FSharpPlus VS FStar

This should all be prefaced by saying that F# tends to avoid such category theory generalizations (unless you're using a library such as F#+ ). So, while I would encourage your continued understanding of the theory (it can be fun!), it's not as practical for writing good F# code as it would be in, say, Haskell. There are no type classes in Haskell, nor are there plans to add them.

There maybe be a way to make it not have overhead. But there is precedent that this is not the case with Statically Resolved Type Parameters, and existing mechanism in F# that already lets you encode Haskell-style typeclasses and is the backbone of FSharpPlus, a typelevel (and more) library for F#. Solving constraints like this at compile-time (as opposed to having a runtime natively understand them) absolutely, positively leads to explosive compile times if you're not careful. I worked on the F# compiler for 5 years and I can attest to numerous reports related to accidental compile-time explosions just because SRTPs or inline was used a particular way.

F# devs tend to use SRTP (Statically resolved type parameters) see F#+ https://github.com/fsprojects/FSharpPlus .

F#+ (FSharpPlus) 1.2 released with the following changes:

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.