agda-stdlib VS l4v

For further reading, there's a paper on arity generic programming and some solutions using dependent typing in Agda.

In Rust I have never seen it. However, in Agda it's a convention, and the code looks beautifully https://github.com/agda/agda-stdlib/blob/master/src/Algebra/Lattice/Structures.agda

Agda is a good example, as it allows you to define arbitrary Unicode-based operators and names: https://github.com/agda/agda-stdlib/blob/master/src/Data/Product.agda

Most of the times you want the first three arguments to be passed implicitly, not just the first. And the syntax for passing arguments implicitly is the same for the type argument A and the term arguments n and m. (For Agda, see e.g. l.49 here: https://github.com/agda/agda-stdlib/blob/master/src/Data/Star/Vec.agda)

> C/C++ can be made memory safe

.. but it's much harder to prove your work is memory safe. sel4 is memory safe C, for example. The safety is achieved by a large external theorem prover and a synced copy written in Haskell. https://github.com/seL4/l4v

Typechecks are form of proof. It's easier to write provably safe Rust than provably safe C because the proofs and checker are integrated.

You can't really retrofit safety to C. The best that can be achieved is sel4, which while it is written in C has a separate proof of its correctness: https://github.com/seL4/l4v

The proof is much, much more work than the microkernel itself. A proof for something as large as webP might take decades.

When something like the seL4 microkernel is formally verified, the remaining bugs should only be bugs in the specification, not the implementation.

seL4 specifications and proofs are not a programming language.

Yes, especially 'logically impossible' when you dig into the details. From the blogpost:

> and the kernel modifications to seL4 that can reclaim the memory used by the rootserver.

MMMMMMMMMMMkkkkkk. So you then have to ask: were these changes also formally verified? There's a metric ton of kernel changes here: https://github.com/AmbiML/sparrow-kernel/commits/sparrow but I don't see a fork of https://github.com/seL4/l4v anywhere inside AmbiML.

I mean, it does also claim to be "almost entirely written in Rust", which is true if you ignore almost the entire OS part of the OS (the kernel and the minimal seL4 runtime).

Probably the only way to prevent this type of issue in an automated fashion is to change your perspective from proving that a bug exists, to proving that it doesn't exist. That is, you define some properties that your program must satisfy to be considered correct. Then, when you make optimizations such as bulk receiver fast-path, you must prove (to the static analysis tool) that your optimizations to not break any of the required properties. You also need to properly specify the required properties in a way that they are actually useful for what people want the code to do.

All of this is incredibly difficult, and an open area of research. Probably the biggest example of this approach is the Sel4 microkernel. To put the difficulty in perspective, I checkout out some of the sel4 repositories did a quick line count.

The repository for the microkernel 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

I mean, just look at the commits with "fix" in the specs folder: https://github.com/seL4/l4v/commits/master?after=4f0bbd4fcbc...