[danparsonson]

We're not speaking about bugs in a verified system so much as writing articles making specific claims about that. Surely if we're at the level of precision of formal verification, it's incumbent upon us to be precise about the nature of a problem with it, no? "Lean proved this program correct and then I found a bug" heavily implies a flaw in the proof, not a flaw in the runtime (which to my mind would also be a compelling statement, for the reasons you describe).

[SAI_Peregrinus]

Or it implies a bug in the specification. The spec differing from the intent is a frequent source of bugs, it doesn't matter what language the spec is written in. Most people have experience with (or have seen news stories about) specification bugs in natural-language specifications: legal loopholes!

[spinningslate]

This is the biggest risk with the rejuvenated interest in formal proof. That LLMs can generate proofs is useful. Proof assistants that can check them (Lean/FStar/Isabelle/...) similarly so.

But it just moves the question to whether the theorems covered in the proof are sufficient. Underlying it all is a simple question:

Does the system meet its intended purpose?

To which the next question is:

What is the intended purpose?

Describing that is the holy grail of requirements specification. Natural language, behaviour-driven development, test-driven development and a host of other approaches attempt to bridge the gap between implicit purpose and explicit specification. Proof assistants are another tool in that box.

It's also one of the key motivators for iterative development: putting software in front of users (or their proxies) is still the primary means of validation for a large class of systems.

None of which is implied criticism of any of those approaches. Equally, none completely solves the problem. There is a risk that formal proofs, combined with proof assistants, are trumpeted as "the way" to mitigate the risk that LLM-developed apps don't perform as intended.

They might help. They can show that code is correct with respect to some specification, and that the specification is self-consistent. They cannot prove that the specification is complete with regards its intended purpose.

[gopiandcode]

Sorry, I'm not sure I follow. We are talking about bugs in a verified system, that is, in this case, a verified implementation of a zlib-based compression tool. Did it have bugs? yes. Several in fact. I'd recommend reading the article for a detailed listing of the bugs in the tool.

[danparsonson]

You give the answers to this in the artcle:

> The most substantial finding was a heap buffer overflow! but, not in lean-zip's code, but in the Lean runtime itself. (emphasis mine)

> The OOM denial-of-service is straightforward: the archive parser was never verified. (me again)

"Lean proved this program correct" vs "I found bugs in the parts that Lean didn't prove was correct". The failure was not in Lean's proof (which as I said is heavily implied by the title), but in ancillary or unverified code.

Do I misunderstand how Lean works? I am by no means an expert (or even an amateur) on Lean or formal systems in general. Surely the first class of bug could be found in any code that uses the framework, and the second class of bug could happen to any system that isn't proven? Does that make sense? Otherwise where's the boundary? If you find a bug in the OS, does that mean Lean failed somehow? How about the hardware? If your definition of a 'formally verified system' goes beyond the code being verified and the most important thing is whether or not you can make it crash, then the OS and the hardware are also part of the system.

Of course bugs are important to users regardless of the cause, but the audience for your article seems to be software engineers and as a software engineer, your article was interesting and you found something useful, but the title was misleading; that's all I'm saying.

[danparsonson]

Further to my earlier reply - a more succinct way to look at it might be:

- When they fix the run time, bug A goes away. So the proof still holds and the zlib code is still correct.

- When they add a system of proofs for the parser and modify that, then bug B goes away. So the proof still holds and the zlib code is still correct; and now more of the library is proven correct.

The formulation of the title is "I was told X but that's not true"... but that's not true. You were told X, and X is true, but you found Y and Z which are also important.

[amoss]

What is the program?

There are two different answers to this question, and which one is "correct" depends entirely on the context of who is asking it.

1. It's the code that is specific to this program that sits above the run-time layer (internal view, that most programmers would take).

2. It's the code in the binary that is executed (external view, that most users would take).

The key question does not seem to be "was the proof correct", rather "did the proof cover everything in the program". The answer depends on whether you are looking at it from the perspective of a programmer, or a user. Given the overly strong framing that the article is responding to - highlighting the difference in this way does seem to be useful. The title is correct from the perspective that most users would take.

[danparsonson]

Yes but, without wishing to be snarky, did you read the article? There is no program as such, in either sense - the announcement from Lean only mentions "a C compression library" (zlib). Not only that, but since we're talking about formal verification, a programmer would likely understand that that is about proving a bounded, specific codebase at source code level, and not operating on a binary along with its associated dependencies (again caveat my limited understanding of these things).

My feeling is that if you told the average non-technical user that some person/organisation had produced a formally verified version of a C compression library, you would likely get a blank look, so I think it's reasonable to assume that both Lean's intended audience, and the audience of the blog post linked here, correspond with number 1. in your list.

[amoss]

The article describes fuzzing the library, this execution requires a program to be compiled. Typically fuzzing involves a minimal harness around the payload (a single call into the library in this case). There is clearly a bug in this program, and it does not exist in the minimal harness. It must be in the library code, which was covered by the proof.

The bounded, specific codebase that you refer to is typically the library *and all of its dependencies*, which in this case includes the Lean runtime. This is why formal verification is difficult: the proof chain needs to extend all the way down to the foundations. In this case the original gushing claim that everything was verified is incorrect and premature. The article seems like a good exposition of why.

[danparsonson]

Thank you, I understand what fuzzing is; that test harness was presumably provided either by the blog post author or generated by Claude somehow, and therefore would not have been part of the proven code, nor part of the original claim by the Lean devs. That's what I meant by saying there is no program as such.

> The bounded, specific codebase that you refer to is typically the library and all of its dependencies, which in this case includes the Lean runtime.

How does that work? I thought the main idea is to write code in the Lean language which has some specific shape conducive to mathematical analysis, along with mathematical proofs that operate on that code. How then does a system like this handle a third party dependency? I've searched around and I can't find any information about how it works. I assumed that the boundary of the proof was the source code - surely they can't also be proving things like, say, DirectX?

> This is why formal verification is difficult: the proof chain needs to extend all the way down to the foundations.

The difficulty is not in explosions of computational complexity due to problems of incompleteness, decidability, the halting problem, those kinds of things? As I said this is not something I know much about but it's surprising to me if 'analysing all the code' is really the difficult bit.

[StilesCrisis]

I am pretty sure you could tell a teenager "there's a ZIP compression program that's scientifically proven to have no bugs" and they'd understand you. People don't have to be CS experts to understand that. (Technically it's Gzip but that's mostly irrelevant to understanding the claim here)

[nathell]

Gentle reminder about this excerpt from HN Guidelines:

> Please don't comment on whether someone read an article. "Did you even read the article? It mentions that" can be shortened to "The article mentions that".

[danparsonson]

Noted, thank you

[vntok]

Say you study some piece of software. And it happens that it has an automated suite of tests. And it happens that some files aren't covered by the test suite. And you happen to find a bug in one of those files that were not covered.

Would you publish a blog post titled "the XXX test suite proved there was no bug. And then I found one"?

It would be a bit silly, right?

[necovek]

A test suite never proves anything except that the code works for the test cases in it.

But yes, it would be equivalent to stating "No tests failed but I found a bug" and one would correctly deduce that test coverage is insufficient.

[eithed]

These were my thoughts as well and it's nothing new, I think, regarding testing altogether:

- testing libraries (and in this case - language itself) can have bugs

- what is not covered by tests can have bugs

Additionally would add that tests verify the assumptions of coder, not expectations of the business.

To give benefit to the author - I'd read the article as: having tests for given thing ensures that it does the thing that you built the tests for. This doesn't mean that your application is free of bugs (unless you have 100% coverage, can control entire state of the system, etc) nor that it does the right thing (or that it does the thing the right way)

[necovek]

I like to differentiate between coverage by lines and semantic coverage: sometimes you need to exercise a single line multiple times to get full semantic coverage, and better semantic coverage usually beats larger line coverage for detecting problems and preventing regressions.

[eithed]

I think mutation testing helps in defining semantic coverage, if I understand what you're saying

[tpoacher]

You're technically right, but what things are versus how they're promoted or understood by most people (rightfully or not) often diverges, and therefore such "grounding" articles are useful, even if the wording addresses the perceived rather than the factual reality.

By way of analogy, if there was an article saying "I bought a 1Tb drive and it only came with 0.91 terabits", I think if you started explaining that technically the problem is the confusion between SI vs binary units and the title should really be "I bought a 0.91 terabit drive and was disappointed it didn't have more capacity", technically you'd be right, but people would rightfully eyeroll at you.

[danparsonson]

To be clear, I think the article was fine and the author did some useful work (finding a bug in the runtime of a supposedly provably correct system is indeed a valuable contribution!). I don't agree that it's pedantic to explain why the title feels like a bait-and-switch (and thus does a disservice to the article itself). It's just a bit of feedback for future reference.

I take some comfort from being technically correct though; it's widely accepted by all of us pedants that that is the best kind of correct ;-)

[tpoacher]

Weeeellll, teeeechnically, I didn't say "technically correct", I said "technically right".

(just kidding xD)

[danparsonson]

Haha dammit - I'll lose my membership at this rate