I'd have assumed, by virtue of being Turing complete, you could express any invariant in almost any language?
Good question. This is the holy grail. This is what everyone in PL research would love. This is where we want to get to.
Turns out a language as “simple” as C has sufficiently complicated semantics as to limit rigorous analysis to the basics. One example is loop analysis: it’s very useful to know that a loop will terminate eventually; if a loop is modifying some state and—worse—if the iteration variable gets modified—kiss your analysis goodbye because mechanically synthesizing strong pre- and post-conditions becomes insurmountable. It’s not an engineering challenge. It’s a math/pure CS theory challenge.
I assume if you were to develop such a system for C, C++, or Rust you'd similarly expect the user to do this.
(Any experts on formal verification please correct any inaccuracies in what I say here.)
The upshot of it is that C, C++, and Rust permit too much behavior that isn’t capturable in the type system. Thus, the properties that you’re interested in are semantic (as opposed to syntactic; type systems turn semantic properties into syntactic ones) so Rice’s theorem applies and there’s no computable way to do the analysis right.
As for being not expressive enough for specifications, isn't the code itself a form of specification? :)
Dafny can compile to and interface with a few languages, including C#.
Are there benchmarks showing dafny is faster than other inefficient options ?
I'm not sure about benchmarks comparing languages, but Dafny goes through a lot of tweaking to make the process faster.
Try writing a^b in integers and proving its correctness. The simple version works (based on a x a^(b-1)). But if you write an "optimised one" using (with handwaved details) (a^(b/2))^2 .... pulled some serious hair trying to prove this function works.
https://glados-michigan.github.io/verification-class/fall202...
dionian•5h ago
gz09•4h ago
ted_dunning•4h ago
That means that most of the proof can be done ahead of time with just some loose ends verified using an SMT prover at runtime.
esafak•1h ago
ted_dunning•4h ago
You could add Scala as a compilation target or you could just use the Java output and call formally verified Java functions from Scala. Even if you do get an implementation that produces Scala, don't expect the full power of idiomatic Scala to be available in the code you formally verify. To verify code, you have to write the code in Dafny with associated assertions to be proven. Since there are multiple compilation targets multiple formal constraints on what can usefully be verified, the data types available will not match the data types that you would use natively from Scala.