Overview
Operator Precedence Parsing uses operator precedence and associativity rules to decide when to shift or reduce expression parts.
CoreSource checked
Operator Precedence Parsing
Parses expressions by comparing precedence relations between operators.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Parsing
- Difficulty
- Intermediate
- Family
- Expression Parsing
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
parse stateoperator precedencebottom-up reductionexpression parsingtoken streamgrammar rule
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n)
Space
O(n)
When to Use
- Use Operator Precedence Parsing when you need to compare precedence between neighboring operators.
- Use it for expression grammars with inputs like expression tokens.
- Use it when text or tokens must be turned into a reliable structured representation.
- Use it when the Expression Parsing tradeoff is acceptable for the problem size.
When Not to Use
- Avoid it when the grammar is ambiguous or left-recursive in ways the parser cannot handle.
- Avoid it when the required output is not expression tree.
What It Does
- Compares precedence between neighboring operators
- Builds expression structure from precedence decisions
Use Cases
- Expression grammars
- Compiler frontends
- Calculator languages
Inputs
- Expression tokens
- Precedence table
Outputs
- Expression tree
- Syntax error
Pseudocode
- 1.Read tokens with an operator stack
- 2.Compare incoming operator precedence with stack top
- 3.Shift when the incoming operator binds tighter
- 4.Reduce when the stack operator should bind first
- 5.Return the completed expression tree
Canonical Example
- Input
- tokens = ['2', '+', '3', '*', '4']
- Output
- structured expression tree or evaluated result
- Explanation
- Operator Precedence Parsing: The parser uses grammar or precedence rules to recover structure from tokens.
Implementation Notes
- Keep the input contract explicit: Expression tokens; Precedence table.
- Keep tokenization separate from parsing unless the algorithm explicitly combines them.
- Keep lexical analysis separate from parsing unless the method explicitly combines them.
Common Pitfalls
- Pratt parsing is often simpler to implement for the same expression-focused problem.
- Producing unclear errors that do not point to the token or rule that failed.
- Handle empty, invalid, and boundary inputs before trusting expression tree.
- Mixing token positions, character offsets, and grammar states can produce misleading parse errors.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow operators deciding whether to shift or reduce.
Input:ABABABCABAB
Window:ABAB
Step 1 of 5: Read tokens with an operator stack
precedence-reductionsNotes
Operator Precedence Parsing operates in O(n) time and O(n) space within the Expression Parsing family. Often compared with Pratt Parsing and LR Parsing.
Sources (1)
What each reference supports for this entry.
Compilers: Principles, Techniques, and Tools
BookCompiler construction reference for Operator Precedence Parsing grammar transformation, parser construction, or syntax-tree workflow.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toPratt Parsing
Operator-precedence parsing and Pratt parsing are expression parsers with different control structures.
Related Algorithms
Tags
ParsingExpression ParsingBottom-Up Parsing