Kind VS FStar

As a developer of a proof assistant (Kind) I'm highly interested in this line of work. Can you point me to some of these papers? And perhaps people involved in this line of work?

Kind: A modern proof language (though functional).

I have seen in languages like KindLang the definition of Array be like a Binary tree, but there is some magic there in the definition of the Array type that I don't understand yet. Also, I don't want to define the contiguous array further., it should be a literal contiguous array. The Kind "Word" type definition (arbitrary number of bytes) is closer to my contiguous array, but it has a similarly complex definition which like I said I don't understand.

Totally agree about the Blub Paradox, but there's definitely value in Self Types. See, for example, [Kind](https://github.com/Kindelia/Kind), which is able to type recursive data types by using Self Types.

For these who don't know, I'm the author of Kind and HVM. I've recently seen a criticism from an influent person in the community, who I often took as an inspiration, that made me really sad. "the guy behind this has built some impressive-sounding stuff before... it looks like his projects tend to just... go nowhere and he just abandons them and does something else?"

This is very easy with dependent types! For example, in Kind:

I don't think something that specific exists. There are a very large number of formal methods tools, each with different specialties / domains.

For verification with proof assistants, [Software Foundations](https://softwarefoundations.cis.upenn.edu/) and [Concrete Semantics](http://concrete-semantics.org/) are both solid.

For verification via model checking, you can check out [Learn TLA+](https://learntla.com/), and the more theoretical [Specifying Systems](https://lamport.azurewebsites.net/tla/book-02-08-08.pdf).

For more theory, check out [Formal Reasoning About Programs](http://adam.chlipala.net/frap/).

And for general projects look at [F*](https://www.fstar-lang.org/) and [Dafny](https://dafny.org/).

Don't get me wrong, there are times when Microsoft got it right the first time that was technically far superior to their competitors. Windows IOCP was theoretically capable of doing C10K as far back in 1994-95 when there wasn't any hardware support yet and UNIX world was bickering over how to do asynchronous I/O. Years later POSIX came up with select which was a shoddy little shit in comparison. Linux caved in finally only as recently as 2019 and implemented io_uring. Microsoft research has contributed some very interesting things to computer science like Z3 SAT solver and in collaboration with INRIA made languages like F* and Low* for formal specification and verification. But all this dwarfs in comparison to all the harm they did.

Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.

F* is a dependently typed language that can be transpiled to idiomatic C via the KReMLin compiler. It’s very ML-ish to write and you can leave out some proofs. It also has the benefit of being used to write a formally verified TLS implementation that’s in wide use throughout industry.

As I said, dependent types attempt to solve this problem. F* is a language where you can express complex logic as a type. The catch is, these types are checked by an SMT solver. If the solver can satisfy the type checking, then great, and you move on. If it can’t, you have no idea why, and either have to guess or manually write the proof anyway. Contrast this with Standard ML which has a proof of the soundness of its type system.

So kind of like F*? https://www.fstar-lang.org/

F*

Nevermind that academia has come up with far safer ways to do a few things but social norms & inertia prevent their wider adoption (well okay, it also has a barrier to entry in the education required to use it but I don't think someone with the knowledge to meaningfully contribute to an OS kernel can be considered uneducated nor unable to learn).

Maybe that's a little off topic here, but if you like fixing bugs, i suspect you might also enjoy showing that there are no bugs at all. Check out languages like F* https://www.fstar-lang.org/ It's a proof-oriented programming language. You can use it to write code that has no bugs at all. And you once you're done, can convert F* to C or other languages.