The array-language landscape, while fascinating, is confusing to no end. Is there a reason to pick one of J or K or APL or A? None of these options seem to be open-sourced --
To add some more information...
There is an open source version of K
called Kona
https://github.com/kevinlawler/kona
For q/kdb+
, there is a trial version. http://kx.com/download/
The main limitations are 2 hour timeout, 32 bit memory, 3 month license expiration, and the license itself. These shouldn't be too bothersome if you just want to play around and learn something.
Personally, I found q
to be the most user friendly since KX translated the monadic (single argument) verbs from K
into English words and there is a good amount of documentation @ http://code.kx.com. In addition, the database system is extremely well thought out and flexible.