LALR

LALR stands for Look-Ahead LR, a family of deterministic parsing algorithms used to recognize context-free languages in compiler design. LALR parsers are commonly generated by tools such as Yacc or Bison and are widely employed to implement the syntax analysis phase of compilers and interpreters. The most common variant is LALR(1), which uses one lookahead token to decide between shifting and reducing actions during parsing.

The construction of an LALR(1) parser begins with building an LR(0) automaton, which represents possible positions within productions. States that share the same core—i.e., the same dotted productions regardless of lookahead—are then merged to form the LALR automaton. The lookahead information from the original LR(1) items is propagated to these merged states, producing a smaller, more compact parsing table than a full canonical LR(1) table while retaining much of the precision needed to resolve conflicts. In effect, LALR(1) combines the efficiency of LR parsing with a reduced table size.

Relation to other parsers: LALR(1) grammars are a subset of LR(1) grammars and typically larger than the class of SLR(1) grammars, since LALR(1) uses more precise lookahead information than SLR. In practice, LALR(1) offers a favorable balance between parsing power and table size, making it the default choice in many practical parser generators. However, there are grammars that are LR(1) but not LALR(1), so LALR is strictly less expressive than full LR(1) in theory.

Applications and limitations: LALR(1) parsers work well for many programming languages and domain-specific languages, but grammar designers may need to adjust rules to avoid rare conflicts that would require a true LR(1) parser or a different parsing strategy.