adjoined with positive infinity under addition, where 0* = 0 and n* = infinity for every n > 0. Another example is the booleans under conjunction or disjunction, where false* = false and true* = true. The booleans under xor, on the other hand, do not have a star operation.
Does this have a name? I found the concept of a "complete monoid", but that seems stronger than what I want: a complete monoid allows making sense of arbitrary infinitary products, but I only want to be able to take infinite powers (though off the top of my head I can't think of an example monoid that has a star but is not complete...)

2026-05-07 14:19:34 GMT

My department is hiring a 1-year visitor in mathematics. Please pass along to anyone you know who might be interested - this is a really fantastic place to work, with engaged students, supportive colleagues, and no one forcing you to use LLMs for anything.
https://hcm.paycor.com/l/r/D555BCF0

2025-09-19 10:13:39 GMT

Happy 8th birthday! Best birthday present ever! @npub1hnv…5hr9
https://media.mathstodon.xyz/media_attachments/files/115/230/418/353/270/847/original/ac84579c90bd994a.jpg

2025-06-16 20:41:33 GMT

New blog post, "Monads are not like burritos", in which I reflect on the history of a meme and continue the process of turning into a cranky old-timer
https://byorgey.github.io/blog/posts/2025/06/16/monads-are-not-burritos.html

2025-03-20 21:07:34 GMT

- reply

I showed this post to my 7yo and he is super excited! (So am I, to be honest!)

2024-12-21 22:46:59 GMT

- reply

Or maybe you could interpret "slaughtered in 3 days" as less than or equal to 3 days, as in, "these had all better be slaughtered 3 days from now". So the lazy servants slaughter one pig the first day, then on the second day they realize their problem and slaughter the remaining 299.

2024-12-14 22:10:28 GMT

I found 7yo drawing on a sheet of paper. He had drawn 8 dots in a circle and was drawing lines between all possible pairs of dots. I told him it was called \(K_8\) (and showed him how to write the 8 as a subscript). He thought that was cool and labelled his drawing. I then asked him to draw \(K_3, K_2, K_1\), and \(K_0\). He did not even hesitate at \(K_0\) but gleefully wrote \(K_0\) labelling a blank part of the paper.
He then wanted to draw \(K_{10}\) but I told him it would take too long (we had to leave shortly). I tried to explain something about how the number of lines grew quadratically, though not in those words of course. "Oh yeah," he said, "like how \(K_8\) has eight times seven lines." He double counted them, of course, but I was impressed he thought of a way to count them at all.
Looks like we have another budding mathematician on our hands! #math #kids

2024-11-06 19:13:53 GMT

- reply

I would think the terms of any "reasonable syntax" could be encoded as natural numbers (via Gödel numbering, or writing down a text encoding and reading off the bits, etc.). Given this purported "reasonable syntax", then, we could define the forbidden f(i,n) by first trying to decode i as a term of the syntax; if it does not decode, return, say, 0, and if it does, interpret the resulting term as a function ℕ→ℕ and output the result of that function on n.

2024-09-28 21:29:43 GMT

- reply

The values of \(n\) in your list seem to be off by one?

2024-09-10 18:52:50 GMT

At #icfp2024 Zubin Duggal (https://well-typed.com/people/zubin/) showed me this picture from a new Operations Control Center for part of Delhi's Metro system. Apparently the system status display on the giant screens is rendered with the Haskell diagrams EDSL!
https://media.mathstodon.xyz/media_attachments/files/113/114/738/657/159/846/original/33adf0a78b9dd0be.jpg