cakeml VS CompCert

If I understand what you are asking about correctly, then I do think you are mistaken.

As a sibling comment observed, you would be proving something about a program, but proving things about programs is both possible and done.

This ranges from things like CakeML (https://cakeml.org/) and CompCert (compilers with verified correctness proofs of their optimizations) to something simple like absence of runtime type errors in statically strongly soundly-typed languages.

Of note is that you are proving properties of your program, not proving them perfect in every way. The properties of your program that you prove can vary wildly in both difficulty and usefulness. A sufficiently advanced formally verified compiler like CakeML can transfer a high-level proof about your source code to a corresponding proof about the behavior of the generated machine-executable code.

> A single IR with multiple passes is a good way to build a compiler

https://mlir.llvm.org/, which is using, is largely claiming the opposite. Most passes more naturally are not "a -> a", but "a -> b". data structures and data structures work hand in hand, it is very nice to produce "evidence" for what is done in the output data structure.

This is why https://cakeml.org/, which "can't cheat" with partial functions, has so many IRs!

Using just a single IR was historically done for cost-control, the idea being that having many IRs was a disaster in repetitive boilerplate. MLIR seeks to solve that exact problem!

You may want to look at [CakeML](https://cakeml.org) done in HOL4, there is also a nice proof pearl about a more .. minimalistic verified bootstrapped compiler also in HOL4.

CakeML

There is also Cake ML which is a formally verified functional programming language compiler and runtime.

There is also a CakeML -> Standard ML compiler though it seems to have been built to translate benchmarks and sort of old so I'm not sure how comprehensive it is: https://github.com/CakeML/cakeml/tree/master/unverified/front-end

> One guess is that lisps cope with being minimal through use of macros and metaprogramming, it's difficult for a typed language to support that level of metaprogramming while maintaining the various guarantees that one wants from such a system.

Difficult, but certainly not impossible [0].

[0] https://cakeml.org/

If this interests you, I'd highly recommend checking out CompCert (docs here) and CakeML.

A big problem is that proving that transformations preserve semantics is very hard. Formal methods has huge potential and I believe it will be a big part of the future, but it hasn't become mainstream yet. Probably a big reason why is that right now it's simply not practical: the things you can prove are much more limited than the things you can do, and it's a lot less work to just create a large testsuite.

Example: CompCert (https://compcert.org/), a formally-verified compiler AKA formally-verified sequence of semantics-preserving transformations from C code to Assembly. It's a great accomplishment, but few people are actually compiling their code with CompCert. Because GCC and LLVM are much faster[1], and have been used so widely that >99.9% of code is going to be compiled correctly, especially code which isn't doing anything extremely weird.

But as articles like this show, no matter how large a testsuite there may always be bugs, tests will never provide the kind of guarantees formal verification does.

[1] From CompCert, "Performance of the generated code is decent but not outstanding: on PowerPC, about 90% of the performance of GCC version 4 at optimization level 1"

Also a C compiler (https://compcert.org/). I did exaggerate bit in saying that anything non-trivial is "nearly impossible".

However, both CompCert and sel4 took a few years to develop, whereas it would only take months if not weeks to make versions of both which aren't formally verified but heavily tested.

From my experience, while many MCUs have settled for the big compilers (GCC and Clang), DSPs and some FPGAs (not Intel and Xilinx, those have lately settled for Clang and a combination of Clang and GCC respectively) use some pretty bespoke compilers (just running ./ --version is enough to verify this, if the compiler even offers that option). That's not necessarily bad, since many of them offer some really useful features, but error messages can be really cryptic in some cases. Also some industries require use of verified compilers, like CompCert[1], and in such cases GCC and Clang just don't cut it.

[1]: https://compcert.org/

CompCert sends its regards

But that's fine, because we can do even better with things like the CompCert C compiler, which is formally proven to produce correct asm output for ISO C 2011 source. It's designed for high-reliability, safety-critical applications; it's used for things like Airbus A380 avionics software, or control software for emergency generators at nuclear power plants. Software that's probably not overly sophisticated and doesn't need to be highly optimized, but does need to work ~100% correctly, ~100% of the time.

For context, CompCert is a formally verified compiler. My former advisor helped with a fuzzer called CSmith which found plenty of bugs in GCC and LLVM but not in CompCert.

Does anybody know how does this compare to https://compcert.org/ ?

This is a common property for proof-oriented languages. Coq shares this property for instance, and you can write an optimizing C compiler in Coq: https://github.com/AbsInt/CompCert .