A processor includes an internal memory and processing circuitry. The internal memory is configured to store a definition of a multi-dimensional array stored in an external memory, and indices that specify elements of the multi-dimensional array in terms of multi-dimensional coordinates of the elements within the array. The processing circuitry is configured to execute instructions in accordance with an Instruction Set Architecture (ISA) defined for the processor. At least some of the instructions in the ISA access the multi-dimensional array by operating on the multi-dimensional coordinates specified in the indices.