l4v

pressive piece of software. Finally, to answer your question. The specification that seL4 meets is published on github: https://github.com/seL4/l4v

xample of this from an excerpt of the book Program Construction by Roland Backhouse. The code is in Pascal. The problem the students had been set was to write a program that would compare two strings for equality. One student's solution was to assign the value true or false to a boolean equal as follows: equal := (string1.length = string2.length) if equal then for i := 1 to string1.length do equal := (string1.character[i] = string2.character[i]) The problem with this code is that it returns the value true whenever the two strings have equal length and their last characters are identical. For example, the two strings 'cat' and 'mat' would be declared equal because they both have length three and end in 't'. The student was quite taken aback when I demonstrated the error. Indeed, upon further questioning, it emerged that the program had been tested quite systematically. First, it had been tested on several pairs of identical strings, and then on several pairs of strings of unequal length. Both these tests had produced satisfactory results. The final test had been to input several pairs of equal length but unequal strings, such as 'cat' and 'dog', or 'house' and 'river'. This final test is interesting because it is possible to use simple probability theory to make a rough estimate of the chances of discovering the programming error. The details are not relevant here. Suffice it to say that, assuming pairs of words of equal length are generated with equal letter frequencies (that is, each letter in the alphabet is chosen with a probability of 1/26), there is only a one in three chance of discovering the error after ten tests; increasing the number of tests to 20 would still only yield a one in two chance, and one would need to perform over 50 tests to achieve a 90% chance of discovering the error. Finally, and most importantly, there is no certainty that one would ever discover the error, no matter how many tests have been performed. This is a great illustration of how testing can't guarantee correctness. It's easy for someone who isn't a beginner programmer to see why the code is incorrect, but it wasn't obvious to the student; this shows that, like the beginner, if you ever write code that is hard for one of your skill level to write, and which is subtly incorrect, you may never actually realize it without extensive testing, and if it's not extensive enough, you may still never find the bug.

crokernel itself [0] has 276,541 The testsuite [1] has 26,397 The formal verification repo [2] has 1,583,410, over 5 times as much as the source code. That is not to say that formal verification takes 5x the work. You also have to write your source-code in such a way that it is ammenable to being formally verified, which makes it more difficult to write, and limits what you can reasonably do. Having said that, this approach can be done in a less severe way. For instance, type systems are essentially a simple form of formal verification. There are entire classes of bugs that are simply impossible in a properly typed programs; and more advanced type systems can eliminate a larger class of bugs. Although, to get the full benefit, you still need to go out of your way to encode some invariant into the type system. You also find that mainstream languages that try to go in this direction always contain some sort of escape hatch to let the programmer assert a portion of code is correct without needing to convince the verifier. [0] https://github.com/seL4/seL4 [1] https://github.com/seL4/sel4test [2] https://github.com/seL4/l4v

.g. "no temporary node failure should result in data loss"). However, having a TLA+ specification usually makes the implementation fairly straightforward, especially in languages/environments with message-passing concurrency. You can use TLAPS [4] to write proofs-by-induction similar to yours for TLA+ specifications, but IMO the real power is in model-checking them with TLC, which gives you a lot of the advantages of formal methods with much less proof work. [1] https://github.com/seL4/l4v [2] https://www.idris-lang.org/ [3] https://idris.readthedocs.io/en/latest/tutorial/typesfuns.ht... [4] https://tla.msr-inria.inria.fr/tlaps/content/Home.html