practicalfm
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practicalfm

We Need Simpler Types (speculations on what can be improved in future type systems and on erasing the boundaries between types and values)
https://github.com/ligurio/practicalfm Look for Coq, Agda, Idris, MS  F*.

Formal Verification Methods in industry
When you say "formal verification methods", what kind of techniques are you interested in? While using interactive theorem provers will most likely not become very widespread, there are plenty of tools that use formal techniques to give more correctness guarantees. These tools might give some guarantees, but do not guarantee complete functional correctness. WireGuard (VPN tunnel) is I think a very interesting application where they verified the protocol. There are also some tools in use, e.g. Mythril and CrossHair, that focus on detecting bugs using symbolic execution. There's also INFER from Facebook/Meta which tries to verify memory safety automatically. The following GitHub repo might also interest you, it lists some companies that use formal methods: practicalfm
haclstar

Let's collect relatively new research programming languages in this thread
Jasmin and F* don't have similar goals, Jasmin is a language designed to precisely express lowlevel code, while F* is a generalist language for verified programming. There is a subsystem of F* that performs extraction to "readable C code", Karamel (used to be called Kremlin), but you get the usual limitations of C code as a highlevel assembler, and also an embedded assembly layer built on Vale. Project Everest therefore generates artifacts that are a mix of C and assembly, rather than a new lowlevel language design as Jasmin.

Ten Years of TypeScript
Traditional design by contract checks the contracts at runtime. They can be understood as a form of dynamic typing with quite complicated types, which may be equivalent to refinement types
But you can check contracts at compile time too. It's quite the same thing as static typing with something like refinement types. That's because, while with contracts we can add preconditions like "the size of this array passed as parameter must be a prime number", with refinement types we can define the type of arrays whose size is a prime number, and then have this type as the function argument. (likewise, postconditions can be modeled by the return type of the function)
See for example this Rust library: https://docs.rs/contracts/latest/contracts/
It will by default check the contracts at runtime, but has an option to check them at compile time with https://github.com/facebookexperimental/MIRAI
Now, this Rust library isn't generally understood as creating another type system on top of Rust, but we could do the legwork to develop a type theory that models how it works, and show the equivalence.
Or, another example, Liquid Haskell: https://ucsdprogsys.github.io/liquidhaskell/ it implements a variant of refinement types called liquid types, which is essentially design by contract checked at compile type. In this case, the type theory is already developed. I expect Liquid Haskell to be roughly comparable to Rust's contracts checked by MIRAI.
Now, what we could perhaps say is that refinement types are so powerful that they don't feel like regular types! And, while that's true, there are type systems even more powerful: dependent types used in languages like Coq, Lean and F* to prove mathematical theorems (your type is a theorem, and your code, if it typechecks, is a proof of that theorem).
Dependent types were leveraged to create a verified TLS implementation that mathematically proves the absence of large class of bugs, miTLS https://www.mitls.org/ (they discovered a number of vulnerabilities in TLS implementations and proved that their implementation isn't vulnerable), and HACL* https://github.com/haclstar/haclstar a verified crypto implementation used by Firefox and Wireguard. They are part of Project Everest https://projecteverest.github.io/ which aims to develop provably secure communications software.

Securing your crypto wallet in a way that gives respect to what cryptography actually is
With that said, it's a very good thought to make sure that the software you're using is actually secure before trusting it. Personally, I think it's safe to use GnuPG and KeePass/Bitwarden, which have all been audited by the likes of Cure53, but if you're really paranoid, you could always use a formallyverified implementation of your desired algorithm (many are supplied in HACL*, for example)... In this case, I use the term "formallyverified" to mean that the implementation is mathematically proven to guarantee the properties of the algorithm (i.e., there are no "bugs" that affect output at the implementation level)...

How We Proved the Eth2 Deposit Contract Is Free of Runtime Errors
CompCert is also very impressive. It's not, however, free software / open source (the source is available though)
https://www.absint.com/compcert/structure.htm
A problem with both seL4 and CompCert is that the code written to express the proofs is huge, much larger than code that actually does stuff. This puts a ceiling on the size of the projects we can verify.
F* is a language that tries to address that, by finding proofs with z3, a smt prover; z3 can't prove everything on its own but it cuts down proof code by orders of magnitude. They have written a verified cryptography stack and TLS stack, and want to write a whole verified http stack.
https://github.com/projecteverest/haclstar
https://projecteverest.github.io/
F* (through Low, a verified lowlevel subset of F) can extract verified code to C, which is kind of the inverse than the seL4 proof: seL4 begins with C code and enriches it with proofs of correctness; hacl* (a verified crypto F* lib) begins with a proven correct F* code and extracts C code (I gather the actual crypto primitives is compiled directly to asm code because C has some problems with constant time stuff). This enables hacl* to make bindings to other languages that can just call C code, like this Rust binding
https://github.com/franziskuskiefer/evercryptrust
Also this F* stuff is all free software / open source, so it might become a very prevalent crypto and TLS stack

Awesome Rust Cryptography list compiled by the Rust Cryptography Interest Group (RCIG)
This is SO exciting!!! Ituses https://github.com/projecteverest/haclstar  a formally verified cryptography library. And it compiles down to C code, so I suppose it's fast.

Formal is fast: performance analysis and tuning of SPARKNaCl
Whats cool with that project and overlaps with SPARKNaCI would be the HACL* Library. Its purpose is to provide a formally verified library of modern cryptographic algorithms all written in a subset of F* called Low* and compiled to C using a compiler called KreMLin. The outputs of this are already being used Firefox, see here & here.
What are some alternatives?
magmide  A dependentlytyped proof language intended to make provably correct bare metal code possible for working software engineers.
acslbyexample  Public snapshots of "ACSL by Example"
evercryptrust  Rust bindings for HACL & Evercrypt
ouroboroshighassurance  Highassurance implementation of the Ouroboros protocol family
CommunityModules  TLA+ snippets, operators, and modules contributed and curated by the TLA+ community
silveroak  Formal specification and verification of hardware, especially for security and privacy.
effekt  A research language with effect handlers and lightweight effect polymorphism
karamel  KaRaMeL is a tool for extracting lowlevel F* programs to readable C code
RCIG_Coordination_Repo  A Coordination repo for all things Rust Cryptography oriented
FStar  A Prooforiented Programming Language
libsparkcrypto  A cryptographic library in SPARK 2014
MIRAI  Rust midlevel IR Abstract Interpreter