coq VS kok.nvim

The page summarizing the considered new names and their pros/cons is interesting: https://github.com/coq/coq/wiki/Alternative-names

Naming is hard...

Are those more important than, say:

- Proven with Coq, a formal proof management system: https://coq.inria.fr/

See in the real world: https://aws.amazon.com/security/provable-security/

And check out Computer-Aided Verification (CAV).

To be ruthlessly, uselessly pedantic - after all, we're mathematicians - there's reasonable definitions of "academic" where logical unsoundness is still academic if it never interfered with the reasoning behind any proofs of interest ;)

But: so long as we're accepting that unsoundness in your checker or its underlying theory are intrinsically deal breakers, there's definitely a long history of this, perhaps more somewhat more relevant than the HM example, since no proof checkers of note, AFAIK, have incorporated mutation into their type theory.

For one thing, the implementation can very easily have bugs. Coq itself certainly has had soundness bugs occasionally [0]. I'm sure Agda, Lean, Idris, etc. have too, but I've followed them less closely.

But even the underlying mathematics have been tricky. Girard's Paradox broke Martin-Löf's type theory, which is why in these dependently typed proof assistants you have to deal with the bizarre "Tower of Universes"; and Girard's Paradox is an analogue of Russell's Paradox which broke more naive set theories. And then Russell himself and his system of universal mathematics was very famously struck down by Gödel.

But we've definitely gotten it right this time...

[0] https://github.com/coq/coq/issues/4294

Dafny and Whiley are two examples with explicit verification support. Idris and other dependently typed languages should all be rich enough to express the required predicate but might not necessarily be able to accept a reasonable implementation as proof. Isabelle, Lean, Coq, and other theorem provers definitely can express the capability but aren't going to churn out much in the way of executable programs; they're more useful to guide an implementation in a more practical functional language but then the proof is separated from the implementation, and you could also use tools like TLA+.

https://dafny.org/

https://whiley.org/

https://www.idris-lang.org/

https://isabelle.in.tum.de/

https://leanprover.github.io/

https://coq.inria.fr/

http://lamport.azurewebsites.net/tla/tla.html

Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.

What ever happened to the effort [1] to rename Coq in order to make it less offensive? There were a number of excellent proposals [2] that seemed to die on the vine.

[1] https://github.com/coq/coq/wiki/Alternative-names

[2] https://github.com/coq/coq/wiki/Alternative-names#c%E1%B5%A3...

Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq

This type of thing can help you formally verify code.

So, if your proof is correct, and your description of the (language/CPU) is correct, you can prove the code does what you think it does.

Formal proof systems are still growing up, though, and they are still pretty hard to use. See Coq for an introduction: https://coq.inria.fr/

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.

In the examples listed on this page https://github.com/ms-jpq/coq_nvim, there is a pattern overlay over the whole screen. Is there a neovim plugin that does this? Thanks.

nvim-cmp or coq_nvim is for autocompletion. Treesitter is for parsing language syntax. (I guess the most typical use case for this would be syntax highlighting.) Note that (neo)vim also has built in manual completion that you can use by setting up your omnifunc and triggering it with in insert mode .

Aw man that's not nice to hear. I have had my own struggle with lsp not gonna lie. I used to use coc until it got too slow, after struggling for like 2 days lol lsp is working fast and neat. I'd suggest you to take a look at coq https://github.com/ms-jpq/coq_nvim which claims to be fast as fuck (literally lol) and also claims to be faster than lsp (because its written using c or something). Haven't tried it personally

Coq_nvim

I'm attempting to use (coq_nvim)[https://github.com/ms-jpq/coq_nvim]. This is my config:

Does your coq_nvim and nvim-lspconfig really load? Because they have opts = true

I'd be happy for someone who knows more about this to correct me. But in my experience as well, nvim-cmp is not as good completion as vscode, its suggestions can be all over the place sometimes. I found that coq_nvim tends to better in this regard. I still prefer nvim-cmp for other reasons but you should definitely try coq_nvim out and see if you have a better experience.

Coq_nvim isn't the same as Coc.nvim. Coq is a completion plugin with lots of caching written in Python that works alongside the builtin LSP. Coc is an LSP client (and has it's own plugin ecosystem) written in Node.

There are some like https://github.com/SirVer/ultisnips and https://github.com/ms-jpq/coq_nvim. Speed is not really an issue, I guess people just prefer to have fewer dependencies and use lua which is already bundled in neovim.

Maybe using coq.nvim instead of nvim-cmp could help (?) dince it caches the LSP responses. I haven't test it, though