Noncanonical SLR(1) Grammars

Abstract

Two noncanonical extensions of the simple LR(1) (SLR(1)) method are presented, which reduce not only handles but also other phrases of sentential forms. A class of context-free grammars called leftmost SLR(1) (LSLR(1)) is defined by using lookahead symbols which appear in leftmost derivations. This class includes the SLR(1), reflected SMSP, and total precedence grammars as proper subclasses. The class of LSLR(1) languages properly includes the deterministic context-free languages, their reflections, and total precedence languages. By requiring that phrases which have been scanned be reduced as early as possible, a larger class of context-free grammars called noncanonical SLR(1) (NSLR(1)) is defined. The NSLR(1) languages can be recognized deterministically in linear time using a two-stack pushdown automaton. An NSLR(1) parser generator has been implemented. Empirical results show that efficient NSLR(1) parsers can be constructed for some non-LR grammars which generate nondeterministic languages. Applications of the NSLR(1) method to improve the parsing and translation of programming languages are discussed.