Agda VS tl

This was recently deemed inappropriate:

"Bye bye Set"

"Set and Prop are removed as keywords"

https://github.com/agda/agda/pull/4629

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.

Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool.

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.

Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?

That's absolutely untrue. From the horse's mouth:

Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda

Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.

Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.

it's based off MIR, does it have something to do with https://mlir.llvm.org/ ?

for typed lua, there is another effort https://github.com/teal-language/tl in addition to the mentioned typescript approach: https://github.com/andremm/typedlua

I had the pleasure of working with Lua 5.1 back in the late noughties. For me it's replaced Tcl whenever I want something I can configure above a C library. At the time I used it I found it quite nice but I'll also not forget the hours I wasted tracking down nil table corruptions which could have easily been caught by a type checker.

I had some hope that Luau https://luau-lang.org or Teal https://github.com/teal-language/tl would make things better but with the following example

    function foo(x: number): string

I wonder why the author doesn't use Teal [0] - a typed dialect of lua.

[O] https://github.com/teal-language/tl

Check out Teal

There is already https://github.com/teal-language/tl, which is typed Lua. I think fennel exists to serve a different niche-- personally I use it not for any type features; I just like the syntax better, and others may find certain features like the macro system useful.

There's also some languages made to compile straight to Lua: - MoonScript is the most popular Lua wrapper - it's built to be more Python-like, featuring indentation-based scopes, function calls without parentheses, lambda syntax, list comprehension, and much more. - Yuescript is a modern update to MoonScript that adds more features (I haven't used it myself, so I'm not entirely sure exactly how it differs from MS). - Teal is a version of Lua that adds static typing for better code standards.

Terra and Nelua are both very different in goals than Teal. Teal is literally gradual types integrated into Lua keeping as many of Lua's idioms as possible (to a fault[1]). Terra and Nelua are both very metaprogrammable systems programming languages. Nelua's goals are primarily to soften C's rough edges, comparable to something like Nim.

There's another one you missed in Pallene[2]. But again, it's goal was to optimize the stack sharing involved in using the C API. It also adds types though and maintains Lua idioms as much as possible.

[1]: https://github.com/teal-language/tl/discussions/339

[2]: https://github.com/pallene-lang/pallene