What is Hackers' Pub?

Hackers' Pub is a place for software engineers to share their knowledge and experience with each other. It's also an ActivityPub-enabled social network, so you can follow your favorite hackers in the fediverse and get their latest posts in your feed.

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LeanTutor: A formally-verified AI tutor for mathematical proofs. ~ Manooshree Patel et als. arxiv.org/abs/2506.08321

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LeanTutor: A Formally-Verified AI Tutor for Mathematical Proofs

We present LeanTutor, a Large Language Model (LLM)-based tutoring system for math proofs. LeanTutor interacts with the student in natural language, formally verifies student-written math proofs in Lean, generates correct next steps, and provides the appropriate instructional guidance. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. The first module faithfully autoformalizes student proofs into Lean and verifies proof accuracy via successful code compilation. If the proof has an error, the incorrect step is identified. The next-step generator module outputs a valid next Lean tactic for incorrect proofs via LLM-based candidate generation and proof search. The feedback generator module leverages Lean data to produce a pedagogically-motivated natural language hint for the student user. To evaluate our system, we introduce PeanoBench, a human-written dataset derived from the Natural Numbers Game, consisting of 371 Peano Arithmetic proofs, where each natural language proof step is paired with the corresponding logically equivalent tactic in Lean. The Autoformalizer correctly formalizes 57% of tactics in correct proofs and accurately identifies the incorrect step in 30% of incorrect proofs. In generating natural language hints for erroneous proofs, LeanTutor outperforms a simple baseline on accuracy and relevance metrics.

arxiv.org · arXiv.org

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So, known parties tirelessly work to make Linux a new Windows. Gnome announces even harder dependency on systemd.
GDM will depend on systemd userdb infrastructure. gnome-session will use systemd service manager instead of its own code that "has received very minimal attention in the 17 years since it was first written".
As per article, even now they do not test Gnome in non-systemd environments.
It's like a writing on the wall.
blogs.gnome.org/adrianvovk/202

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Dia Browser

我一開始連自己arc member的電郵地址都忘記了 :ablobglarezoom: 後來註冊又一直報錯,看了顯示不全的錯誤信息有「country」字眼,我超懷疑是AI服務在香港不能使用,所以就不讓註冊使用

開啟VPN改成台灣後,果然就可以了 :ablobdundundun:

然後這UI...怎麼退回Chrome了??

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[랜선효도] 6월 12일 기준 가격표. 싱귤생귤 등급 여름 하우스 감귤 시작. 초당옥수수 떨이 중입니다. 4종 감귤(타로코/한라봉/천혜향/타로코) 냉동 휴롬 쥬스 추천. 타로코오렌지 완숙 주문 가능합니다. 주문 : tinyurl.com/jejuorange7766 (구글폼) 문의 : open.kakao.com/o/snBLcewf (오픈카톡)

RE: https://bsky.app/profile/did:plc:a6qvfkbrohedqy3dt6k5mdv6/post/3lqissbmgqk2l

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My 25 years of palaeoart chronology...

My 2023 Struthiomimus and ostrich comparison illustration, from DINOSAUR BEHAVIOUR, by Prof Michael Benton (published by Princeton University Press).

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Although everyone is into large models these days I like small models that you can understand.

I good example is the Bradley-Terry model of tournaments that I've mention before. If you have historical data on who beat whom in the past then you can build a model by assigning everyone a score s_i and say that the probability that i beats j is

f(s_i-s_j)

where f is the logistic function

f(x)=1/(1+exp(-x)).

The task is then to fit s_i to your historical data. This formula is almost the simplest thing you might make up using the toolkit of machine learning, but it turns out to be a maximum entropy model. (Weird how this happens more often than it should.)

The task of fitting the s_i has a long history and a popular method was developed by Zermelo (yes, that Zermelo) back in 1929.

Anyway, I noticed a very recent paper that does a simple algebraic rearrangement of the underlying mathematics and results in a much faster algorithm to find the globally optimal fit.

jmlr.org/papers/volume24/22-10

Tangential: I'm amused by the fact that this model of game playing was developed by Milton (Terry) and (Ralph) Bradley but has nothing to do with Milton Bradley.

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I'm a week late to it but @glyph pretty much sums up my genAI coding feelings here. In particular the piece on aesthetics (probably not the kind of aesthetics you are imagining as you read this!) is going to bounce around in my head for a while.

blog.glyph.im/2025/06/i-think-

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I'm really loving how Mastodon has become a refuge for all the grizzled seafarers on the ocean of the internet. They pop up in my feed and their bios all say something like

"I've been online for longer than the internet. I've seen things you people wouldn't believe. 56k modems on fire in the light of Usenet. I watched IRC forks glitter in the dark near the Gateway 3000. All those moments will be lost in slop, like tears in rain. Time to deshittify."

From my original profile:

mastodonapp.uk/@Janeishly/1142

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구석에 있던 '동물화하는 포스트모던' 꺼내서 아무 페이지나 펼쳐봤는데 이런 문장 나왔다. "예를 들어 아사히신문을 읽고 선거에 가는 것과 애니메이션 잡지를 한 손에 들고 판매전에 줄을 서는 것 중 어느 쪽이 친구들과의 커뮤니케이션을 보다 원활하게 할 수 있는가 하는 그 유효성을 저울질한 결과이다."
이 책은 이걸 오타쿠가 '다른 가치규범'을 가져 그런거라고 표현했는데 지금 시대에는 이걸 뭐라고 불러야 할지 다들 알고 있다. '정치혐오'.

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"2020년 7월 9일, 여섯 살 브리저 워커 군이 개에게 습격당한 여동생을 구했다. 그는 온몸을 90바늘 꿰맸지만 세 살배기 여 동생을 빈사 상태에서 구했다. 그는 이렇게 말했다. 누군가 죽 어야 한다면 그건 나다. 저는 오빠예요. 세계복싱평의회는 그를 풀타임 세계 챔피언으로 인정했다." 캡아가 방패 보내주고, 마크러펄러, 톰홀랜드, 휴잭맨이 응원 메세지 보냈다고.

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