Continued from my last post, I think I will be in the neutral point of view enough to do the analysis for these claims. All of this analysis are solely based on my opinion, so discussion is always welcome.
It is possible to write a statically typed compiler for Groovy keeping all goodies of the beautiful language.This is partially true. I do not think I can create a static compiler to cover all Groovy features at once.
It is possible to implement very powerful type inference of local variable and closures, so we don't need to provide verbose type information more than necessary and/or useful for documentation purposes.This is partially true. A language cannot fully support type inference. Type inference itself has its own limits, and it is a known P-complete or NP-complete problem depending on its implementation) [see this].
It is possibly to have compile-time metagrogramming (properies, categories, default groovy methods, mixins, ast transformations - all but runtime meta-programmings).This is also true. But adding more phases to the compiler will make it slow. When the compilation time is slow + startup time of the JVM, you might not be happy using the language as a scripting tool. Pluggable type systems would be possible to help this issue.
It is possible to support Scala-like traits (also knows as interfaces with default implementation), which is extremly strong meta-programming tool.This is true. No doubt.
It is even possibly to compile piece of code in so called mixed mode (resolve and call statically what we can and call the rest dynamically). This mode is great for example for mixing computation with building markup or populating UI elements with results of computation.This is true. There is also something called Soft typing and Gradual typing which could help one archieve both static and dynamic call in the same language. However, the way of building markup can be just a simpler trick. I have it in my last post.
It is even possibly that because of type inference staticly compiled code can be a little bit less verbose compare to Groovy (almost no need in 'as' conversion for example).This is probably false. In general, I do not think there will be a better way than a dynamic language to do so.