Psi, the Indexing Function: a basis for FFP with arrays

An array of arbitary components can be viewed as a variable whose value is a function from subscripts into its components[17]. The subscripts(or indices) of a 1-dimensional array are related to the system of integers, more precisely the natural numbers, which play an important role in the theory of groups. A Mathematics of Arrays(MOA)[13]_builds upon these ideas to construct permutation and transformation groups into a calculus of n-dimensional arrays with the Psi function as the fundamental building block. We propose that this calculus provide a basis for Formal Functional Programming(FFP)[2]_with arrays for parallel architectures.