coq VS devd

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.

Your technique is one I would turn towards as a developer who understands HTML/CSS flow so much better than I do any typesetting tool. I actually use a very similar technique for managing my CV and generating invoices for clients; I have a little "static site" generator I've written that takes JSON, throws it through a templating engine, and spits out HTML files. I then host a server in the output folder and print-to-pdf directly from there. This approach seems quite rare; I don't think enough people appreciate just how flexible CSS is or its support for common print-related tasks.

There are plenty of solutions to that specific problem. Nowadays, I only work on Nuxt/Next/Astro projects that come with hot reload out of the box so I don't have a need for it anymore, but I have used https://github.com/cortesi/devd a lot in the past, with much success.

A no-install solution would be to use the "workspace" feature of Chrome's Dev Tools:

1. Open your .html file in Chrome.

2. Open the Dev Tools.

3. In the "Sources" tab, activate the "Filesystem" sub-tab.

4. Click on "+ Add folder to workspace" and choose the directory containing your .html and .css files.

5. Edit the .css file with autocompletion and live preview.

6. Save your work so that it is synchronized with your filesystem.

In action: https://i.imgur.com/slcSt9X.gif

Try https://github.com/cortesi/devd

This pair of tools do both front-end and back-end live reloading with a small amount of config: https://github.com/cortesi/modd https://github.com/cortesi/devd

In tandem with https://github.com/cortesi/devd I've found it a good setup for web development.

Modd watches file changes and rebuilds, while Devd enables livereload, letting me make changes in my text editor and then see the rendered changes in the browser, side-by-side, in near real-time.

This is for go web development but I'm pretty sure these two tools are language-agnostic.

My favourite is https://github.com/cortesi/devd