Direct-access storage functions, as usually applied to the implementation of arrays,
may be useful in many other cases as well. The theory developed here provides a
general method for the effective construction of a one-to-one mapping from a given
set of keywords onto an interval of contiguous relative addresses. This mapping is
based on a specific ordering of the keywords. A general index formula is derived
which represents this mapping. The index formula is interpreted by means of the
finite-state acceptor which accepts the set of keywords. Several examples show how
this theory can be applied to the derivation of direct-access storage formulas.