On constructing LL(k) parsers

Abstract

A method for constructing canonical LL(k) parsers for context-free grammars is presented. This method can be regarded as a dual of the well-known LR(k) parser construction technique involving so-called LR(k) items and viable prefixes. The counterparts of LR(k) items and viable prefixes are called LL(k) items and viable suffixes, respectively. Modifications of the basic method give rise to subclasses of the canonical LL(k) grammars corresponding to the LALR(k) and SLR(k) grammars. The duals of LALR(k) grammars are called LALL(k) grammars and they form a proper subclass of the canonical LL(k) grammars when k>1. The duals of SLR(k) grammars, called SLL(k) grammars, in turn coincide with the so-called strong LL(k) grammars and form a proper subclass of the LALL(k) grammars when k>1.