Index Ranges for Matrix Calculi The paper describes a scheme for symbolic manipulation of index expressions which arise as a by-product of the symbolic manipulation of expressions in the matrix calculi described by the authors in a previous paper. This scheme attempts program optimization by transforming the original algorithm rather than the machine code. The goal is to automatically generate code for handling the tedious address calculations necessitated by complicated data structures. The paper is therefore preoccupied with "indexing by position." The relationship of "indexing by name" and "indexing by position" is discussed. CACM December, 1972 Bayer, R. Witzgall, C. address calculations, algorithm transformation, compilation, data structures, indexing by name, indexing by position, index domain, index map, index range, matrix expressions, normal form, programming languages, program optimization, range operations, symbolic manipulation, syntactic analysis, well-formed expressions 4.12 4.22 5.14 CA721202 JB January 27, 1978 1:12 PM 1614 4 2253 2253 4 2253 2253 4 2253 2254 4 2253 2557 4 2253 2081 5 2253 2253 5 2253 2253 5 2253 2253 5 2253 437 5 2253