CoreSource checked

Parser Combinators

Builds parsers by composing small parser functions into larger grammar rules.

Explore relationships Open constellationBrowse atlas

Quick Facts

Compact metadata for implementation and discovery.

Category: Parsing
Difficulty: Intermediate
Family: Composable Parsing
Tier: Core
Status: Verified
Review: Source Checked
Sources: 2
Formulas: 1
Relationships: 1
Code example: Ready
Visualization: Ready

Overview

Parser combinators represent grammar pieces as functions that can be sequenced, alternated, repeated, and transformed directly in code.

Core Concepts

parser functioncompositionbacktrackinggrammar rule

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n)

Average

O(n * rules)

Worst

O(exponential)

Space

O(parse state)

When to Use

Use when language parsing needs parser function.
Use when the input matches the assumptions behind composable 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 parsers by composing small parser functions into larger grammar rules
Uses parser function and composition 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)

Sequence combinator

parse(A then B) = parse(B, parse(A, input).rest)

parse(A then B) = parse(B, parse(A, input).rest)

Runs the second parser on the remaining input from the first parser.

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: Parser Combinators applies parser function to produce parse tree.

Implementation Notes

Report errors with token position and expected grammar symbols.
Keep the parser function 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 Alignment

Show 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-mechanism

Notes

Parser Combinators should be used with the assumptions and tradeoffs of composable Parsing in mind.

Sources (2)

What each reference supports for this entry.

Parsing Techniques

Book

Parsing reference for Parser Combinators's control flow, grammar assumptions, and parser construction tradeoffs.

Open source

Monadic Parsing in Haskell

Paper

Specific reference for parser combinators as first-class parsers with sequencing, choice, repetition, and monadic composition.