Statically typed Lua
Please see this Metalua blog post.
-{ extension "types" }
function sum (x :: list(number)) :: number
local acc :: number = 0
for i=1, #x do acc=acc+x[i] end
return acc
end
This is looks like a run-time solution though.
Anyway, feel free to ask your question in Metalua mailing list. If you want to extend Lua syntax, Metalua is the first tool to look at.
P.S. Please never write Lua as all-caps!
This question is six years old... but here's a new answer: http://terralang.org/
Like C, Terra is a simple, statically-typed, compiled language with manual memory management. But unlike C, it is designed from the beginning to interoperate with Lua. Terra functions are first-class Lua values created using the terra keyword. When needed they are JIT-compiled to machine code.
In the summer of 2005 or thereabouts, I worked with an incredibly smart undergraduate student on the problem of doing some compile-time type inference for Lua, possibly assisted by annotations. This problem turns out to be incredibly hard! (My student wrote a short technical note, but it's not really intended for general circulation.)
If I wanted to solve the problem you have posed, with the twin constraints that it allow significant static type checking and that it interoperate with standard bytecode-compiled Lua code, I would design a new language from scratch to satisfy these two constraints. It would be a substantial amount of work but significantly easier than trying to retrofit a type system to Lua.
There is no such thing. It may be possible to extend MetaLua to do this but nobody has done it, and AFAIK, there are no plans to do so. Lua is meant to be a dynamic language, if you want a statically typed language, use one.
What you are essentially looking for is something like Java or C#. In that case, you could use a project like Lua.NET to integrate existing Lua code with C#. There is also Kahlua for Java.