Arrays, Functional Languages, and Parallel Systems

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.