LALR parsers

In computer science, an LALR parser or Look-Ahead LR parser is a simplified version of a canonical LR parser, to parse (separate and analyze) a text according to a set of production rules specified by a formal grammar for a computer language. ("LR" means left-to-right, rightmost derivation.)

The LALR parser was invented by Frank DeRemer in his 1969 PhD dissertation, Practical Translators for LR(k) languages, in his treatment of the practical difficulties at that time of implementing LR(1) parsers. He showed that the LALR parser has more language recognition power than the LR(0) parser, while requiring the same number of states as the LR(0) parser for a language that can be recognized by both parsers. This makes the LALR parser a memory-efficient alternative to the LR(1) parser for languages that are LALR. It was also proved that there exist LR(1) languages that are not LALR. Despite this weakness, the power of the LALR parser is enough for many mainstream computer languages, including Java, though the reference grammars for many languages fail to be LALR due to being ambiguous.

The original dissertation gave no algorithm for constructing such a parser given some formal grammar. The first algorithms for LALR parser generation were published in 1973. In 1982, DeRemer and Tom Pennello published an algorithm that generated highly memory-efficient LALR parsers. LALR parsers can be automatically generated from some grammar by an LALR parser generator such as Yacc or GNU Bison. The automatically generated code may be augmented by hand-written code to augment the power of the resulting parser.

In 1965, Donald Knuth invented the LR parser (Left to Right, Rightmost derivation). The LR parser can recognize any deterministic context-free language in linear-bounded time. Rightmost derivation has very large memory requirements and implementing an LR parser was impractical due to the limited memory of computers at that time. To address this shortcoming, in 1969, Frank DeRemer proposed two simplified versions of the LR parser, namely the Look-Ahead LR (LALR) and the Simple LR parser that had much lower memory requirements at the cost of less language-recognition power, with the LALR parser being the most-powerful alternative. In 1977, memory optimizations for the LR parser were invented but still the LR parser was less memory-efficient than the simplified alternatives.

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