Multipass precedence analysis

TLDR: A hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family.

Abstract: This paper defines a hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family. The hierarchy is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family. The families of the hierarchy have properties analogous to those of the context free family, in particular, the new mechanism introduced is very suitable for parsing. A language in the n-th family is specified by a sequence of n -- 1 labeled linear grammars and a context free grammar. By assuming that the reversals of the first n -- 1 grammars and the last labeled linear grammar are precedence grammars, the concepts and parsing algorithm of Wirth and Weber extend to yield a parsing algorithm within the hierarchy. This considerably enhances the usefulness of the construction and allows much of the power of the context sensitive languages to become accessible in measured amounts for potential programming applications.