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Earley CFG Nullable Left-Recursive Packed Parse Forest
x402
Earley CFG Nullable Left-Recursive Packed Parse Forest is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Runs the Earley parsing algorithm on a supplied word and context-free grammar (supporting nullable and left-recursive rules) to recover recognition status and the complete finite packed parse forest.
Price / call$0.003
Success—
StatusUnknown
How this service works
Recover recognition and the complete finite or cyclic packed parse forest for a supplied word and nullable/left-recursive context-free grammar, rather than LL1 prediction or language-finiteness checks.
Output
Returns the recognition result (whether the input word is accepted) and the complete finite packed parse forest representing all valid parse derivations of the word under the supplied context-free grammar, including support for ambiguous, nullable, and left-recursive grammars.
Example use cases
Ambiguous grammar parse forest recovery
“I have an ambiguous context-free grammar with 4 nonterminals and left-recursive rules, and I want to parse the token sequence ['x','+','x','*','x'] — can you run Earley parsing on it and give me every possible parse tree packed into a forest?”
Nullable grammar recognition verification
“My grammar has nullable nonterminals and I need to verify that the empty word is accepted by it — the grammar has 2 nonterminals, productions [[0],[0,1,0]], starts at 0, and the claim is that it recognizes the empty input. Can you check that claim and return the parse forest?”
Left-recursive CFG correctness check
“I'm building a parser for a left-recursive arithmetic expression grammar with 3 nonterminals and I want to confirm that the string ['num','op','num','op','num'] is in the language — run Earley parsing and show me the full packed parse forest so I can inspect all derivations.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-TD2000-DATASTRUCTURES-10/earley-cfg-nullable-leftrecursive-packed-parse-forest?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need to parse input against a context-free grammar that is nullable, left-recursive, or ambiguous — cases where LL(1), LR, or recursive-descent parsers fail. It is the right choice when you need the complete packed parse forest (all derivations) rather than a single parse tree, and when you cannot restrict your grammar to meet LL or LR constraints.
Side effects
- Invalid grammar encoding (malformed productions array or out-of-range nonterminal indices) returns an error
- Word exceeds maxItems limit of 512 tokens
- Productions array exceeds maxItems limit of 512
- Malformed claim object causes schema validation failure
- Grammar is well-formed but word is not in the language — returns recognition failure with empty forest
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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