Overview
LALR parsing keeps much of LR parsing's power while reducing table size, which made it common in parser generators.
CoreSource checked
LALR Parsing
Builds compact LR-style parse tables by merging states with the same cores.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Parsing
- Difficulty
- Advanced
- Family
- Bottom-Up Parsing
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
lr item corelookahead setparse tableshift-reduce action
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n)
Space
O(parse table)
When to Use
- Use when language parsing needs lr item core.
- Use when the input matches the assumptions behind bottom-Up Parsing.
When Not to Use
- Avoid when the grammar class does not match the parser's assumptions.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Builds compact LR-style parse tables by merging states with the same cores
- Uses lr item core and lookahead set to guide the work.
- Produces parse tree.
Use Cases
- Language parsing
- Compiler front ends
- Structured text processing
Inputs
- Tokens or grammar
- Parser state
Outputs
- Parse tree
- Automaton
- Grammar table or parse result
Key Formulas (1)
State merge rule
merge states when LR(0) cores match
merge states when LR(0) cores matchCombines compatible LR states while preserving lookahead actions.
Pseudocode
- 1.Prepare tokens, grammar rules, tables, or automaton states
- 2.Advance through tokens or grammar items according to the parsing rule
- 3.Create parse nodes, state transitions, or table entries when a rule applies
- 4.Report an error or return the completed structure
Canonical Example
- Input
- tokens = ['id', '+', 'id', '*', 'id'] with a tiny grammar or precedence table
- Output
- Parse tree
- Explanation
- LALR Parsing applies lr item core to produce parse tree.
Implementation Notes
- Report errors with token position and expected grammar symbols.
- Keep the lr item core step separate enough to test independently.
- Keep lexical analysis separate from parsing unless the method explicitly combines them.
Common Pitfalls
- Ambiguity and left recursion must be handled according to the parser type.
- Test edge cases, not only clean examples.
- Mixing token positions, character offsets, and grammar states can produce misleading parse errors.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow grammar items, parser states, and consumed input as parsing progresses.
Input:ABABABCABAB
Window:ABAB
Step 1 of 4: Prepare tokens, grammar rules, tables, or automaton states
parsing-mechanismNotes
LALR Parsing should be used with the assumptions and tradeoffs of bottom-Up Parsing in mind.
Sources (2)
What each reference supports for this entry.
Compilers: Principles, Techniques, and Tools
BookCompiler textbook support for LALR Parsing's grammar analysis, parser construction, and implementation constraints.
Practical Translators for LR(k) Languages
PaperSpecific reference for practical LR-family parser construction and state merging used by LALR parsing.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageVariant ofLR Parsing
LALR parsing merges LR item sets to reduce parse table size.
Related Algorithms
Tags
ParsingBottom-Up ParsingGrammarParser Generator