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Does using formal methods mean anything?
What counts as use of formal methods in software development?
Mathematics is involved, but then mathematics is involved in almost every aspect of software.
Formal methods are founded on the lie that doing things in mathematics means the results must be correct. There are plenty of mistakes in published mathematical proofs, as any practicing mathematician will tell you. The stuff that gets taught at school and university has been thoroughly checked and stood the test of time; the new stuff could be as bug written as software.
In the 1970s and 1980s formals methods was all about use of notation and formalisms. Writing algorithms, specifications, requirements, etc. in what looked like mathematical notation was called formal methods. The hope was that one day a tool would be available to check that what had been written did indeed have the characteristics being claimed, e.g., consistency, completeness, fault free (whatever that meant).
While everybody talked about automatic checking tools, what people spent their time doing was inventing new notations and formalisms. You were not a respected formal methods researcher unless you had several published papers, and preferably a book, describing your own formalism.
The market leader was VDM, mainly due to the work/promotion by Dansk Datamatik Center. I was a fan of Denotational semantics. There are even ISO standards for a couple of formal specification languages.
Fast forward to the last 10 years. What counts as done using formal methods today?
These days researchers who claim to be “doing formal methods” seem to be by writing code (which is an improvement over writing symbols on paper; it helps that today’s computers are orders of magnitude more powerful). The code written involves proof assistants such as Coq and Isabelle and programming languages such as OCaml and Haskell.
Can anybody writing code in OCaml or Haskell claim to be doing formal methods, or does a proof assistant of some kind have to be involved in the process?
If a program’s source code is translated into a form that can be handled by a proof assistant, can the issue of correctness of the translation be ignored? There is one research group who thinks it is ok to “trust” the translation process.
If one component of a program (say, parts of a compiler’s code generator) have been analyzed using a proof assistant, is it ok to claim that the entire program (perhaps the syntax and semantics processing that happens before code generation) has been formally verified? There is one research group who think such claims can be made about the entire program.
If I write a specification in Visual Basic, map this specification into C and involve formal methods at some point(s) in the process, then is it ok for me to claim that the correctness of the C implementation has been formally verified? There seem to be enough precedents for this claim to be viable.
In this day and age, is the use of formal methods anything more than a sign of intellectual dishonesty? Or is it just that today’s researchers are lazy, unwilling to put the effort into making sure that claims of correctness are proved start to finish?
Adverts during compilation; the future for gcc and llvm?
Many of the larger open source projects have most of their manpower supplied by commercial companies. Companies pay developers to work on open source projects because it is in their interest to do so. The current level of funding will not last forever and some open source projects will either have to significantly slim down their operations or find other revenue streams.
For the last few years (and probably the next few) Mozilla obtained most of its funding from Google through a licensing agreement (Google is the default search engine in the search box). No company wants to be dependent on a single source for a large chunk of its income and Mozilla is no exception. But where are the review streams for open source companies? Training and consulting are the obvious choices for technical products, but web browsers are supposed to user friendly, not technical. Another option is advertising and Mozilla has indicated an intent to go down this path.
How are open source compilers funded? A lot of the work on gcc used to be done by the folk at Code Sourcery, which is not owned by Mentor Graphics, and I was told their income primarily came from companies interested in ports to new processors and platforms. I have no idea how the gcc group is funded inside Mentor Graphics, but the long term prognosis does not look good; there is a long history of large tech companies buying compiler outfits and closing them down some years later (because the income they produce is not worth the hassle). The LLVM project, I’m told, gets most of its funding from Apple and one of my predictions for 2009 was that this funding would go away and LLVM would die; ok I was wrong about the year, but eventually Apple will stop funding this project.
Advertising is a possible revenue stream for compiler vendors; compilers could show adverts while compiling. Anybody who has used a commercial compiler will be familiar with the copyright notices that appear at the start of every compilation, so having a text message appear at the start of every compile is not new. Advertising could take the form of product placement “This version of gcc is brought to you by Wizzo Wash” or display material downloaded during compilation.
Adverts during compilation are not going to be popular with developers. One solution is to offer a subscription service for an ads free version of the compiler. It will certainly be necessary to make it much more difficult to build the compiler from source.
This form of revenue generation will have to be sold to developers; a group not known for its willingness to pay for tools (new tool vendors quickly learn to sell to management and ignore developers) combined with compiler writers not being known for having any selling ability.
Verified compilers and soap powder advertising
There’s a new paper out claiming to be about a formally-verified C compiler, it even states a Theorem about its abilities! If this paper appeared as part of a Soap powder advert the Advertising Standards Authority would probably require clarification of the claims. What clarifications might appear in the small print tucked away at the bottom of the ad?
- C source code is not verified directly, it is first translated to the formal notations used by the verification system; the software that performs this translation is assumed to be correct.
- The CompCert system may successfully translate programs containing undefined behavior. Any proof statements made about such programs may not be valid.
- The support tools are assumed to be correct; primarily the Coq proof assistant, which is written in OCaml.
- The CompCert system makes decisions about implementation dependent behaviors and any proofs only apply in the context of these decisions.
- The CompCert system makes decisions about unspecified behaviors and any proofs only apply in the context of these decisions.
Some notes on the small print:
The C source translator used by CompCert rarely gets mentioned in any of the published papers; what was done to check its accuracy (I have previously discussed some options)? Presumably the developers who wrote it tried very hard to make sure they did a good job, just like the authors of f2c, a Fortran to C translator, did. Connecting f2c as a front-end of the CompCert system gives us a verified Fortran compiler! I think the f2c translator is much more likely to be correct than the CompCert C source translator, it has been used by a lot more people, processed a lot more source and maintained over a longer period.
When they encounter undefined behavior in source code production C compilers sometimes generate code that has very unexpected behavior. Using the CompCert system will not avoid unexpected behavior in these situations; CompCert simply washes its hands for this kind of code and says all bets are off.
Proving the support tools correct would simply move the assumption of correctness to a different set of tools. I am not aware of any major effort to test whether the Coq system behaves as intended, but have not read all the papers describing it (the list of reported faults is does not appear to be publicly available); bugs have been found in the OCaml implementation.
Like all compilers that generate code, CompCert has to make implementation dependent decisions and select one of the possible unspecified behaviors. The C-Semantics tool generates all unspecified behaviors, rather than just one.
Why do companies fix faults in software they sell?
Once I buy some software from a company they have my money, if sometime later I find a fault software what incentive does that company have to fix the software and provide me with an update (assuming the software is not so fault ridden that I take advantage of laws allowing me to return a purchase for a refund)?
There are three economic incentives for companies to fix faults:
- because I am paying them a fee for updates that include fixes to known faults,
- because they want to make future sales to me and to others (faults encountered by customers contribute towards the perception of product quality),
- they don’t want to lose money because a fault had consequences that resulted in legal action (this reason is overhyped, in practice software engineering has a missing dead body problem).
Which faults get fixed? Software is surprisingly fault-tolerant and there is no point in fixing faults that customers are unlikely to encounter. This means that once a product has been released and known to be acceptable to many customers, there is no incentive to actively search for faults; this means that the only faults likely to be fixed are the ones reported by customers.
When reporting a fault, customers are often asked to rate its severity. This is a useful technique for prioritizing what gets fixed first, or perhaps what does not get fixed at all. Customers who actively set out to find faults are not appreciated and are labelled as disruptive if they continue doing it. Finding faults is surprisingly easy, finding the faults that have a high probability of being encountered by customers and ranked by them as critical is very hard (this is one of the reasons static analysis tools are not widely used).
What is the motivation for developers to fix faults in Open Source?
- There are companies who provide support services for a fee, just like commercial offerings,
- Open Source is free, gaining more users is not an obvious incentive to fix faults. However, being known as the go-to guys for a given package is a way of attracting companies looking to hire somebody to provide support services or make custom modifications to that package. Fixing faults is a way of getting visibility, it is advertising.
- Developers hate the thought of doing something wrong resulting in a fault in code they have written, and writing faulty code is not socially acceptable behavior in software development circles. These feelings about what constitutes appropriate behavior are often enough to make developers want to spend time fixing faults in code they have written or feel responsible for, provided they have the time. I suspect a lot of faults get fixed by developers when their manager/wife thinks they are working on something more ‘useful’.
Would you buy second hand software from a formal methods researcher?
I have been reading a paper on formally proving software correct (Bridging the Gap: Automatic Verified Abstraction of C by Greenaway, Andronick and Klein) and as often the case with papers on this topic the authors have failed to reach the level of honest presentation required by manufacturers of soap power in their adverts.
The Greenaway et al paper describes a process that uses a series of translation steps to convert a C program into what is claimed to be a high level specification in Isabelle/HOL (a language+support tool for doing formal proofs).
The paper was published by an Australian research group; I could not find an Australian advertising standards code dealing with soap power but did find one covering food and beverages. Here is what the Australian Association of National Advertisers has to say in their Food & Beverages Advertising & Marketing Communications Code:
“2.1 Advertising or Marketing Communications for Food or Beverage Products shall be truthful and honest, shall not be or be designed to be misleading or deceptive or otherwise contravene Prevailing Community Standards, and shall be communicated in a manner appropriate to the level of understanding of the target audience of the Advertising or Marketing Communication with an accurate presentation of all information…”
So what claims and statements do Greenaway et al make?
2.1 “Before code can be reasoned about, it must first be translated into the theorem prover.” A succinct introduction to one of the two main tasks, the other being to prove the correctness of these translations.
“In this work, we consider programs in C99 translated into Isabelle/HOL using Norrish’s C parser … As the parser must be trusted, it attempts to be simple, giving the most literal translation of C wherever possible.”
“As the parser must be trusted”? Why must it be trusted? Oh, because there is no proof that it is correct, in fact there is not a lot of supporting evidence that the language handled by Norrish’s translator is an faithful subset of C (ok, for his PhD Norrish wrote a formal semantics of a subset of C; but this is really just a compiler written in mathematics and there are umpteen PhDs who have written compilers for a subset of C; doing it using a mathematical notation does not make it any more fault free).
The rest of the paper describes how the output of Norrish’s translator is generally massaged to make it easier for people to read (e.g., remove redundant statements and rename variables).
Then we get to the conclusion which starts by claiming: “We have presented a tool that automatically abstracts low-level C semantics into higher-level specifications with automatic proofs of correctness for each of the transformation steps.”
Oh no you didn’t. There is no proof for the main transformation step of C to Isabelle/HOL. The only proofs described in the paper are for the post processing fiddling about that was done after the only major transformation step.
And what exactly is this “high-level specification”? The output of the Norrish translator was postprocessed to remove the clutter that invariably gets generated in any high-level language to high-level language translator. Is the result of this postprocessing a specification? Surely it is just a less cluttered representation of the original C?
Actually this paper does contain a major advance in formally proving software correct, tucked away at the start it says “As the parser must be trusted…”. There it is in black and white, if you have some software that must be trusted don’t bother with formal proofs just simply follow the advice given here.
But wait a minute you say, I am ignoring the get out of jail wording “… shall be communicated in a manner appropriate to the level of understanding of the target audience …”. What is the appropriate level of understanding of the target audience, in fact who is the target audience? Is the target audience other formal methods researchers who are familiar with the level of intellectual honesty within their field and take claims made by professional colleagues with a pinch of salt? Are non-formal methods researchers not the target audience and so have no redress to being misled by the any claims made by papers in this field?
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