Generating parsers for BNF grammars

Abstract

The procedure described herein is in essence an extension, albeit a simplification, of the work Earley which in turn was based on Evans, Feldman, Floyd, and Standish. For a large subset of grammars, the procedure maps the Backus Naur Form (BNF) definition of the grammar of a language into a deterministic, left-to-right parser for the sentences in that language. It is shown below that the procedure by design, covers all bounded right context grammars and, as a by-product, some LR(k) grammars which are not bounded right context. See Knuth for the definitions of these classes of grammars. If two parameters are incorporated a priori into the procedure, one limiting the look-back and the other limiting the look-ahead capabilities of the parser to be generated, an algorithm results. For each BNF grammar G the algorithm either rejects G as not bounded right context for the specified limits or it generates a parser for G.