During a meeting in Toronto last winter, Mike Jenkins, Bob Bernecky and I were discussing how the two existing theories on arrays influenced or were in fluenced by programming languages and systems. More's Army Theory was the basis for NIAL and APL2 and Mullin's A Mathematics of A rmys(MOA), is being used as an algebra of arrays in functional and A-calculus based pro gramming languages. MOA was influenced by Iverson's initial and extended algebra, the foundations for APL and J respectively. We discussed that there is a lot of interest in the Computer Science and Engineering communities...