Parsing methods streamlined

TL;DR

This paper unifies top-down and shift-reduce parsing into a single framework for extended context-free grammars, providing provably correct deterministic and tabular parsing methods, with implementations and theoretical analysis.

Contribution

It introduces a unified minimalist framework for various parsing methods, including new constructions for EBNF ELR(1) parsers and adaptations of LL(1) and Earley parsers.

Findings

Unified parsing framework for top-down and shift-reduce methods

Proof of correctness for new EBNF ELR(1) parser construction

Implementations using deterministic push-down and vector-stack machines

Abstract

This paper has the goals (1) of unifying top-down parsing with shift-reduce parsing to yield a single simple and consistent framework, and (2) of producing provably correct parsing methods, deterministic as well as tabular ones, for extended context-free grammars (EBNF) represented as state-transition networks. Departing from the traditional way of presenting as independent algorithms the deterministic bottom-up LR(1), the top-down LL(1) and the general tabular (Earley) parsers, we unify them in a coherent minimalist framework. We present a simple general construction method for EBNF ELR(1) parsers, where the new category of convergence conflicts is added to the classical shift-reduce and reduce-reduce conflicts; we prove its correctness and show two implementations by deterministic push-down machines and by vector-stack machines, the latter to be also used for Earley parsers. Then the Beatty's theoretical characterization of LL(1) grammars is adapted to derive the extended ELL(1 parsing method, first by minimizing the ELR(1) parser and then by simplifying its state information. Through using the same notations in the ELR(1) case, the extended Earley parser is obtained. Since all the parsers operate on compatible representations, it is feasible to combine them into mixed mode algorithms.