The question I always have is "why would the formal verification be any more correct than the program it is verifying?", Note: not bugs in the verification engine, but the spec made for the program.
It is not a big deal, I think formal verification is a very useful tool to help one approach correctness, but let me explain myself. When a program is written it is trying to solve a problem, when it solves that problem correctly it has no bugs, and when it solves that problem incorrectly those are bugs. For complex problems it turns out to be very difficult(impossible) to solve them correctly. Why is there an assumption that the formal verification spec will be any more correct than the program itself? They are both trying to solve very complex problems.
I was trying to get a feel for this by reading through the sel4 git changes trying to figure out how many bug fixes were for the OS and how many were for the spec. No real conclusion unfortunately.
What i found is that it is amazing once you determine and the invariants that are essential to the guarantees you want to keep.
I built my own formally verified workflow engine, it was easy but mostly because i already knew the pitfalls and the foundational pillars of Cadence and Temporal.
Also, it doesnt seem like common knowledge, but you can export libraries that compile to C from lean. With them you do get performant code that that has been verified and easily call them as C bindings from elsewhere.
Lean itself does not have a good IO stack in general but its good enough for small projects.
There is a caveat to exporting libs or native_decide in general. Once you export into C, ABI its now outside of the scope of the Lean kernel which means that bugs can creep in from the compiler itself.
"The counterpoint is that specifications are closer to informal requirements than implementations are (and thus a mistake is easier to spot)."
I found exactly the opposite to be true when I took formal verification at university, and that was the major point that made formal specification / verification unattractive to me.
I think it very much depends on the domain. For instance, I've seen specs for floating point ops that were 1-3 pages compared to 30,000 lines of RTL. That holds pretty well for many other cases. For example, a properties like decompress(compress(x)) = x are beautifully simple compared to the details of the algorithms, and are pretty compelling correctness evidence.
Part of it may be that you need experience writing formal specifications just as you need experience writing programs; everyone has a lot of the second, but little of the first. They're related skills, but not the same. The first is a much more abstract (but also much more concise and powerful) method of reasoning. This sort of skill hasn't been taught well in CS education yet, owing to the fact that the underlying languages and tools were too niche.
Suppose I write a distributed algorithm in Rust. To verify it, I might describe the algorithm again in TLA+, model-check that specification, and prove that it satisfies the properties I care about.
Now I have two artifacts:
TLA+ specification --> proved
Rust implementation --> runtime
But the proof establishes something like:
TLA_Spec => Safety
What I actually need is:
Rust_Program => Safety
I believe this is called model-code gap and there are ways to address it but I haven't found an easy-to-follow approach.
I last touched formal verification methods 20 years ago. Back then, Coq had the capacity to automatically transform your proof into OCaml. I would have expected that this would have only gotten better with time.
LLMs are pretty good at this. Not perfect by any means as the model is just a model after all - always wrong, sometimes useful - but the act of writing a TLA+ model helps the frontier LLMs to write correct executable code. It also works the other way around - given code, it can build a model in TLA+ and find latent bugs which it'll likely miss otherwise. (https://github.com/specula-org/Specula)
I think the reality is that it has to be baked into the language. Here's my real attempt at that - if you model the system in the language, the compiler can reason about the distributed fleet: https://hale-lang.org/proof/
Something like TLA is to prove the design of an algorithm is what you intended.
Proving a specific implementation in a specific language is really the domain of that language or tools targeting that language.
In digital design for example, SystemVerilog has a whole sub-language for specifying formal properties that can be proved in simulation or with tools that prove the properties mathematically.
As I remember it, he was formalising compilation by connecting the semantics of the higher level to the lower level one inside the proof assistant, so that proofs would carry through.
The title may be slightly misleading if you haven't bothered to read the article. It's responding to a famous paper from 1979 critiquing formal verification. The article ends up disagreeing with most of its strongest claims in hindsight, though a couple appear to remain worthwhile.
Everyone knows that the weak link is the specification. But this is a spurious argument, since, by definition, if you guarantee the implementation the only thing that's left exposed is the spec itself. At least you're reducing the attack surface
I haven't seen the Lipton/Perlis/De Millo paper in years. I was around for that argument. Which really dates me. Those guys were pushing for mutation analysis.[1] That's a test for the test suite - you make some random change to the program and see if the test suite catches it. Fuzzing is related to that concept.
It's taken way too long for verification to catch on. Here's where I was almost 50 years ago.[2] Part of the problem is that most of the interest came from people in love with the formalism. The notations used by most researchers were terrible, as is pointed out in the Lipton/Perlis/De Millo paper. You want a notation that matches the programming language.
We had the basic architecture back then - use a SAT solver on the easy stuff, and something with some AI capability on the hard stuff. We had the Oppen-Nelson simplifier, the first SAT solver, for the easy stuff. We had the Boyer-Moore prover for the hard stuff. It's Good Old Fashioned AI, and very good for the late 1970s. The SAT solver knocks off over 90% of the verification conditions. Then you want verification notation that creates hard but abstract problems for the AI solver. Like writing two asserts in a row, with the hard problem being to prove the second one from the first.
We didn't have enough compute back then. It took about 45 minutes on a VAX 11/780 for the Boyer-Moore prover to build up number theory from something similar to the Peano axioms. Now it takes about a second. I ported the Boyer-Moore prover to GNU Common LISP a few years ago, just to see it live again.[3]
With LLMs to do the grunt work, this is a lot less labor-intensive. And it's really needed to keep LLM garbage under control. Given a concrete goal against which to optimize, LLM coding is much more effective.
Formal specifications are still hard to write, but there are many important areas of software for which the specification is simple but an efficient implementation is hard. File systems. Databases. Networking. Some kinds of control systems. Stuff that really needs to work right.
The problem here is that more compute also helps testing. So it's not clear verification will pull ahead over just doing more testing, especially if there's any manual part of the verification workflow. The bugs that remain after testing become more and more difficult to stimulate.
The problem is that the people getting good results with AI-assisted formal methods are the same people who get good results with formal methods without AI assistance. They then extrapolate the benefits they are getting from AI today to what it may do for others in the future, and this is where we get into trouble.
There's a lot of art to using formal methods around how to specify the system at the right level of abstraction (to make verification tractable) and how to specify the correctness properties so they can be easily evaluated. Even with AI assistance as it currently exists, users need to know formal methods well enough to at least understand the specification of the system and the correctness properties, which requires ~90% of the effort of learning formal methods in the world before AI.
But the real hope is that one day AI will be able to use formal methods correctly on its own, benefitting those who don't know formal methods. AI can sometimes do that today, but sometimes isn't good enough for people who don't know formal methods. It is certainly possible that soon enough AI will be able to do this more reliably, but then we get into the hard problem of speculating the "AI future". It is very hard to predicat what an AI that can take over the art of using formal methods cannot do. Predicting that AI will be able to do that yet not be able to collect requirements and build software autonomously, or even come up with the idea for what software to build in the first place, or even replace the software's users seems arbitrary to me.
Software is buggy when people are more willing to buy the cheaper buggy software vs the higher price of more robust software.
When people want more robust software, they pay for it and it is delivered. None of the modern world would work without immense amounts of highly robust software you don't even think about, from your bank, to the airplane you fly on.
I don't understand what you're trying to say here. If I sell a car that doesn't start half of the time, I can just say "well people pay more for cars that always work, you chose to spend less so you got what you deserved"?
For used vehicles, we already have that in practice; when you sell a vehicle “as is,” that’s putting a buyer on notice that that they’re going to bear the risk of future failure.
Similarly, when you buy a cooler at Wal-Mart for $25, you know it’s not going to perform the same as a $250 Yeti model.
Agree in part, but remember that formal verification need not be done in full. By analogy, we don't avoid testing simply because everything under the sun can't be tested. Even simple things like verifying that certain API endpoints are idempotent, or as a few steps up, that the datastores used by Facebook have distributed consistency and fault-tolerance properties, are of enormous utility.
Exactly, it feels dishonest that this point is so rarely brought up in essays on formal methods. You can do things like prove that all possible faults are always caught, or any memory that is accessed has first been malloc’d, or that the API endpoint will always respond (liveness). These are often both easy to specify and difficult to guarantee with conventional testing.
Facebook runs a number of quite complex internal distributed systems - databases, caches, proxies, etc. all of these are amenable to various forms of formal verification, and verifying them is the kind of thing that helps prevent outages and data loss.
Well. Facebook has invested a fortune in proving that its systems follow expected properties of respecting consent—that all the data flows that happen are permitted. That turns out to be helpful for them in avoiding fines.
Anything with a GUI seems really daunting to specify. And then later you need to update specs to match GUI if you make any changes and you need to decide which is wrong: the implementation of the specification.
The final proof you get from formal methods is often irrelevant in my opinion. Most of the benefit comes from architecting the system so as much as possible can be verified and forcing yourself to make intentional decisions on the edge cases. The results are for other people.
I'm not sure you want to create a record of intentional decisions if you're at Facebook though.
> For some programs, the shortest descriptions of what they do are the programs themselves.
There is almost no real-world program for which this is true. One corollary of this would be that it is impossible to refactor the program to be any cleaner, which is not true for basically any large real-world program.
Another corollary of this is that no observable aspect of a program could be changed without breaking user expectations, but this too is almost always wrong (e.g. almost always, but not 100% via e.g. the famous xkcd comic about spacebar heating, a global performance optimization would be viewed as good).
The case against it is very simple: fixing your shit in software world is super easy - just release a patch! From a perspective of hardware world where fixing a single bug can cost you up to couple of million - we have for every code producing engineer up to 3 verification engineers that pseudo-randomly fuzz your design against all possible stimuli and collect coverage. Software world wouldnt bother because fixing shit is just so easy. If you regress to shipping golden CDs and next bugfix only via expansion packs - maybe you can get your shit together and start shipping good software again
and if producing a single CD copy would cost you a fortune then C-Suite business MBA morons would beg (or even mandate) you to use formal verification methods
It reads like not much has changed, and given what the two underlying issues are, that's not surprising.
I've been considering getting into formal verification, but the learning curve and the illusions of rigor angle are keeping me away so far. It's great that an agent can now figure out a formal spec on my behalf and check the program it generates on my behalf for compliance, but that doesn't make me any better equipped to keep it all honest end to end. The hard part is gone, remains the hard part.
Anecdotally, what I've been doing with agents instead is I made more things declarative. Config, policy, etc. manifests can be linted for syntax and schema compliance, and the logic only has to be written once. The agents can then go ham emitting their silly little JSONs or whatever, the risk is a lot more bounded that way. Just gotta be mindful to not smuggle in too much logic, and not walking the configuration complexity clock too hard, and all remains well. I feel with agents this is now more scalable, but maybe I'll come to think different later.
It is not a big deal, I think formal verification is a very useful tool to help one approach correctness, but let me explain myself. When a program is written it is trying to solve a problem, when it solves that problem correctly it has no bugs, and when it solves that problem incorrectly those are bugs. For complex problems it turns out to be very difficult(impossible) to solve them correctly. Why is there an assumption that the formal verification spec will be any more correct than the program itself? They are both trying to solve very complex problems.
I was trying to get a feel for this by reading through the sel4 git changes trying to figure out how many bug fixes were for the OS and how many were for the spec. No real conclusion unfortunately.
What i found is that it is amazing once you determine and the invariants that are essential to the guarantees you want to keep.
I built my own formally verified workflow engine, it was easy but mostly because i already knew the pitfalls and the foundational pillars of Cadence and Temporal.
Also, it doesnt seem like common knowledge, but you can export libraries that compile to C from lean. With them you do get performant code that that has been verified and easily call them as C bindings from elsewhere.
Lean itself does not have a good IO stack in general but its good enough for small projects.
There is a caveat to exporting libs or native_decide in general. Once you export into C, ABI its now outside of the scope of the Lean kernel which means that bugs can creep in from the compiler itself.
I found exactly the opposite to be true when I took formal verification at university, and that was the major point that made formal specification / verification unattractive to me.
Now I have two artifacts:
TLA+ specification --> proved
Rust implementation --> runtime
But the proof establishes something like:
TLA_Spec => Safety
What I actually need is:
Rust_Program => Safety
I believe this is called model-code gap and there are ways to address it but I haven't found an easy-to-follow approach.
[1] https://rocq-prover.org/docs
It seemed to me from the survey that most people didn't want it changed or didn't care, but due to anglophone users they decided to change it anyway.
I would say Ada SPARK solves this problem.
Proving a specific implementation in a specific language is really the domain of that language or tools targeting that language.
In digital design for example, SystemVerilog has a whole sub-language for specifying formal properties that can be proved in simulation or with tools that prove the properties mathematically.
https://pit-claudel.fr/clement/
As I remember it, he was formalising compilation by connecting the semantics of the higher level to the lower level one inside the proof assistant, so that proofs would carry through.
Also note that a specification can be input to other tools, such as a formal verification system for an encompassing system.
It's taken way too long for verification to catch on. Here's where I was almost 50 years ago.[2] Part of the problem is that most of the interest came from people in love with the formalism. The notations used by most researchers were terrible, as is pointed out in the Lipton/Perlis/De Millo paper. You want a notation that matches the programming language.
We had the basic architecture back then - use a SAT solver on the easy stuff, and something with some AI capability on the hard stuff. We had the Oppen-Nelson simplifier, the first SAT solver, for the easy stuff. We had the Boyer-Moore prover for the hard stuff. It's Good Old Fashioned AI, and very good for the late 1970s. The SAT solver knocks off over 90% of the verification conditions. Then you want verification notation that creates hard but abstract problems for the AI solver. Like writing two asserts in a row, with the hard problem being to prove the second one from the first.
We didn't have enough compute back then. It took about 45 minutes on a VAX 11/780 for the Boyer-Moore prover to build up number theory from something similar to the Peano axioms. Now it takes about a second. I ported the Boyer-Moore prover to GNU Common LISP a few years ago, just to see it live again.[3]
With LLMs to do the grunt work, this is a lot less labor-intensive. And it's really needed to keep LLM garbage under control. Given a concrete goal against which to optimize, LLM coding is much more effective.
Formal specifications are still hard to write, but there are many important areas of software for which the specification is simple but an efficient implementation is hard. File systems. Databases. Networking. Some kinds of control systems. Stuff that really needs to work right.
[1] https://en.wikipedia.org/wiki/Mutation_testing
[2] https://www.animats.com/papers/verifier/verifiermanual.pdf
[3] https://github.com/John-Nagle/nqthm
The problem here is that more compute also helps testing. So it's not clear verification will pull ahead over just doing more testing, especially if there's any manual part of the verification workflow. The bugs that remain after testing become more and more difficult to stimulate.
It's like 80% of the work after raising a PR is just socializing ideas and getting people to agree on stuff
There's a lot of art to using formal methods around how to specify the system at the right level of abstraction (to make verification tractable) and how to specify the correctness properties so they can be easily evaluated. Even with AI assistance as it currently exists, users need to know formal methods well enough to at least understand the specification of the system and the correctness properties, which requires ~90% of the effort of learning formal methods in the world before AI.
But the real hope is that one day AI will be able to use formal methods correctly on its own, benefitting those who don't know formal methods. AI can sometimes do that today, but sometimes isn't good enough for people who don't know formal methods. It is certainly possible that soon enough AI will be able to do this more reliably, but then we get into the hard problem of speculating the "AI future". It is very hard to predicat what an AI that can take over the art of using formal methods cannot do. Predicting that AI will be able to do that yet not be able to collect requirements and build software autonomously, or even come up with the idea for what software to build in the first place, or even replace the software's users seems arbitrary to me.
Maybe with formal verification the laws around that can change?
When people want more robust software, they pay for it and it is delivered. None of the modern world would work without immense amounts of highly robust software you don't even think about, from your bank, to the airplane you fly on.
Similarly, when you buy a cooler at Wal-Mart for $25, you know it’s not going to perform the same as a $250 Yeti model.
I agree with this counterargument.
I mean, you can verify that Euclid's algorithm computes the GCD. Or that quicksort produces a sorted version of the input array.
But how do you verify Facebook? Facebook computes what?
For some programs, the shortest descriptions of what they do are the programs themselves.
Edit: I agree with the replies that you can verify individual parts and properties, like with testing.
You start by verifying the permissions structure for Facebook posts.
And by verifying the shortest, least complex functions in Facebook's server side code base.
I'm not sure you want to create a record of intentional decisions if you're at Facebook though.
There is almost no real-world program for which this is true. One corollary of this would be that it is impossible to refactor the program to be any cleaner, which is not true for basically any large real-world program.
Another corollary of this is that no observable aspect of a program could be changed without breaking user expectations, but this too is almost always wrong (e.g. almost always, but not 100% via e.g. the famous xkcd comic about spacebar heating, a global performance optimization would be viewed as good).
I've been considering getting into formal verification, but the learning curve and the illusions of rigor angle are keeping me away so far. It's great that an agent can now figure out a formal spec on my behalf and check the program it generates on my behalf for compliance, but that doesn't make me any better equipped to keep it all honest end to end. The hard part is gone, remains the hard part.
Anecdotally, what I've been doing with agents instead is I made more things declarative. Config, policy, etc. manifests can be linted for syntax and schema compliance, and the logic only has to be written once. The agents can then go ham emitting their silly little JSONs or whatever, the risk is a lot more bounded that way. Just gotta be mindful to not smuggle in too much logic, and not walking the configuration complexity clock too hard, and all remains well. I feel with agents this is now more scalable, but maybe I'll come to think different later.