Kind VS tlaplus

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:

```

https://github.com/tlaplus/tlaplus/blob/master/tlatools/org....

In any case, our whole team thinks TLA is great, and we're happy people like you and Ron find it so useful and insightful. We also think it is a very insightful.

There are no tests! There are various ways to test concurrent data structures. You could use a stress test, where you spawn a lot of threads and let them mutate the map in a random way and then check the consistency of the map and some invariants. You could learn TLA+ and write a formal model of the map and then verify it.

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

I wish something like Lamport's TLA+ (https://lamport.azurewebsites.net/tla/tla.html) was supported in modern language compilers - perhaps with annotations/macros and a mini formal DSL.

Checking the invariant with assert is also useful in my limited experience with concurrency.

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

One advantage of formal methods is in determining "what was expected" (including all the goofy edge cases) without having to burrow into the details of code.

Take a look at Alloy (http://alloytools.org/) and TLA+ (https://lamport.azurewebsites.net/tla/tla.html) for example. (Or even the ancient Z ("Zed") notation (https://www.cs.cmu.edu/~15819/zedbook.pdf)).

The pcal generator does *not* generate a definition for the set of labels. However, some users have suggested to add such a feature: https://github.com/tlaplus/tlaplus/issues/613