I wrote a rather basic J-ish interpreter, but it was understand the mindset of the language, rather than to have a practical implementation. (I don't think I have it anymore, but it was only about two pages of Lua.) To do it well, real experience with J/K/APL would probably be necessary. It wouldn't need to be absolutely compatible with K, just a similar language.

FWIW, there's A+ (http://www.aplusdev.org/), but I would far rather stick to the ASCII character set.

* http://www.jsoftware.com/jwiki/Essays/Incunabulum

The source to Mr Whitney's prior language, A+, is available.

I know a guy who wrote an open mostly Q interpreter. KX Systems did not appreciate it very much.