LR(k)

In computer science, LR parsers are a type of bottom-up parsers that efficiently handle deterministic context-free languages in guaranteed linear time. The LALR parsers and the SLR parsers are common variants of LR parsers. LR parsers are often mechanically generated from a formal grammar for the language by a parser generator tool. They are very widely used for the processing of computer languages, more than other kinds of generated parsers.

The name LR is an initialism. The L means that the parser reads input text in one direction without backing up; that direction is typically Left to right within each line, and top to bottom across the lines of the full input file. (This is true for most parsers.) The R means that the parser produces a Rightmost derivation in reverse: it does a bottom-up parse - not a top-down LL parse or ad-hoc parse. The name LR is often followed by a numeric qualifier, as in LR(1) or sometimes LR(k). To avoid backtracking or guessing, the LR parser is allowed to peek ahead at k lookahead input symbols before deciding how to parse earlier symbols. Typically k is 1 and is not mentioned. The name LR is often preceded by other qualifiers, as in SLR and LALR.

LR parsers are deterministic; they produce a single correct parse without guesswork or backtracking, in linear time. This is ideal for computer languages, but LR parsers are not suited for human languages which need more flexible but inevitably slower methods. Some methods which can parse arbitrary context-free grammars (e.g., Cocke-Younger-Kasami, Earley, GLR) have worst-case performance of O(n³) time. Other methods which backtrack or yield multiple parses may even take exponential time when they guess badly.

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