Hi, Teal creator here!

> How confident are you in the soundness of the type system?

I am confident it is not sound! That is by design. A typical example is how function arguments are bivariant, to allow for callbacks expressed the way programmers usually expect them to work (TypeScript does something similar).

> Also, are there any Lua constructs that are difficult/impossible to type?

Yes, many of them. The type system and the compiler are pragmatically very simple -- there are many design decisions made to favor simplicity of specification and/or implementation. (Compare the single-file, single-pass Teal compiler done mostly by a single person with the amount of engineering resources that Microsoft has put into TypeScript.) For a concrete example, we have special-cased polymorphism for functions, intended to use with very dynamically-typed Lua functions from the broader Lua ecosystem, but you cannot express similar polymorphism in Teal itself.

> Is type checking decidable? (Is the type system Turing complete?)

There is a proof (which I can't find right now) that type checking is not decidable once you combine parametric polymorphism (generics) and intersection types (like the poly functions I mentioned above), but the forms of these features supported by Teal have some restrictions which make me not extend such claims directly. And of course, I can't even claim that the implementation of the theoretical model is bug-free. The model is evolving, the implementation always lags a bit behind.

In any case, the goal for Teal's type system is not academic purity, but pragmatic utility. Other comments in this thread alluded to this as well -- there are practical constraints that come from targeting an existing language and ecosystem. Of course, there are many ways one can approach such challanges. Teal is one of them and there were and are certainly others! Everyone is free to take their shot at where they want to be in the Unix-Philosophy/Worse-is-Better vs. Lisp-Philosophy/The-Right-Thing design gradient.