Abstract
The paper is the first in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. An LR(k) parser of a context-free grammar is treated as a formal system where the derivations are reversals of rightmost derivations in the grammar. Deriving in the system is possible if and only if a corresponding reduction by the conventional LR(k) parser may occur. This general approach establishes a mathematical treatment of LR(k) parsing which does not rely on the actual construction of an LR(k) parser. For example, the approach allows a decisive comparison of properties of different LR(k) parsers, such as canonical LR(k), LALR(k) and SLR(k) parsers, as well as those optimized by the so-called default reductions.
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