1. A method of generating nested addressing sequences for accessing a multidimensional data array in response to an array transformation of a high-level programming language comprising the steps of: generating a plurality of multidimensional indices specified by a least one pair of displacement and length parameters of said array transformation relative to an initial reference point parameter of said array transformation; translating said multidimensional indices into said nested addressing sequences for serially addressing all elements of said data array located in a memory means specified by said array transformation; controlling the generating of said multidimensional indices and the translating of said indices to said nested addressing sequences in accordance with each pair of said displacement and length parameters with signals from a unified control means; and providing said array transformation parameters to said address generator over a bus means in the form of a displacement control word and a length control word.