Formal verification is ultimately an epistemological problem, how do we know that our model of reality corresponds to reality?
People have commented that validation is different from verification, but I think validation can be done by formally specifying the environment the program runs in.
For example, the question whether user can do X in your software corresponds to a question, is there a sequence of user inputs such that the software plus operating system leads to the output X.
By including the environment (like the operating system) into the formal spec we could answer (in theory) such questions.
Even if the question is fuzzy, we can today formalize it with AI models. For example, if we ask, does paint program allow user to draw a rose? We can take a definition of a rose from a neural network that recognizes what a rose is, and formally verify the system of paint program and rose verifier given by the NN.
> how do we know that our model of reality corresponds to reality?
This is the main issue I have with formal methods in commercial settings. Most of the time, the issue is that the model reality map is far from accurate. If you have to rewrite your verification logic every time you have to update your tests, development would go very slowly
> We can take a definition of a rose from a neural network that recognizes what a rose is
Can we? That just shifts the problem to building such a NN.
I think it would already be pretty tricky to get a decent sized panel of humans to agree on what a "rose" is. Do rose-shaped but yellow flowers count? How about those genetically altered thornless ones? How about perfectly imitatations that are made of plastic? Images of roses? The flowers from the list at https://www.epicgardening.com/rose-lookalikes/?
And of course there's the problem of getting a NN to recognise just roses. The mythical neural network with 0% error rate is exceptionally rare and usually not very useful for real world applications. I very much doubt humanity could build a neural network that perfectly recognises roses and only roses.
Now you’ve just shifted the problem to a much harder statement: proving the things the NN recognizes as a rose is actually a rose.
You cannot get rid of the enviroment, and the best thing you can do is be explicit in what you rely on. For example, formally verified operating systems often rely on hardware correctness, even though the errata sheets for modern CPUs are hundreds of pages long.
Yeah. That's why I am saying it's the epistemological problem.
In the above example, that NN recognizes rose as a rose is an assumption that it is correct as a model of the (part of the) world. On that assumption, we get a formal definition of "an image of a rose in the pixelated image", and we use that to formally prove our system allows roses to be painted.
But getting rid of that assumption is I believe epistemologically impossible; you have to assume some other correspondence with reality.
I agree with you on the hardware. I think the biggest obstacle to software formal correctness is the lack of formal models of which we can be confident describe our environment. (One obstacle is the IP laws - companies do not like to share the models of things they produce.)
Right, the problem is that one can't formally describe the environment, and any one thing has to interact with it. So formallness goes right out the window.
Formal verification is a pure logic problem. You are making a proof, and a proof is just a demonstration that you can reach a given expression given certain axioms and the rules of formal logic.
You can't just chuck a neural network into the mix because they aren't formally verified to do basically anything beyond matrix multiplication and the fact that they are universal approximators.
What is your product goal? Both for the customer (solving a problem) and for the company(solve a marketing need, make money)?
Can you proof that you are meeting both? Then you are validating your goals successfully.
Most of the time products are missing defined goals, so lots of people have no idea what the fuck they are developing and everyone ends up with their own idea of the product.
Usually there's a separate document that has the requirements, and from that document you have a "software detailed design" which has the specifications for how to build the software such that it upholds the requirements. Subtle but important difference.
Just by reading the headlines I immediately suspected the topic of Verification vs Validation would be involved. I still cannot comprehend why it is still such a gap in many software projects I have worked in. Everyone knows about testing but barely a few understand or want to understand why Validation is equally important.
While this is a good general rule of thumb, this terminology has nothing to do with how these terms are formally defined.
Verification first and foremost concerns design and development stage, a formal definition would be something like "outputs of design and development step meet specified requirements for that step". For example, you could verify that a formal specification for a module actually implements imposed requirements. Especially in software this can get murky as you cover different phases with different tests/suites, e.g. unit, integration, e2e implicitly test different stages, yet are often part of the same testing run.
Validation first and foremost concerns the whole system/product and fitness for market availability.
For example you would verify that e.g. for a motor vehicle ABS functions correctly, airbags deploy in a crash and frame meets passenger safety requirements in a crash, and you would still not be able to sell such vehicle. You would validate the vehicle as a whole with corresponding regulatory body to get vehicle deemed fit for market.
TLDR: Verification is getting passing grade in a lab test, validation is submitting all relevant lab test protocols to get CE certified.
- Did we correctly understand and build what the customer asked for
- Did the customer actually ask for what would solve the problem they are trying to solve
The second one is very important to ask early on, and _not_ asking it can cause a lot of wasted time. When I'm in a position to comment on whether I think someone fits the requirements of a senior developer, whether or not they ask that question plays directly into it.
Etymology to the rescue. "Valid" and "value" share a root, and so do "verify" and "verity." You validate something to see if it has value, meaning it works and is fit for purpose. You verify it to check that it is true and meets its specifications. Does that help? :)
> I wrote that the "binary search" bug happened because they proved the wrong property, but you can just as well argue that it was a broken assumption (that integers could not overflow).
No, you can't argue that (well, argue that successfully). If you are trying to prove some properties of a program X written in a certain programming language Y, you can't "just assume" that the semantics of Y are different from what they are! The integers do overflow in Java, that's explicitly stated in the Java's spec.
The article did not also point out issues like the compiler or interpreter having a runtime error, the hardware the software is running on having a defect, etc.
Do we consider these out of scope of the discussion?
Many interesting statements aren't a property of the code alone. They're a property of the code when it's run in a particular environment. If you want the proof to be portable then it should only make assumptions that are true in any environment.
Aye, but in many cases a theoretical limit can be ignored in practice. (Stupid example: I need more cooling = "I need more fans", not "I'm running out of air".)
From a quick look at it, it seems to be a "case 1" potential error, as the proof is done by hand. That is the warning is likely because it is a mathematical exercise first, and the code is for illustration and not for inclusion in production software.
It's not a substitute, an assertion only makes sure that it doesn't happen unnoticed, a proof says that it doesn't happen at all. I might prefer to know that my reactor control system has no overflow ahead of time, rather than getting an assertion and crashing if it happens (though it would be a bad reactor control system if it couldn't handle crashes).
What if it's an internal tool, where correctness matters a lot, but failures matter little? E.g. roll back all database changes in case of assertion failure. Perhaps an accounting thing or something of that nature.
I think other responses here may miss an important line of thought.
There seems to be confusion around the differences between bug and correct.
In the referenced study on binary searches, the Google researchers stated that most implementations had bugs AND were "broken" because they did:
int mid =(low + high) / 2;
And low + high can overflow.
Ostensibly, a proof may require mid to be positive at all times and therefore be invalid because of overflow.
The question is: if we put in assertions everywhere that guarantee correct output, where aborting on overflow is considered correct, then are folks going to say that's correct, or are they going to say oh that's not what binary search is so you haven't implemented it?
EDIT: thinking about it more, it seems that null must be an accepted output of any program due to the impossibility of representing very large numbers.
If you're flying a plane, you probably don't want safety critical code to throw an assertion. It's for this reason that Airbus spends a bunch of money & time on proving their flight control software.
Better to use a type which cannot represent an invalid state.
For example, instead of defining `inc` with `Int`s, the equivalent of an `IncrementalInt` type parameter for the `inc` function will ensure correctness without requiring runtime assertions.
By "asserting X" do you mean "checking whether X is true and crashing the program if not", like the assert macro in C or the assert statement in Python? No, that is almost never done, for three reasons:
• Crashing the program is often what you formally verified the program to prevent in the first place! A crashing program is what destroyed Ariane 5 on its maiden flight, for example. Crashing the program is often the worst possible outcome rather than an acceptable one.
• Many of the assumptions are not things that a program can check are true. Examples from the post include "nothing is concurrently modifying [variables]", "the compiler worked correctly, the hardware isn't faulty, and the OS doesn't mess with things," and, "unsafe [Rust] code does not have [a memory bug] either." None of these assumptions could be reliably verified by any conceivable test a program could make.
• Even when the program could check an assumption, it often isn't computationally feasible; for example, binary search of an array is only valid if the array is sorted, but checking that every time the binary search routine is invoked would take it from logarithmic time to linear time, typically an orders-of-magnitude slowdown that would defeat the purpose of using a binary search instead of a simpler sequential search. (I think Hillel tried to use this example in the article but accidentally wrote "binary sort" instead, which isn't a thing.)
When crashing the program is acceptable and correctness preconditions can be efficiently checked, postconditions usually can be too. In those cases, it's common to use either runtime checks or property-based testing instead of formal verification, which is harder.
This becomes an interesting conversation then. First of all, it could mean "checking whether X is true and logging an error" instead of exiting the program.
- But if you aren't comfortable crashing the program if the assumptions are violated, then what is your formal verification worth? Not much, because the formal verification only holds if the assumptions hold, and you are indicating you don't believe they will hold.
- True, some are infeasible to check. In that case, you could then check them weakly or indirectly. For example, check if the first two indices of the input array are not sorted. You could also check them infrequently. Better to partially check your assumptions than not check at all.
> "checking whether X is true and logging an error"
You now have some process or computation which is in an unknown state. Presumably it was important! There are lots of cases where runtime errors are fine and expected -- when processing input from the outside world, but if you started a chain of computation with good input and somehow ended up with bad input, then you have a bug! That is bad! Everything after that point can no longer be trusted, and there was some place where the code went wrong before that and made everything between there and where you caught the error invalid. And that has possibly poisoned your whole system.
I mean to ask both: "checking whether X is true and crashing the program if not", like the assert macro, OR assert as in a weaker check that does not crash the program (such as generate a log event).
When crashing the program is acceptable and correctness preconditions can be efficiently checked, postconditions usually can be too.
What's interesting to me is the combination of two claims: formal verification is used when crashes are not acceptable, and crashing when formal assumptions are violated is therefore not acceptable. This makes sense on the surface - but the program is only proven crashproof when the formal assumptions hold. That is all formal verification proves.
I believe this is a false dichotomy. It's interesting but it also demands no third way exist.
For example I have run services which existed inside a forever() loop. They exit, and are forceably restarted. Is that viable for a flight control system? No. Does it allow me to meet a low bounds availability problem with OOM killers? Yes, until the size of a quiescent from-boot system causes OOM.
BGP speakers who compile in runtime caps on the prefix count can be entirely stable and run BGP "correctly" right up to the point somebody sends them more than the cap in prefixes. That can take hours to emerge. I lived in that world for a while too.
That’s impractical. Take binary search and the assumption the list is sorted. Verifying the list is sorted would negate the point of binary search as you would be inspecting every item in the list.
There is a useful middle ground here. When picking the middle element, verify that it is indeed within the established bounds. This way, you'll still catch the sort order violations that matter without making the whole search linear.
ASSERTING the list is sorted as an assumption is significantly different form VERIFYING that the list is sorted before executing the search. Moreover, type systems can track that a list was previously sorted and maintained it's sorted status making the assumption reasonable to state.
What do you mean when you say "assert" and "verify"? In my head, given the context of this thread and the comment you're replying to, they can both only mean "add an `if not sorted then abort()`."
I know that Solaris (or at least, ZFS) has VERIFY and ASSERT macros where the ASSERT macros are compiled out in production builds. Is that the kind of thing you're referring to?
You can aslo mark certain codepaths as unreachable to hint to the compiler that it can make certain optimisations (e.g., "this argument is never negative"), but if you aren't validating that the assumption is correct I wouldn't call that an assertion -- though a plain reading of your comment would imply you would still call this an "assertion"? AFAIK, no language calls this construct "assert".
This is probably one of those "depends on where you first learned it" bits of nomenclature, but to me the distinction here is between debug assertions (compiled out in production code) and assertions (always run).
I'm not clear what definition of assert anyone is using. Thus I'm trying to create a new one that I think is useful (in the context of this type of discussion only!).
Verify means you checked.
Assert means you are suggesting something is true, but might or might not have checked. Sometimes an assert is "too hard" to verify but you have reason to think it is true. This could be because of low level code, or just that it is possible to verify but would cost too much CPU (runtime, or possibly limits of our ability to prove large systems) Sometimes assert is like a Mafia boss (It is true or I'll shoot - it might or might not really be true but nobody is going to argue the point now. This can sometimes be needed to keep a discussion on a more important topic despite the image)
In many (most?) languages assert is an optional crash if false. The language can choose to run the check or not. A function to check if a list is sorted and return a boolean is not hard to write - but of course you then need to prove that function is correct.
> Moreover, type systems can track that a list was previously sorted and maintained it's sorted status making the assumption reasonable to state.
This is true, but if you care about correct execution, you would need to re-verify that the list is sorted - bitflips in your DRAM or a buggy piece of code trampling random memory could have de-sorted the list. Then your formally verified application misbehaves even though nothing is wrong with it.
It's also possible to end up with a "sorted" list that isn't actually sorted if your comparison function is buggy, though hopefully you formally verified the comparison function and it's correct.
Only if you verify it for every search. If you haven't touched the list since the last search, the verification is still good. For some (not all) situations, you can verify the list at the start of the program, and never have to verify it again.
Add(x,y):
Assert( x >= 0 && y>= 0 )
z = x + y
Assert( z >= x && z >= y )
return z
There’s definitely smarter ways to do this, but in practice there is always some way to encode the properties you care about in ways that your assertions will be violated. If you can’t observe a violation, it’s not a violation https://en.wikipedia.org/wiki/Identity_of_indiscernibles
Best I can tell is that overflow is undefined behavior for signed ints in C/C++ so -O3 with gcc might remove a check that could only be true if UB occurred.
The compound predicate in my example above coupled with the fact that the compiler doesn’t reason about the precondition in the prior assert (y is non-negative) means this specific example wouldn’t be optimized away, but bluGill does have a point.
An example of an assert that might be optimized away:
int addFive(int x) {
int y = x + 5;
assert(y >= x);
return y;
}
Yes, you can not meaningfully assert anything after UB in C/C++. But you can let the compiler add the trap for overflow -fsanitize=signed-integer-overflow -sanitize-trap=all, or you could also write your assertion in a way where it does not rely on the result (e.g. ckd_add), or you use "volatile" to write in a way the compiler is not allowed to assume anything.
They do if they’re in the specs. See near-universal use of lockstep processors, ECC etc in safety-critical and high radiation cases, which comes from the two requirements that “a single bit flip from a cosmic ray shall be detectable” and “multiple simultaneous hit flips from cosmic rays shall be shown to be sufficiently rare in the operating environment.”
No hardware failure is considered? No cosmic rays flipping bits? No soft or hard real-time guarantees are discussed? What about indeterminate operations that can fail such as requesting memory from some operating system dynamically?
I'm asking because I thought high integrity systems are generally evaluated and certified as a combination of hardware and software. Considering software alone seems pretty useless.
Specifications that are formally verified can definitely cover real-time guarantees, behaviour under error returns from operations like allocation, and similar things. Hardware failures can be accounted for in hardware verification, which is much like software verification: specification + hardware design = verified design; if the spec covers it, the verification guarantees it.
Considering software alone isn't pretty useless, nor is having the guarantee that "inc x = x - 1" will always go from an Int to an Int, even if it's not "fully right" at least trying to increment a string or a complex number will be rejected at compile time. Giving up on any improvements in the correctness of code because it doesn't get you all the way to 100% correct is, IMO, defeatist.
(Giving up on it because it has diminishing returns and isn't worth the effort is reasonable, of course!)
Hardware verification doesn't prevent hardware failures. There is a reason RAM comes with ECC. It's not because RAM designers are too lazy to do formal verification. Even with ECC RAM, bit flips can still happen if multiple bits flip at the same time.
There are also things like CPUs taking the wrong branch that occasionally happen. You can't assume that the hardware will work perfectly in the real world and have to design for failure.
Well of course hardware fails, and of course verification doesn't make things work perfectly. Verification says the given design meets the specification, assumptions and all. When the assumptions don't hold, the design shouldn't be expected to work correctly, either. When the assumptions do hold, formal verification says the design will work correctly (plus or minus errors in tools and materials).
We know dynamic RAM is susceptible to bit-flip errors. We can quantify the likelihood of it pretty well under various conditions. We can design a specification to detect and correct single bit errors. We can design hardware to meet that specification. We can formally verify it. That's how we get ECC RAM.
CPUs are almost never formally verified, at least not in full. Reliability engineering around systems too complex to verify, too expensive to engineer to never fail, or that might operate outside of the safe assumptions of their verified specifications, usually means something like redundancy and majority-rules designs. That doesn't mean verification plays no part. How do you know your majority-rules design works in the face of hardware errors? Specify it, verify it.
Designing around hardware failure in software seems cumbersome to insane. If the CPU can randomly execute arbitrary code because it jumps to wherever, no guarantees apply.
What you actually do here is consider the probability of a cosmic ray flip, and then accept a certain failure probability. For things like train signals, it's one failure in a billion hours.
> Designing around hardware failure in software seems cumbersome to insane.
Yet for some reason you chose to post this comment over TCP/IP! And I'm guessing you loaded the browser you typed it in from an SSD that uses ECC. And probably earlier today you retrieved some data from GFS, for example by making a Google search. All three of those are instances of software designed around hardware failure.
If "a cosmic ray could mess with your program counter, so you must model your program as if every statement may be followed by a random GOTO" sounds like a realistic scenario software verification should address, you will never be able to verify anything ever.
An approach that has been taken for hardware in space is to have 3 identical systems running at the same time.
Execution continues while all systems are in agreement.
If a cosmic ray causes a bit-flip in one of the systems, the system not in agreement with the other two takes on the state of the other two and continues.
If there is no agreement between all 3 systems, or the execution ends up in an invalid state, all systems restart.
>Designing around hardware failure in software seems cumbersome to insane
I mean there are places to do it. For example ZFS and filesystem checksums. If you've ever been bit by a hard drive that says everything is fine but returns garbage you'll appreciate it.
"formal verification of the code" -> "high integrity system"
Formal verification is simply a method of ensuring your code behaves how you intend.
Now, if you want to formally verify your program can tolerate any number of bits flip on any variables at any moment(s) in time, it will happily test this for you. Unfortunately, assuming presently known software methods, this is an unmeetable specification :)
Even then you have other physical issues to consider. This is one of the things I love about the Space Shuttle. It had 5 computers for redundancy during launch and return. You obviously don't want to put them all in the same place so you spread them out among the avionics bays. You also obviously don't want them all installed in the same orientation so you install them differently with respect to the vehicles orientation. You also have a huge data network that requires redundancy and you take all the same steps with the multiplexers as well.
The best example on the Shuttle were the engine control computers. Each engine had two controllers, primary and backup, each with its own set of sensors in the engine itself and each consisting of a lock-step pair of processors. For each engine, the primary controller would use processors built by one supplier, while the backup would use processors of the same architecture but produced by an entirely different supplier (Motorola and TRW).
Today, even fairly standard automotive ECUs use dual-processor lock-step systems; a lot the the Cortex-R microcontrollers on the market are designed around enabling dual-core lock-step use, with error/difference checking on all of the busses and memory.
Requiring specialized hardware seems overly strict now that we can handle such things at a higher level via something like the fault tolerant lambda calculus.
For portable libraries and apps, there's only so much you can do. However, there are some interesting properties you can prove assuming the environment behaves according to a spec.
> [ FizzBee, Nagini, Deal-solver, Dafny; icontract, pycontracts, Hoare logic, DbC Design-by-Contract, invariants, parallelism and concurrency and locks, io latency, pass by reference in distributed systems, "FaCT: A DSL for Timing-Sensitive Computation" and side channels [in hw and software] https://news.ycombinator.com/item?id=38527663 ]
People have commented that validation is different from verification, but I think validation can be done by formally specifying the environment the program runs in.
For example, the question whether user can do X in your software corresponds to a question, is there a sequence of user inputs such that the software plus operating system leads to the output X.
By including the environment (like the operating system) into the formal spec we could answer (in theory) such questions.
Even if the question is fuzzy, we can today formalize it with AI models. For example, if we ask, does paint program allow user to draw a rose? We can take a definition of a rose from a neural network that recognizes what a rose is, and formally verify the system of paint program and rose verifier given by the NN.
This is the main issue I have with formal methods in commercial settings. Most of the time, the issue is that the model reality map is far from accurate. If you have to rewrite your verification logic every time you have to update your tests, development would go very slowly
Can we? That just shifts the problem to building such a NN.
I think it would already be pretty tricky to get a decent sized panel of humans to agree on what a "rose" is. Do rose-shaped but yellow flowers count? How about those genetically altered thornless ones? How about perfectly imitatations that are made of plastic? Images of roses? The flowers from the list at https://www.epicgardening.com/rose-lookalikes/?
And of course there's the problem of getting a NN to recognise just roses. The mythical neural network with 0% error rate is exceptionally rare and usually not very useful for real world applications. I very much doubt humanity could build a neural network that perfectly recognises roses and only roses.
You cannot get rid of the enviroment, and the best thing you can do is be explicit in what you rely on. For example, formally verified operating systems often rely on hardware correctness, even though the errata sheets for modern CPUs are hundreds of pages long.
In the above example, that NN recognizes rose as a rose is an assumption that it is correct as a model of the (part of the) world. On that assumption, we get a formal definition of "an image of a rose in the pixelated image", and we use that to formally prove our system allows roses to be painted.
But getting rid of that assumption is I believe epistemologically impossible; you have to assume some other correspondence with reality.
I agree with you on the hardware. I think the biggest obstacle to software formal correctness is the lack of formal models of which we can be confident describe our environment. (One obstacle is the IP laws - companies do not like to share the models of things they produce.)
You can't just chuck a neural network into the mix because they aren't formally verified to do basically anything beyond matrix multiplication and the fact that they are universal approximators.
verification - Are we building the software right?
validation - Are we building the right software?
makes many a thing easier to talk about at work
Verification aligns with a specification. E.g. verify if what was implemented matches what was specified.
Validation aligns with a requirement. E.g. verify if what was implemented solves the actual problem.
What is your product goal? Both for the customer (solving a problem) and for the company(solve a marketing need, make money)?
Can you proof that you are meeting both? Then you are validating your goals successfully.
Most of the time products are missing defined goals, so lots of people have no idea what the fuck they are developing and everyone ends up with their own idea of the product.
EDIT: more formally, specification is a document stating requirements
Verification: formal theoretical proof
Validation: Empirical test based approach
Verification first and foremost concerns design and development stage, a formal definition would be something like "outputs of design and development step meet specified requirements for that step". For example, you could verify that a formal specification for a module actually implements imposed requirements. Especially in software this can get murky as you cover different phases with different tests/suites, e.g. unit, integration, e2e implicitly test different stages, yet are often part of the same testing run.
Validation first and foremost concerns the whole system/product and fitness for market availability.
For example you would verify that e.g. for a motor vehicle ABS functions correctly, airbags deploy in a crash and frame meets passenger safety requirements in a crash, and you would still not be able to sell such vehicle. You would validate the vehicle as a whole with corresponding regulatory body to get vehicle deemed fit for market.
TLDR: Verification is getting passing grade in a lab test, validation is submitting all relevant lab test protocols to get CE certified.
Like "Customer validation" and "Verification against the spec"
Like "sympathy" and "empathy". I finally heard a mnemonic but if I need a mnemonic maybe it's a sign that the words are just too hard to understand
- Did we correctly understand and build what the customer asked for
- Did the customer actually ask for what would solve the problem they are trying to solve
The second one is very important to ask early on, and _not_ asking it can cause a lot of wasted time. When I'm in a position to comment on whether I think someone fits the requirements of a senior developer, whether or not they ask that question plays directly into it.
There was some meta-bug with encoding which almost is like an internal joke but I don't think it's intentional. The Haskell code examples have:
several times, and that `>` entity should very likely just be a `<` in the source code.No, you can't argue that (well, argue that successfully). If you are trying to prove some properties of a program X written in a certain programming language Y, you can't "just assume" that the semantics of Y are different from what they are! The integers do overflow in Java, that's explicitly stated in the Java's spec.
Posh example: Axiom of choice.
"Beware of bugs in the above code; I have only proved it correct, not tried it." - Donald Knuth
Source: https://staff.fnwi.uva.nl/p.vanemdeboas/knuthnote.pdf
From a quick look at it, it seems to be a "case 1" potential error, as the proof is done by hand. That is the warning is likely because it is a mathematical exercise first, and the code is for illustration and not for inclusion in production software.
Why not just use an assertion? It costs more at runtime, but it's far less dev time than developing a proof, right?
(the tradeoff of course being that they might get your code later because it took more time to prove the code is correct)
The point of proofs is to not get yourself (or the customer) into that point in the first place.
There seems to be confusion around the differences between bug and correct.
In the referenced study on binary searches, the Google researchers stated that most implementations had bugs AND were "broken" because they did:
And low + high can overflow.Ostensibly, a proof may require mid to be positive at all times and therefore be invalid because of overflow.
The question is: if we put in assertions everywhere that guarantee correct output, where aborting on overflow is considered correct, then are folks going to say that's correct, or are they going to say oh that's not what binary search is so you haven't implemented it?
EDIT: thinking about it more, it seems that null must be an accepted output of any program due to the impossibility of representing very large numbers.
You may want to prove some things. Test others.
Types are proofs by the way. Most programmers find that handy.
I think assertions are rediculously underused BTW
For example, instead of defining `inc` with `Int`s, the equivalent of an `IncrementalInt` type parameter for the `inc` function will ensure correctness without requiring runtime assertions.
• Crashing the program is often what you formally verified the program to prevent in the first place! A crashing program is what destroyed Ariane 5 on its maiden flight, for example. Crashing the program is often the worst possible outcome rather than an acceptable one.
• Many of the assumptions are not things that a program can check are true. Examples from the post include "nothing is concurrently modifying [variables]", "the compiler worked correctly, the hardware isn't faulty, and the OS doesn't mess with things," and, "unsafe [Rust] code does not have [a memory bug] either." None of these assumptions could be reliably verified by any conceivable test a program could make.
• Even when the program could check an assumption, it often isn't computationally feasible; for example, binary search of an array is only valid if the array is sorted, but checking that every time the binary search routine is invoked would take it from logarithmic time to linear time, typically an orders-of-magnitude slowdown that would defeat the purpose of using a binary search instead of a simpler sequential search. (I think Hillel tried to use this example in the article but accidentally wrote "binary sort" instead, which isn't a thing.)
When crashing the program is acceptable and correctness preconditions can be efficiently checked, postconditions usually can be too. In those cases, it's common to use either runtime checks or property-based testing instead of formal verification, which is harder.
- But if you aren't comfortable crashing the program if the assumptions are violated, then what is your formal verification worth? Not much, because the formal verification only holds if the assumptions hold, and you are indicating you don't believe they will hold.
- True, some are infeasible to check. In that case, you could then check them weakly or indirectly. For example, check if the first two indices of the input array are not sorted. You could also check them infrequently. Better to partially check your assumptions than not check at all.
You now have some process or computation which is in an unknown state. Presumably it was important! There are lots of cases where runtime errors are fine and expected -- when processing input from the outside world, but if you started a chain of computation with good input and somehow ended up with bad input, then you have a bug! That is bad! Everything after that point can no longer be trusted, and there was some place where the code went wrong before that and made everything between there and where you caught the error invalid. And that has possibly poisoned your whole system.
When crashing the program is acceptable and correctness preconditions can be efficiently checked, postconditions usually can be too.
What's interesting to me is the combination of two claims: formal verification is used when crashes are not acceptable, and crashing when formal assumptions are violated is therefore not acceptable. This makes sense on the surface - but the program is only proven crashproof when the formal assumptions hold. That is all formal verification proves.
For example I have run services which existed inside a forever() loop. They exit, and are forceably restarted. Is that viable for a flight control system? No. Does it allow me to meet a low bounds availability problem with OOM killers? Yes, until the size of a quiescent from-boot system causes OOM.
BGP speakers who compile in runtime caps on the prefix count can be entirely stable and run BGP "correctly" right up to the point somebody sends them more than the cap in prefixes. That can take hours to emerge. I lived in that world for a while too.
But you make some sort of distinction here.
You can aslo mark certain codepaths as unreachable to hint to the compiler that it can make certain optimisations (e.g., "this argument is never negative"), but if you aren't validating that the assumption is correct I wouldn't call that an assertion -- though a plain reading of your comment would imply you would still call this an "assertion"? AFAIK, no language calls this construct "assert".
This is probably one of those "depends on where you first learned it" bits of nomenclature, but to me the distinction here is between debug assertions (compiled out in production code) and assertions (always run).
> Is asserting the assumptions during code execution not standard practice for formally verified code?
Are you using the same definition of "assert" as that post does?
Verify means you checked.
Assert means you are suggesting something is true, but might or might not have checked. Sometimes an assert is "too hard" to verify but you have reason to think it is true. This could be because of low level code, or just that it is possible to verify but would cost too much CPU (runtime, or possibly limits of our ability to prove large systems) Sometimes assert is like a Mafia boss (It is true or I'll shoot - it might or might not really be true but nobody is going to argue the point now. This can sometimes be needed to keep a discussion on a more important topic despite the image)
If you want to assert that a list is sorted, you need some function that checks if it is sorted and returns a boolean.
This is true, but if you care about correct execution, you would need to re-verify that the list is sorted - bitflips in your DRAM or a buggy piece of code trampling random memory could have de-sorted the list. Then your formally verified application misbehaves even though nothing is wrong with it.
It's also possible to end up with a "sorted" list that isn't actually sorted if your comparison function is buggy, though hopefully you formally verified the comparison function and it's correct.
The compound predicate in my example above coupled with the fact that the compiler doesn’t reason about the precondition in the prior assert (y is non-negative) means this specific example wouldn’t be optimized away, but bluGill does have a point.
An example of an assert that might be optimized away:
https://gcc.godbolt.org/z/3Y4aheG6x
(That was one of my texts at uni)
I'm asking because I thought high integrity systems are generally evaluated and certified as a combination of hardware and software. Considering software alone seems pretty useless.
Considering software alone isn't pretty useless, nor is having the guarantee that "inc x = x - 1" will always go from an Int to an Int, even if it's not "fully right" at least trying to increment a string or a complex number will be rejected at compile time. Giving up on any improvements in the correctness of code because it doesn't get you all the way to 100% correct is, IMO, defeatist.
(Giving up on it because it has diminishing returns and isn't worth the effort is reasonable, of course!)
There are also things like CPUs taking the wrong branch that occasionally happen. You can't assume that the hardware will work perfectly in the real world and have to design for failure.
We know dynamic RAM is susceptible to bit-flip errors. We can quantify the likelihood of it pretty well under various conditions. We can design a specification to detect and correct single bit errors. We can design hardware to meet that specification. We can formally verify it. That's how we get ECC RAM.
CPUs are almost never formally verified, at least not in full. Reliability engineering around systems too complex to verify, too expensive to engineer to never fail, or that might operate outside of the safe assumptions of their verified specifications, usually means something like redundancy and majority-rules designs. That doesn't mean verification plays no part. How do you know your majority-rules design works in the face of hardware errors? Specify it, verify it.
What you actually do here is consider the probability of a cosmic ray flip, and then accept a certain failure probability. For things like train signals, it's one failure in a billion hours.
Yet for some reason you chose to post this comment over TCP/IP! And I'm guessing you loaded the browser you typed it in from an SSD that uses ECC. And probably earlier today you retrieved some data from GFS, for example by making a Google search. All three of those are instances of software designed around hardware failure.
If "a cosmic ray could mess with your program counter, so you must model your program as if every statement may be followed by a random GOTO" sounds like a realistic scenario software verification should address, you will never be able to verify anything ever.
Execution continues while all systems are in agreement.
If a cosmic ray causes a bit-flip in one of the systems, the system not in agreement with the other two takes on the state of the other two and continues.
If there is no agreement between all 3 systems, or the execution ends up in an invalid state, all systems restart.
I mean there are places to do it. For example ZFS and filesystem checksums. If you've ever been bit by a hard drive that says everything is fine but returns garbage you'll appreciate it.
Now, if you want to formally verify your program can tolerate any number of bits flip on any variables at any moment(s) in time, it will happily test this for you. Unfortunately, assuming presently known software methods, this is an unmeetable specification :)
Today, even fairly standard automotive ECUs use dual-processor lock-step systems; a lot the the Cortex-R microcontrollers on the market are designed around enabling dual-core lock-step use, with error/difference checking on all of the busses and memory.
A man with a watch knows what time it is. A man with two watches is never sure.
https://en.wikipedia.org/wiki/Segal%27s_law
From https://news.ycombinator.com/context?id=39938759 re: s2n-tls:
> [ FizzBee, Nagini, Deal-solver, Dafny; icontract, pycontracts, Hoare logic, DbC Design-by-Contract, invariants, parallelism and concurrency and locks, io latency, pass by reference in distributed systems, "FaCT: A DSL for Timing-Sensitive Computation" and side channels [in hw and software] https://news.ycombinator.com/item?id=38527663 ]
There are so many things to consider;
/? awesome-safety https://westurner.github.io/hnlog/#search:awesome-safety :
awesome-safety-critical: https://awesome-safety-critical.readthedocs.io/en/latest/
Hazard (logic) https://en.wikipedia.org/wiki/Hazard_(logic)
Hazard (computer architecture); out-of-order execution and delays: https://en.wikipedia.org/wiki/Hazard_(computer_architecture)
Soft error: https://en.wikipedia.org/wiki/Soft_error
SEU: Single-Event Upset: https://en.wikipedia.org/wiki/Single-event_upset
And then cosmic ray and particle physics