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Introduction to Formal Verification with Lean Part 1

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Re: Introduction to Formal Verification with Lean Part 1

#31

a) Thanks for putting this together! b) Please don't hijack my scrolling. c) I really wish Lean were more mature as an application programming language. Its standard library is really lacking.

I'll need to fix b! That is not intentional whatsover. Sorry for that. Thank you for the feedback

Re: Introduction to Formal Verification with Lean Part 1

#32
post #10

Great tutorial, really enjoyed it! Personally, I think languages that can check very much at compile time in combinations with LLMs have a bright future ahead. Additionally, if one wanted to give Haskell a try, Lean4 might be a good language to check out before, as it is more modern and ticks many of the same boxes (Still has some unique features, and the communities quite a lot). Small feedback: - Great flow, explai…

Vitalik recently wrote about vibe-coding in Lean and assembly language, using proof verification in Lean, saying "if done right, this has potential to both output extremely efficient code, and be far more secure than the way programming has been done before." https://vitalik.eth.limo/general/2026/05/18/fv.html

Yeah, his post resulted in a rise in everyone and their mother becoming formal verification "experts" now. But I think he's right. We no longer have good excuses for not trying to secure code with FV in this brave new world of agentic coding

Re: Introduction to Formal Verification with Lean Part 1

#33

a) Thanks for putting this together! b) Please don't hijack my scrolling. c) I really wish Lean were more mature as an application programming language. Its standard library is really lacking.

They’re working on adding a whole HTTP API right now

Re: Introduction to Formal Verification with Lean Part 1

#35

Please please please don't hijack scrolling :(

…and for no discernible reason, too. Ordinarily, irritating stuttering pages like this at least do some sort of visually fun thing. This is just a diabolical Framer design with a ton of needlessly overlapping nested containers. I deleted more than 20 invisible divs from the DOM and scrolling improved dramatically.

I'd inform the webmaster but the telephone number listed on the site is "(123) 456 789", so I guess AI slop is AI slop.

Re: Introduction to Formal Verification with Lean Part 1

#37

Great tutorial, really enjoyed it! Personally, I think languages that can check very much at compile time in combinations with LLMs have a bright future ahead. Additionally, if one wanted to give Haskell a try, Lean4 might be a good language to check out before, as it is more modern and ticks many of the same boxes (Still has some unique features, and the communities quite a lot). Small feedback: - Great flow, explai…

If you're excited about the relationship of Lean4 to LLMs/AI (like I am), you might find my recent post interesting [1].

TL;DR: I'm using automated theorem provers within my research on AI for automated algorithm design. To make it easier to run/benchmark different models/harnesses, I created an open-source Python package called OpenATP [2]. I recently added support to use Grok 4.5 in the OpenCode harness as a prover and found it to be surprisingly competitive with Claude Code and Codex at a fraction the cost and wall-clock time.

[1] https://news.ycombinator.com/item?id=49010310

[2] https://github.com/henryrobbins/open-atp

Re: Introduction to Formal Verification with Lean Part 1

#38
post #21

I think the explosion in the popularity of Lean probably means that tactic-based proofs have won. I wrote many proofs in college and on mere aesthetic grounds I avoided the use of theorem provers with tactics. Invoking a tactic is like calling a function without writing down what the arguments to the function are and what the result of the function is. As a reader you gain little knowledge about the proof unless you…

> I think the explosion in the popularity of Lean probably means that tactic-based proofs have won

The number of mentions of Lean in HN submissions aside, how do we gauge that? HN has odd trends like that - a decade ago, we loved everything "Bayesian" - but they don't necessarily translate to anything that's happening in the mainstream.

Re: Introduction to Formal Verification with Lean Part 1

#39

I built an automated math research system using Lean to verify the results: https://alethean.org

This is super cool! I see you are using Aristotle as the automated theorem prover. I know Aristotle is free (for now at least), and it's hard to beat free... But, you still might be interested in a recent post of mine [1]! I'm working on an open-source Python package called OpenATP [2] to make it easy to run/benchmark different models and harnesses as automated theorem provers. I recently added support for Grok 4.5 and found it to be surprisingly good.

[1] https://news.ycombinator.com/item?id=49010310

[2] https://github.com/henryrobbins/open-atp

Re: Introduction to Formal Verification with Lean Part 1

#40
Just in case anyone else decides to write along like the article suggests. I chose to use the live.lean-lang.org link, but it seems to default to a newer version of lean where the simp[xor] actually returns both sides still wrapped in the lambdas so the next simp[add_comm] will actually fail. The way to get around it is changing the version to v4.32.0 which the article doesn't seem to mention.
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