Phrase Parsers from Multi-Axiom Grammars

The multi-axiom grammars (MAG) are alternatives to the single-axiom context free grammars (CFG) and all-axiom algebraic grammars (AG) for programming language speci cation. Neither phrase recognition nor algebraic mechanisms for language processing are supported by CFGs. AGs support algebraic mechanisms for language processing but specify a smaller class of languages. MAGs avoid these limitations. This paper describes a new parsing algorithm developed on this basis which recognizes any phrase in the language. Moreover, it does so by distributing the parsing task among a collection of smaller parsers which handle well-de ned layers of the language in a piping manner. These language-layers are determined by the algebraic properties of the MAGs and are described in the paper. Basic de nitions are given for multi-axiom grammar and language as well as for algebraic notions of subgrammar, primitive subgrammar, quotient grammar, and grammar/language layer. Algorithms are described to stratify a programming language into a hierarchy of layers, to construct parsers for each layer analogous to LR construction, and to accomplish the overall task of multi-layered parsing in pipeline fashion based on a tokenization which occurs between the language layers. This pipeline parallel process is a model for high speed, left-to-right language translation.