The handling of multiway tables on computers

A notation is proposed which concisely describes many forms of table manipulation in terms of a concept called scanning. Methods of programming a scanning subroutine are discussed and examples are given of the use of the scanning notation to formulate typical table operations in symbolic form. It is often convenient to store marginal values (usually totals or means) with the main table, and this requires some modification of the notation and the subroutine. Proposals are outlined for inclusion of scanning facilities in automatic programming languages and examples are given of the form this could take in a language related to the Mercury Autocode compiler.