Two level grammars: CF-grammars with equation schemes

Abstract

The paper gives another understanding of the two-level grammar formalism: any two-level grammar can be splitted into two parts — a context-free "syntax" and an equational "semantics". It has been shown that in the case of a repetition-free and regular based two-level grammar one can always solve the equations assigned to each derivation of the resulting CF grammar. This suggests an approach to the parsing problem of two-level grammars based on well known methods for CF grammars and the algorithm presented. The approach may occur efficient however, only if some restrictions are imposed on two-level grammars. One sort of restrictions we have discussed in the paper (repetition-free and regular based grammars). Others should result from the requirements of programming languages. For example, one obvious requirement is that two-level grammars should be (semanticaly) unambiguous, i.e., here — in terms of the corresponding CF grammars and equations — that each set of equations has at most one solution.

It could be promising to experiment with (fragments of) ALGOL 68 in order to better understand the described method, its complexity and feasibility with respect to the two-level programming language definitions.