LR Parser

LR Parser

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 acronym. 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 reversed Rightmost derivation; 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 slower methods. Other parser methods that backtrack or yield multiple parses may take O(n2) or O(n3) time when they guess badly.

The above properties of L, R, and k are actually shared by all shift-reduce parsers, including precedence parsers. But by convention, the LR name stands for the form of parsing invented by Donald Knuth, and excludes the earlier, less powerful precedence methods. LR parsers can handle a larger range of languages and grammars than precedence parsers or top-down LL parsing. This is because the LR parser waits until it has seen an entire instance of some grammar pattern before committing to what it has found. An LL parser has to decide or guess what it is seeing much sooner, when it has only seen the leftmost input symbol of that pattern. LR is also better at error reporting. It detects syntax errors as early in the input stream as possible.