Lean proved this program correct; then I found a bug

https://kirancodes.me/posts/log-who-watches-the-watchers.html

by bumbledraven • 3 months ago

395 177 3 months ago

porcoda• 3 months ago

I’ve had similar experiences with code I’ve proven correct, although my issues were of the more common variety than the overflow issue - subtle spec bugs. (I think the post mentions the denial of service issue as related to this: a spec gap)

If you have a spec that isn’t correct, you can certainly write code that conforms to that spec and write proofs to support it. It just means you have verified a program that does something other than what you intended. This is one of the harder parts of verification: clearly expressing your intention as a human. As programs get more complex these get harder to write, which means it isn’t uncommon to have lean or rocq proofs for everything only to later find “nope, it has a bug that ultimately traces back to a subtle specification defect.” Once you’ve gone through this a few times you quickly realize that tools like lean and rocq are tricky to use effectively.

I kinda worry that the “proof assistants will fix ai correctness” will lead to a false sense of assurance if the specs that capture human intention don’t get scrutinized closely. Otherwise we’ll likely have lots of proofs for code that isn’t the code the humans actually intended due to spec flaws.

jmalicki2• 3 months ago

I have experience with similar things!

But that's not saying the proofs are an issue - usually the spec you can reasonably prove in lean or another prover, say TLA+ or Z3 depending on your kind of program - has to be overly simplified and have a lot of assumptions.

However, that is powerful.

It doesn't mean your program doesn't have bugs.

It means this big scary complicated algorithm you think works but are skeptical doesn't have bugs - so when you encounter one, you know the bug is elsewhere, and you start really looking at the boundaries of what could be misspecified, if the assumptions given to the prover are actually true, etc.

It eliminates the big scary thing everyone will think is the cause of the bug as the actual cause.

This has been insanely valuable to me lately. It is also something I never really was able to do before the help of AI - vibe coding proofs about my programs is IMO one of the killer apps of AI, since there aren't a ton of great resources yet about how to do it well since it is rarely done.

Nevermark2• 3 months ago

That is damn insightful.

cubefox• 3 months ago

This has been insanely valuable to me lately.

This surprises me. Formal verification so far has been a very niche thing apart from conventional type systems. I didn't think lack of vibe coding was much of a bottleneck in the past. Where do you use it?

brookst2• 3 months ago

Been thinking about this a lot recently.

I think we need a way to verify the specs. A combo of formal logic and adversarial thinking (probably from LLMs) that will produce an exhaustive list of everything the program will do, and everything it won’t do, and everything that is underspecified.

Still not quite sure what it looks like, but if you stipulate that program generation will be provable, it pushes the correctness challenge up to the spec (and once we solve that, it’ll be pushed up to the requirements…)

frumplestlatz• 3 months ago

What’s important is to prove useful, high-level properties derived from the specs. The specs of program behavior are just the price of admission.

somat• 3 months ago

Whenever I read an article about formal verification systems there is always that nagging thought in the back of my head. Why can you trust your formal verification system to be bug free but you can't trust the program. should not the chance of bugs be about equal in both of them?

You have a program that does something and you write another program to prove it. What assurance do you have that one program has fewer bugs then the other? Why can one program have bugs but the other can't? How do you prove that you are proving the right thing? It all sort of ties into Heisenberg's uncertainty theorem. A system cannot be fully described from within that system.

Don't get me wrong, I think these are great systems doing great work. But I always feel there is something missing in the narrative.

I think a more practical view is that a program is already a sort of proof. there is a something to be solved and the program provides a mechanism to prove it. but this proof may be and probably is incorrect, as bugs are fixed it gets more and more correct. A powerful but time consuming tool to try and force correctness is to build the machine twice using different mechanisms. Then mismatched output indicates something is wrong with one of them. and your job as an engineer is to figure out which one. This is what formal verification brings to the table. The second mechanism.

rdevilla• 3 months ago

It all sort of ties into Heisenberg's uncertainty theorem. A system cannot be fully described from within that system.

Surely you are talking about Godel incompleteness, not Heisenberg's uncertainty principle; in which case they're actually not the same system - the verification/proof language is more like a metalanguage taking the implementation language as its object.

(Godel's observation for mathematics was just that for formal number systems of sufficient power, you can embed that metalanguage into the formal number system itself.)

CJefferson• 3 months ago

The chances of significant bugs in lean which lead to false answers to real problems are extremely small (this bug still just caused a crash, but is still bad). Many, many people try very hard to break Lean, and think about how proofs work, and fail. Is it foolproof? No. It might have flaws, it might be logic itself is inconsistent.

I often think of the ‘news level’ of a bug. A bug in most code wouldn’t be news. A bug which caused lean to claim a real proof someone cared about was true, when it wasn’t, would in the proof community the biggest news in a decade.

raincole3• 3 months ago

should not the chance of bugs be about equal in both of them?

Why?

Are you saying that all the programs ever written have the exact same chance of bugs? A hello world is as buggy as a vibe-coded Chromium clone?

If you accept the premise that different programs have different chances to have bugs, then I'd say:

1. Simpler programs are likely less buggy.

2. Programs used by more people are likely less buggy.

3. Programs maintained by experts who care about correctness are likely less buggy.

4. Programs where the stakes are higher are likely less buggy.

All things considered, I think it's fair to say Lean is likely less buggy then a random program written by me at weekend.

Heisenberg's uncertainty theorem

It has nothing to do with the uncertainty principle. If you think otherwise, it means your understanding of uncertainty principle comes from sci-fi :)

majormajor• 3 months ago

Whenever I read an article about formal verification systems there is always that nagging thought in the back of my head. Why can you trust your formal verification system to be bug free but you can't trust the program. should not the chance of bugs be about equal in both of them?

A bug in the formal verification tool could be potentially noticed by any user of that formal verification tool. (And indirectly by any of their users noticing a bug about which they say "huh, I thought the tool told me that was impossible.")

A bug in your program can only be potentially noticed by you and your users.

There are also entirely categories of bugs that may not be relevant. For instance, if I'm trying to prove correctness of a distributed concurrent system and I use a model+verifier that verifies things in a sequential, non-concurrent way, then I don't have to worry about the prover having all the same sort of race conditions as my actual code.

But yeah, if you try to write your own prover to prove your own software, you could screw up either. But that's not what is being discussed here.

ngruhn• 3 months ago

I think formal verification brings a bit more to the table. The logical properties are not just a second implementation. They can be radically simpler. I think quantifiers are doing a lot of work here (forall/exists). They are not usable directly in regular code. For example, you can specify that a shortest path algorithm must satisfy:

    forall paths P from A to B:
        len(shortest(A,B)) <= len(P)

That's much simpler than any actual shortest path algorithm.

zarzavat• 3 months ago

Formal verification is just an extra step up from the static types that you might have in a language such as Rust.

Common static types prove many of the important properties of a program. If I declare a variable of type String then the type checker ensures that it is indeed a String. That's a proof. Formal verification takes this further and proves other properties such as the string is never empty.

Common static types are very effective. Many users of Rust or Haskell will claim that if a program compiles then it usually works correctly when they go to run it.

However there is a non-linear relationship between probability of program correctness and the amount of types required to achieve it. Being almost certain requires vastly more types than just being confident.

That's the real issue with formal verification, being 75% sure and having less code is better than being 99% sure in most situations, though if I were programming a radiotherapy machine I might think differently.

Nevermark2• 3 months ago

A program is a hard proof of existence.

It runs (maybe crashes), therefore … it exists.

The tension between spec bugs vs. implementation bugs is real. But i will take a bug in a situation where the implementation has been verified any day.

Working over what we really want is problem solving in the problem domain.

As apposed to going into the never ending implementation not-what-we-were trying to solve weeds.

Dylan16807• 3 months ago

should not the chance of bugs be about equal in both of them?

Even if it is, the verification is still very useful. The verifier is going to run for a few minutes and probably not hit many edge cases. The chance it actually hits a bug is low, and the chance a bug makes it wrongly accept your program is a lot lower. Especially if it has to output a proof at the end. Meanwhile it's scrutinizing every single edge case your program has.

andai• 3 months ago

Let me try wrap my head around this.

I notice two classes of bugs in my own programs:

- I meant the code to do X, but it does Y

- I meant the code to do X, and it does X, but X causes problems I didn't foresee

A proof assistant can help you prove the code does X, but it can't help you prove doing X doesn't cause problems you didn't foresee.

In other words, it can prove the soundness of the implementation, but not the design?

Is that right? Though I imagine if there are internal contradictions in the design, lean would catch those too.

So the issue would be "internally consistent yet incorrect designs"?

In the case of TFA, the issue was exhaustiveness, right? "What happens if..."

That sounds like a pretty important quality as far as security goes. Is there a way to make sure everything is actually verified?

I heard actually verifying everything is prohibitively expensive though, like it took 10-20 years to verify seL4 (10K LoC).

davesque2• 3 months ago

Am I reading the article wrong? It appears that the author did not test the claims of the proof. Wouldn't a "bug" in this case mean she found an input that did not survive a round trip through the compression algorithm?

Update: Actually, I guess this may have been her point: "The two bugs that were found both sat outside the boundary of what the proofs cover." So then I guess the title might be a bit click baity.

gopiandcode9• 3 months ago

Hi! Author here. When we speak of bugs in a verified software system, I think it's fair to consider the entire binary a fair target.

If a buffer overflow causes the system to be exploited and all your bitcoins to be stolen, I don't think the fact that the bug being in the language runtime is going to be much consolation. Especially if the software you were running was advertised as formally verified as free of bugs.

Secondly, I did find a bug in the algorithm. in Archive.lean, in the parsing of the compressed archive headers. That was the crashing input.

quantummagic4• 3 months ago

I think it's fair to consider the entire binary a fair target.

Yes, it's still very much a bug. But it has nothing to do with your program being formally verified or not. Formal verification can do nothing about any unverified code you rely on. You would really need a formal verification of every piece of hardware, the operating system, the runtime, and your application code. Short of that, nobody should expect formal verification to ensure there are no bugs.

davesque2• 3 months ago

Thanks for responding!

When we speak of bugs in a verified software system, I think it's fair to consider the entire binary a fair target.

Yeah, I would actually agree. We wouldn't want to advertise that a system is formally verified in some way if that creates a false sense of security. I was just pointing out that, by my reading, the title appears to suggest that the core mechanism of the Lean proof is somehow flawed. When I read the title, I immediately thought, "Oooh. Looks like someone demonstrated a flaw in the proof. Neat." But that's not what is shown in the article. Just feels a bit misleading is all.

tarasglek• 3 months ago

sorry to hijack the thread. Really cool post. How long did the whole exercise including porting zlib to lean take?

i have a hard real time system that i would love to try this on, but that's a lot of tools to learn and unclear how to model distributed systems in lean.

also, please add rss so i could subscribe to your blog

NewsaHackO6• 3 months ago

I notice you didn't put a code reference for the second bug. Where is the code exactly?

NewsaHackO6• 3 months ago

OK, so now I see the shadow edit you did for the code source, thanks. Unfortunately, it shows that you are incorrect. For one, the function is a private function and can only be called by local code. Everywhere that the function is called, the size given to it is verified by the program; there is even a note that says it limits the maximum zip file size to avoid a zip bomb. In addition, the code you are quoting isn't even the final code; it is an interim step from what Claude was iterating on. Sucks that this got so much traction, as you are purposely being deceptive in trying to say that this is a bug. You intentionally removed the 'private' keyword in the function signature, as you knew that it would tip off most people to then check when it is actually used.

lmm4• 3 months ago

Not verifying the parser seems like a pretty big oversight. Parsing binary formats is notoriously dangerous!

ctmnt7• 3 months ago

This article’s framing and title are odd. The author, in fact, found no bugs or errors in the proven code. She says so at the end of the article:

The two bugs that were found both sat outside the boundary of what the proofs cover. The denial-of-service was a missing specification. The heap overflow was a deeper issue in the trusted computing base, the C++ runtime that the entire proof edifice assumes is correct.

Still an interesting and useful result to find a bug in the Lean runtime, but I’d argue that doesn’t justify the title. Or the claim that “the entire proof edifice” is somehow shaky.

It’s important to note that this is the Lean runtime that has a bug, not the Lean kernel, which is the part that actually does the verification (aka proving). [1] So it’s not even immediately clear what this bug would really apply to, since obviously no one’s running any compiled Lean code in any kind of production hot path.

[1] https://lean-lang.org/doc/reference/latest/Elaboration-and-C...

gopiandcode9• 3 months ago

Repeating myself, when we speak of bugs in a verified software system, I think it's fair to consider the entire binary a fair target.

Second, there was a bug in the code. Maybe not a functional correctness bug, but I, along with many and most end users, would consider a crashing program buggy. Maybe we just have different tastes or different standards on what we consider an acceptable level of software quality.

W.r.t people running Lean in production, you'd be surprised...

danparsonson8• 3 months ago

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).

monocasa• 3 months ago

Totally agreed. For instance that's why sel4 just throws the whole binary at the proof engine. That takes any runtime (minimal in sel4's case) and compiler (not nearly as minimal) out of the TCB.

saithound• 3 months ago

Repeating myself, when we speak of bugs in a verified software system, I think it's fair to consider the entire binary a fair target.

Yes, and that would be relevant if this was a verified software system. But it wasn't: the system consisted of a verified X and unverified Y, and there were issues in the unverified Y.

The article explicitly acknowledges this: "The two bugs that were found both sat outside the boundary of what the proofs cover."

dyauspitr• 3 months ago

Well then formally verify the language system. I’m not sure what the confusion is. They didn’t say the whole system is formally verified.

Someone• 3 months ago

when we speak of bugs in a verified software system, I think it's fair to consider the entire binary a fair target.

I agree, but it’s not fair to imply that the verification was incorrect if the problem lies elsewhere.

This is a nice example of how careful you have to be to build a truly verified system.

germandiago3• 3 months ago

I don't think the fact that the bug being in the language runtime is going to be much consolation. Especially if the software you were running was advertised as formally verified as free of bugs.

Reminds of what some people in the Rust community do: they fight how safe this is or not. I always challenge that the code is composed of layers, from which unsafe is going to be one. So yes, you are righ to say that. Unsafe means unsafe, safe means safe and we should respect the meaning of those words instead of twisting the meaning for marketing (though I must say I heard this from people in the community, not from the authors themselves, ever).

IshKebab2• 3 months ago

if the software you were running was advertised as formally verified as free of bugs.

Nobody should be advertising that. Even ignoring the possibility of bugs in the runtime, there could also be bugs in the verifier and bugs or omissions in the specification. Formally verified never means guaranteed to be free of bugs.

ctmnt7• 3 months ago

Hi Kiran, thanks for following up. FWIW, I enjoy your blog and your work. And I do think it was a valuable bug you found; also nice to see how quickly Henrik fixed it.

Say more about people running Lean in production. I haven’t run into any. I know of examples of people using Lean to help verify other code (Cedar and Aeneas being the most prominent examples), but not the actual runtime being employed.

I took a quick scan of lean-lang.org just now, and, other than the two examples I mentioned, didn’t see a single reference to anything other than proving math.

I’m sure you’re in the Lean Zulup, based on what you’ve been up to. Are you seeing people talk about anything other than math? I’m not, but maybe I’m missing it.

raincole3• 3 months ago

I found the list of articles on this site amusing:

https://kirancodes.me/posts/log-who-watches-the-watchers.htm...

You can see the clickbaitiness increases over time.

minimaltom4• 3 months ago

Looks like a normal distribution about the chaos mean to me. I appreciate its not everyones cup of tea, but I like this style of writing.

NewsaHackO6• 3 months ago

To me, saying that there is a bug in the lean runtime means lean-zip has a bug is like saying a bug in JRE means a Java app that uses the runtime has a bug, even though the Java app code itself does have a bug. It seems like the author is being intentionally misleading about his findings.

aidenn03• 3 months ago

I think it's ambiguous and fair game for the idea of answering the question "if we write programs in this manner, will there be exploitable bugs?

brabel2• 3 months ago

No. It would be like finding a memory unsafe caused bug in a Java application that is due to a bug in the JRE. That would absolutely warrant a title like “I found memory unsafe bug in my Java code” when everyone expects Java code to be memory safe, which is analogous to the article in question.

kuruczgy• 3 months ago

It’s important to note that this is the Lean runtime that has a bug, not the Lean kernel, which is the part that actually does the verification (aka proving). [1] So it’s not even immediately clear what this bug would really apply to

Well, Lean is written in Lean, so I am pretty sure a runtime bug like this could be exploited to prove `False`. Yes, since the kernel is written in C++, technically it's not the part affected by this bug, but since you cannot use the Lean kernel without the Lean compiler, this difference does not matter.

ctmnt7• 3 months ago

Sure, but are you worried about someone cheating on their arXiv submission by exploiting a buffer overflow? It’s a real bug, it’s just not very important.

alimw• 3 months ago

I think this must be wrong. If the kernel is free of bugs then it's not going to pass a proof of false no matter what the Lean compiler gets up to.

koito172• 3 months ago

Yeah, the title made me think the author found a bug in the Lean kernel, thus making an invalid proof pass Lean's checks. The article instead uncovers bugs in the Lean runtime and lean-zip, but these bugs are less damning than e.g. the kernel, which must be trusted to be correct, or else you can't trust any proof in Lean.

brabel2• 3 months ago

When the Lean runtime has bugs, all Lean applications using the Lean runtime also have those bugs. I can’t understand people trying to make a distinction here. Is your intent to have a bug free application or to just show the Lean proof kernel is solid?? The latter is only useful to Lean developers, end users should only care about the former!

dbdr• 3 months ago

obviously no one’s running any compiled Lean code in any kind of production hot path

Ignorant question: why not? Is there an unacceptable performance penalty? And what's the recommended way in that case to make use of proven Lean code in production that keeps the same guarantees?

ctmnt7• 3 months ago

Yes, it isn’t performant. Lean isn’t a language for writing software, though you technically can; it’s a language for proving math.

dchftcs3• 3 months ago

A missing specification in the proof of lean-zip, a lean component, is a real problem to the philosophy and practice of software verification.

To illustrate, let's say you want to verify a "Hello world" program. You'd think a verification involves checking that it outputs "Hello, world!".

However, if a contractor or AI hands you a binary, what do you need to verify? You will need to verify that it does exactly print "Hello, world!", no more, no less. It should write to stdout not stderr. It shouldn't somehow hold a lock on a system resource that it can't clean up. It cannot secretly install a root-kit. It cannot try to read your credentials and send it somewhere. So you will need to specify the proof to a sufficient level of detail to capture those potential deviations.

Broadly, with both bugs, you need to ask a question: does this bug actually invalidate my belief that the program is "good"? And here you are pulling up a fact that the bug isn't found in the Lean kernel, which makes an assumption that there's no side-effect that bleeds over the abstraction boundary between the runtime and the kernel that affects the correctness of the proof; that safety guarantee is probably true 99.99% of the time - but if the bug causes a memory corruption, you'd be much less confident in that guarantee.

If you're really serious about verifying an unknown program, you will really think hard "what is missing from my spec"? And the answer will depend on things that are fuzzier than the Lean proof.

Now, pragmatically, there many ways a proof of correctness adds a lot of value. If you have the source code of a program, and you control the compiler, you can check the source code doesn't have weird imports ("why do I need kernel networking headers in this dumb calculator program?"), so the scope of the proof will be smaller, and you can write a small specification to prove it and the proof will be pretty convincing.

All in all, this is a toy problem that tells you : you can't verify what you don't know you should verify, and what you need to verify depends on the prior distribution of what the program is that you need to verify, so that conditional on the proof you have, the probability of correctness is sufficiently close to 1. There's a lesson to learn here, even if we deem Lean is still a good thing to use.

naasking• 3 months ago

A missing specification in the proof of lean-zip, a lean component, is a real problem to the philosophy and practice of software verification.

Every time someone makes this point, I feel obliged to point out that all alternatives to software verification have this exact same problem, AND many, many more.

fainpul• 3 months ago

This article’s framing and title are odd.

It's called clickbait.

armchairhacker• 3 months ago

“‘Proven’ code turns out buggy, because of a bug outside the proven specification” is relatively common. It happened in CompCert: https://lobste.rs/s/qlrh1u/runtime_error_formally_verified

thomastjeffery• 3 months ago

Misalignment of trust is a category of bug in my book; right next to logic error.

dchftcs3• 3 months ago

This is analogous to the fundamental problem of better automation in programming - eventually, the complexity and correctness of of the spec takes over, and if we don't manage that well, creating the spec is not that much less work than the programming part. If your program was for the wrong thing, a proof of it is also wrong.

butvacuum• 3 months ago

everybody also ignores that even hello world isn't deterministic anymore. It just doesn't matter to execution if something broke unless it kicks back an error.

although, this is the best example of how quickly a trivality can knock so called "correct" programs over.

jongjong3• 3 months ago

Fully agree. I started hitting this bottleneck when I combined a low-code backend I built with Claude Code to generate web applications.

I can build applications rapidly but the requirements and UX are the bottleneck. So much so that I often like to sit on a concept for multiple days to give myself the time to fully absorb the goal and refine the requirements. Then once I know what to build, it snaps together in like 4 hours.

There are a lot of ambiguities which need to be resolved ahead of time. Software engineering becomes a kind of detailed business strategy role.

Paracompact2• 3 months ago

I'm curious about your learning experience, but what was the nature of your bottleneck, exactly? Was the backend perfectly fine as a backend, but Claude struggled to wire it to a frontend gracefully?

spullara2• 3 months ago

claude making a statement that sounds impressive but it is actually the first codebase it has ever analyzed.

"This is genuinely one of the most memory-safe codebases I've analyzed."

germandiago3• 3 months ago

Maybe we do not know what Claude has been doing and he keeps it secret...? :D

gwern2• 3 months ago

It is definitely not the first codebase an extensively RL-trained Claude has ever analyzed. How do you think it got so good?

spullara2• 3 months ago

Meaning it has no episodic memory of any of those analyses that it has done.

mindcrime• 3 months ago

"Beware of bugs in the above code; I have only proved it correct, not tried it." -- Donald Knuth

ernsheong• 3 months ago

Alan Turing already proved with the Halting Problem that reasoning about program correctness is not possible. But we still try.

Wikipedia: [1] Turing proved no algorithm exists that always correctly decides whether, for a given arbitrary program and input, the program halts when run with that input. The essence of Turing's proof is that any such algorithm can be made to produce contradictory output and therefore cannot be correct.

[1] https://en.wikipedia.org/wiki/Halting_problem

ashton314• 3 months ago

reasoning about program correctness is not possible

Not possible for all problems. We cannot decide correctness (ie adherence to a specification) for all programs, but we can definitely recognize a good chunk of cases (both positive and negative) that are useful.

The Halting Problem itself is recognizable. The surprising result of Turing’s work was that we can’t decide it.

mkl• 3 months ago

We care only about a very small and narrow subset of possible programs, not any arbitrary one. It's possible to solve this kind of problem in large enough classes of program to be useful.

raincole3• 3 months ago

a given arbitrary program and input

Keyword emphasis mine.

grg04• 3 months ago

That one little word that changes everything in how you interpret the statement.

muraiki• 3 months ago

When you write a recursive function, Lean’s kernel requires a termination proof, unless the function is a partial or marked as unsafe. In those cases, they can’t be used in proofs. https://lean-lang.org/doc/reference/latest/Definitions/Recur...

DonaldPShimoda2• 3 months ago

Alan Turing already proved with the Halting Problem that reasoning about program correctness is not possible.

This is so reductive a framing as to be essentially useless [0]. I think maybe you want to learn more about program correctness, formal verification, and programming language semantics before you make such statements in the future.

[0] See, e.g., type-checking.

lmm4• 3 months ago

And Alonzo Church proved in 1940 that you can avoid this problem by using a typed language in which all programs halt. But sadly some programmers still resist this.

AnimalMuppet• 3 months ago

Some correct programs are supposed to run forever.

When is an OS supposed to halt? When you shut it down, or when you power down the hardware, and no other times. So if you don't do either of those things, then the OS is supposed to run forever. Does that, by itself, mean that the program is incorrect, or that the language is inadequate? No, it means that the definition is worthless (or at least worthless for programs like OSes).

jongjong3• 3 months ago

Formal proofs can only ever work to validate against requirements... But a major issue with a lot of modern software is that the requirements themselves can be incorrect and some requirements can logically conflict with other requirements... So long as we have non-technical people formulating requirements, we can never have provably correct software.

I've come across issues in the past which weren't actually bugs. For example, the software was behaving exactly as intended but it looked like a bug to a user who didn't understand the nuances and complexities of what was happening.

I also cannot count how many times a non-technical person asked me to implement conflicting functionality or functionality which would have made the UX incredibly confusing for the user.

grg04• 3 months ago

Clickbait title, the proved part of the program had no bugs?

As an aside, why can't people just write factually? This isn't a news site gamed for ad revenue. It's also less effort. I felt this post was mostly an insulting waste of time. I come to HN to read interesting stuff.

nickvec2• 3 months ago

Yeah, extremely misleading title even if it is technically true semantically. The phrasing gives the impression that a bug was found in `lean-zip` as part of the proof boundary when it was part of the unverified archive-handling code.

grg04• 3 months ago

And it took them several thousand words to explain what you just said in a sentence.

minimaltom4• 3 months ago

The archive-handling code was in lean-zip, it just seems the verifiers forgot to write proofs for it (still a bug).

Thats not the main finding of the article however. The main bug found was actually in the lean runtime, affecting all proofs using scalar arrays where the size of the array is not bounded.

minimaltom4• 3 months ago

Is it fair when it comes to formally-verified software to only consider bugs that violate a proof, and ignore everything else?

Formally-verified software is usually advertised "look ma no bugs!" Not "look ma no bugs*" *As long as this complicated chain of lemmas appropriately represents the correctness of everything we care about.

In boating theres often debate of right of way rules in certain situations, and some people are quick to point out that giant tanker ships should be giving way to tiny sailboats and get all worked up about it*. The best answer I've heard: they're dead right! that is to say as right as they are dead (if they didnt yield) lol. In the same vein, I think someone who assumed that a formally-verified software was perfect and got hacked or whatever is going to be a bit wiggly about the whole thing.

* = Technically the rules prioritize the tankers if they are "restricted in ability to maneuver" but everyone loves to argue about that.

grg04• 3 months ago

Nobody with experience in the field advertises formally-verified software like that, and it is understood that the spec may as well be wrong. It is also understood that the non-verified parts may have bugs (surprise). There is no news here.

nicce• 3 months ago

Also it seems to be just bindings for Zlib? The repo says "Lean 4 bindings for zlib compression, plus tar and ZIP archive support."

xxs• 3 months ago

Generally if I see 'this' to refer to some unknown part in any title, I'd consider it low quality.

MaxBarraclough• 3 months ago

Agreed, it's subtle but it's definitely a form of clickbait-style writing.

j2kun• 3 months ago

It reads to me as a cogent and measured response to a very clickbaity advertisement about the result.

Not tested. Proved. For every possible input.

Finding inputs that crashed and then saying, "be clear about what is in the scope of what you proved" is interesting and factual.

NewsaHackO6• 3 months ago

Also, he even just created the second bug out of thin air. There is no code reference, and the reason why he downplays it is because he knows that if someone looks into it, they will realize he misrepresented the actual code.

youknownothing• 3 months ago

I'll probably get a lot of hate mail for this but here goes nothing... Despite what many people like to claim, you cannot prove that a program has no bugs. That means proving the absence of bugs, and you cannot prove a negative. The best thing you can do is fail to find a bug, but that doesn't mean it isn't there.

Before everyone starts blabbing about formal verification, etc., consider this: how do you know that you didn't make a mistake in your formal verification? IOW, how do you know your formal verification is bug-free? Answer: you don't. Or if you try to formally verify your formal verification then you're just translating the problem to a new layer. It's just a chain of proofs that is always ultimately based on an unproven one, which invalidates the whole chain.

You can get asymptotically close to zero-bug proof, but you can never get there 100% of the way.

zitterbewegung• 3 months ago

The better look at this is not to prove that you have no bugs is that to prove that a program conforms to a specification that Lean can verify.

Even with the addition of two numbers the execution of a program can be wrong if the CPU has a fault or if the runtime of the program has a bug.

I think you just need to look at why formal verification exists.

aaronblohowiak• 3 months ago

I disagree but the constraints required to get there are probably untenable for most practical applications, so in practice I agree.

thatguysaguy• 3 months ago

What is up with people saying you cannot prove a negative? Of course you can! (At least in formal settings)

For example it's extremely easy to prove there is no square with diagonals of different lengths. I'm the hard end, Andrew Wiles proved Fermat's Last Theorem which expresses a negative.

That's just a nit though, you're right about the infinite regress problem.

pxc• 3 months ago

It's pretty easy to prove lots of negatives outside of mathematics, too. It's easy to prove there's no elephant in my living room at the moment.

mr_mitm• 3 months ago

Also, what even is "a negative"? The following statements are equivalent:

"There are no squares with diagonals of different lengths"

"All squares have diagonals of equal lengths"

Similarly, I can rephrase the statement about the absence of bugs. These are equivalent:

"This program has no bugs"

"This program always does exactly what it is supposed to do"

If you think you can't prove the first statement, then go ahead and prove the second one.

Are people thinking of falsification when talking about "proving negatives"? I.e. you can only falsify statements about the physical world, never prove them.

necovek5• 3 months ago

I believe it is rooted in legal proceedings where you are usually not required to in principle because it can be hard and/or impossible.

Eg. it is extremely hard to prove you "weren't there" (eg. at a crime site) if you cannot easily prove you were somewhere else (an affirmative): we do not keep court-admissible record of our whereabouts in case we get suspected of being in a place we were not in.

So it does hold in a number of cases where keeping evidence is required for proof. In software, that evidence would be formal specs and test reports which prove that cases covered with those are indeed working as specced, but provide no proof outside those "specs" (loosely considering an automated test a spec too).

_alternator_• 3 months ago

This comment conflates a number of ideas that obscures its own epistemological point. For example, yes, you can prove a negative (for instance, you can prove there is no largest integer).

The question of who validates the validator is real, but the abstraction of "formal verification" does serve a purpose, like any good mathematical or programming abstraction. Whole classes of bugs are removed; what's left to verify is usually much shorter.

lmm4• 3 months ago

That means proving the absence of bugs, and you cannot prove a negative.

You can prove that the program implements a specification correctly. That doesn't require proving a negative, but it does prove the absence of bugs. (I think you know this argument is weak, since your next paragraph is a complete non-sequitur)

Or if you try to formally verify your formal verification then you're just translating the problem to a new layer. It's just a chain of proofs that is always ultimately based on an unproven one, which invalidates the whole chain.

All proofs ultimately rest on axioms. That's normal and not really an argument unless you want to doubt everything, in which case what's the point in ever saying anything?

kvuj• 3 months ago

This feels like a thought exercise rather than an argument.

By your logic, it's impossible to prove that a car is driving at 60mph. There could be an error in the speedometer which makes it impossible to verify that said car is going at the speed. You can get asymptomatically close to being sure that you're driving at 60 mph but you can never be 100% sure.

This is useless and serves no purpose.

Gigachad2• 3 months ago

That's not correct. You can prove a car is driving 60mph as soon as you measure it doing that. "proving a negative" is for statements like "There are no purple zebra". You can never prove this because there is always the possibility the purple zebra is somewhere you haven't looked yet. As soon as you find one the statement becomes falsified, but until then it always remains unresolved even if almost certainly true.

Linking back to the parent statement, it's hard to prove a program has no bugs when there is always the possibility the bug just hasn't been found yet. On the flip side it's easy to prove something does have bugs as soon as you find one.

Paracompact2• 3 months ago

Formal methods practitioner here.

That means proving the absence of bugs, and you cannot prove a negative. The best thing you can do is fail to find a bug, but that doesn't mean it isn't there.

You can conclusively (up my next point) prove a specific bug or class of bugs aren't there. But "entirely free of (all) bugs" is indeed a big misconception for what formal methods does.

how do you know your formal verification is bug-free? Answer: you don't. Or if you try to formally verify your formal verification then you're just translating the problem to a new layer. It's just a chain of proofs that is always ultimately based on an unproven one, which invalidates the whole chain.

It's another misconception of formal methods to say that any result is established conclusively, without any caveats whatsoever. But then again neither is mathematics, or any other intellectual discipline. What formal methods does is reduce the surface area where mistakes could reasonably be expected to reside. Trusting the Rocq kernel, or a highly scrutinized model of computation and language semantics, is much easier than trusting the totality of random unannotated code residing in the foggiest depths of your average C compiler, for instance.

yjftsjthsd-h• 3 months ago

Even if all your claims are true (which I'm not 100% sold on but bear with me)... who cares? Sure, it won't get literally 100% of the way, but if we can get to a place where the only bugs in software are in the spec, in the proof assistants, and in weird hardware bugs, that would be an enormous win!

readthenotes1• 3 months ago

I didn't like the clickbait title. I would have preferred something along the lines of

"Lean proves other program correct but not itself"

vatsachak• 3 months ago

You guys are missing the forest for the trees.

They used an AI agent sending ideas to a fuzzer and discovered a heap buffer overflow in Lean. This is big.

germandiago3• 3 months ago

Indeed this is a nice discovery and I think it is useful in its own right.

akoboldfrying• 3 months ago

Nice work. Amusing that Lean's own standard library has a buffer overflow bug, which "leaked out" due to being exempted from the verification.

Regarding the DoS in the lean-zip application itself: I think this is a really neat example of the difficult problem of spec completeness, which is a subcase of the general problem (mentioned by porcoda in a sibling comment) of being sure that the spec is checking the right things. For a compression program, the natural, and I would also say satisfyingly beautiful thing to prove is that decomp(comp(x)) = x for all possible inputs x. It's tempting to think that at that point, "It's proven!" But of course the real world can call decomp() on something that has never been through comp() at all, and this simple, beautiful spec is completely silent on what will happen then.

ozten• 3 months ago

HN to be renamed Flex Social. Damn.

sebstefan• 3 months ago

So that's just one more win for formal verification despite the title it seems

I'm genuinely excited about AI agents and formal verification languages. To me it's obviously the way forward instead of moonshots trying to make agents that program in their own AI blackbox binary, or agents that code in current programming languages.

If we are heading in the direction of "huge codebases that nobody has written", or, "code is an artifact for the machine", I don't see a way out without making it proved.

If humans can review and edit the spec, then verify that the implementation matches it, suddenly leaving the implementation be an artifact for the machines seems okay

The downside of provers also being that they are a massive pain in the ass that very few want to use, this is also a complete win.

ajaystream• 3 months ago

The spec-completeness problem here is the same one that bites distributed systems verification: the proof holds inside an operating envelope (no adversarial inputs, trusted runtime, bounded sizes), and the interesting failures live at the boundary. TLA+ has the same property - you can prove liveness under a fairness assumption the deployment silently violates, and nothing in the proof tells you when reality drifted outside.

What I'd actually want from the tooling is a machine-checkable statement of the envelope itself, propagated as a runtime guard rather than a compile-time comment. Then "proof holds" and "we are still inside the proof's domain" are two separate, observable properties, and the unverified-parser / unverified-runtime cases stop being invisible.

aidenn03• 3 months ago

As someone who has discovered a bug in a CPU that was previously unknown to our chip vendor, I would like to point out that the rabbit hole is deep.

On the other hand, I've discovered thousands of bugs that weren't hardware bugs, and dozens of bugs due to people not having read hardware errata documents, so just formally modeling what we can model will absurdly reduce the bug quantity.

Animats• 3 months ago

Compression/decompression is a good problem for proof of correctness. The specification is very simple (you must get back what you put in), while the implementation is complex.

What seems to have happened here is that the storage allocator underneath is unverified. That, too, has a relatively simple spec - all buffers disjoint, no lost buffers, no crashes.

raverbashing• 3 months ago

"Beware of bugs in the above code; I have only proved it correct, not tried it." - Donald Knuth

https://news.ycombinator.com/item?id=12761986 (being this link more than 10yrs old is not surprising)

ButlerianJihad• 3 months ago

Incorrect usage of semicolon in title/headline. Should be a comma.

Tsk, tsk.

rhdunn• 3 months ago

Tools like this (formal verification, sparse, etc.) and built-in mechanism (types, generics, RAII, rust's borrow checker) can only verify issues within the scope of that framework. There are also trade-offs and limitations with each type and each implementation.

Type checking allows you to (outside of type casting such as in languages like C/C++ and casting to object for generic containers in Java) verify that an object is of a given type. That allows you to be sure that a well-formed program isn't doing things like putting a random object in a list.

Languages like C#, Scala, and Kotlin improve Java generics by making the generic type of a container or other interface/type part of the type system. This allows generic types of a generic type to preserve the inner type. This makes it possible to implement things like monads and mapping functions to preserve the generic type.

A similar thing is possible with union types, sealed interfaces/traits, etc. that allow you to check and verify the return type instead of defaulting it to a generic object/any type.

Likewise with other features like nullable/non-null annotations (or corresponding nullable type annotations like in Kotlin and recent C# versions).

All of these can be abused/circumvented, but if you keep your code within that framework the compiler will stop that code compiling. Likewise, these solve a limited set of bugs. For example, nullable types can't verify memory management and related bugs.

seanhunter• 3 months ago

This is very cool work but the author is labouring under a false premise about how axiomatic systems work:

Every Lean proof assumes the runtime is correct.

No. Every valid Lean proof assumes that if the runtime/mathlib etc is correct, then it too is correct.

Tangentially also, most lean proofs are not dependent on whether or not the runtime has things like buffer overflows or denial of service against lean itself at all, because if I prove some result in Lean (without attacking the runtime) then a bug in the runtime doesn’t affect the validity of the result in general. It does mean however that it’s not ok to blindly trust a proof just because it only relies on standard axioms and has no “sorry”s. You also need to check that the proof doesn’t exploit lean itself.

crvdgc• 3 months ago

Unfortunately, the discussion focused on the somewhat click baity title "proved this program correct". It's unclear what "this program" is. If it refers to the core algorithm with a proof, then there's no bug. If it includes the runtime and the header parser, then Lean didn't prove it correct.

That being said, using a coding agent to direct fuzzying and find bugs in the Lean kernel implementation is the big news here. (After all the kernel's implementation is not proved.)

The moral of the story is to push for more verified code not less and try AI bug hunting.

sylware• 3 months ago

c++, you asked for it.

aesopturtle• 3 months ago

This is a great reminder that ‘proved correct’ always has an invisible suffix: ‘with respect to the thing you actually specified.’ The hard part was never just proving things, it was pinning reality down tightly enough that the proof is about the right world.

vfclists• 3 months ago

Correctness with respect to a specification is not the same as correctness with respect to intent(ion) or expectation

DoctorOetker• 3 months ago

So this is very good news and was predictable.

LLM's are capable of producing code that passes formal verification.

The writing is on the wall: in the future more and more software on the abstract or platonic side of our computing base will be hermetically sealed against bugs and exploits. This quenching of bugs in the assured side will shift the mean location of bugs closer to the hardware side: at some point bugs and exploits will rely more and more on hardware quirks, and simply unspecified hardware.

Afterwards we can expect a long exponential decay of preventable safety violations: people mistakenly or surreptitiously disengaging the formal verification steps and shipping malicious or unverified code. Each such event will be its own big or small scandal, at some point there will be no deniability left: something must be on purpouse, either a malicious vulnerability or intentional disengagement of safety measures.

As the attack surface recedes towards the lower level hardware stack, it will open the debate that the community needs proper formal hardware descriptions (at least at the interface initially, not necessarily how the hardware has implemented it). As interface bugs get formalized 3 things can happen:

either vulnerabilities go extinct, and full formal hardware descriptions are not released

or vulnerabilities remain in each new generation of hardware, and malicious intent or negligence on behalf of the manufacturer can only be presumed, this will set up the community against manufacturers, as they demand full hardware descriptions (verilog, VHDL,...).

or vulnerabilities are tactically applied (vulnerabilities appear extinct to the bulk of the population, but only because manufactured vulnerabilities are sparingly exploited by the manufacturing block)

It is hard to predict what is more valuable: embedding HW vulnerabilities for the status quo and being able to exploit it for while before the public demands full hardware IP descriptions (verilog, VHDL) etc. or facing the end of vulnerabilities a little sooner but keeping hardware IP private (if the bugs stop with full interface descriptions).

Alifatisk• 3 months ago

The two bugs that were found both sat outside the boundary of what the proofs cover

Are we baiting people with headlines now?

vvern• 3 months ago

Now I want to see benchmarks

justinclift• 3 months ago

105,823,818 fuzzing executions.

That sounds like quite the monthly bill. o_O

deterministic• 3 months ago

"The two bugs that were found both sat outside the boundary of what the proofs cover. The denial-of-service was a missing specification. The heap overflow was a deeper issue in the trusted computing base, the C++ runtime that the entire proof edifice assumes is correct (and now has a PR addressing)."

In other words, the code was proven correct according to spec by LEAN. Which is exactly what LEAN claims to do.

Lean proved this program correct; then I found a bug

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