I quite liked this description of J from The Encyclopedia of Computer Languages:

A very high-level general-purpose language, partially derivative and partially 
a rethink of APL, with strong emphasis on functional programming and array 
processing. 

Purely functional with lexical scope and more conventional control structures, 
plus several new concepts such as function rank and function arrays. 

J was designed and developed by Ken Iverson and Roger Hui, and implemented by 
Iverson Software Inc.(ISI). J is distinguished by it's simple and consistent 
rules, a large set of built-in functions, powerful facilities for defining new 
operations, and a general and systematic treatment of arrays. It is ideal for 
complex analytical work, modeling, and RAD ( Rapid Application Development).

http://hopl.murdoch.edu.au/showlanguage.prx?exp=1558&language=J


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