ground_truth_schema.md

semantic_lean_errors Schema

This file documents the schema of the exported semantic_lean_errors.jsonl and semantic_lean_errors.json files. Both files contain the same records.

• semantic_lean_errors.jsonl stores one record per line.
• semantic_lean_errors.json stores the same records as a pretty-printed JSON array.

Record Format

Each record is one labeled NL/Lean pair.

Fields:

• id (string)
  • Stable example identifier.
• source (string)
  • Source benchmark: one of FormalMath, ProofNet, ProverBench, CombiBench.
• problem_nl (string)
  • Natural-language problem statement.
• lean_code (string)
  • Canonical Lean statement being judged.
• expected_verdict (string)
  • Row-level binary label.
  • YES means the row contains a semantic error.
  • NO means the row is a clean example.
• error_primary (string or null)
  • Primary semantic error category.
  • Null for clean examples.
• error_secondary (array[string])
  • Optional secondary semantic categories.
• error_tags (array[string])
  • Detail tags refining the error type.
• meta_tags (array[string])
  • Optional non-prompt metadata tags.
• gold_explanation (string)
  • Human-written explanation of the label.

Primary Categories

The dataset uses six primary semantic-error categories:

• problem_statement_error
• specification_error
• formalization_error
• domain_mismatch
• definition_mismatch
• quantifier_indexing_mismatch

See error_tags.md for category definitions, boundaries, and detail-tag guidance.

Label Semantics

Two label views are represented in the export:

1. Binary row-level view

• Use expected_verdict.
• YES = some semantic error is present.
• NO = clean example.

2. Category-specific view

• Use error_primary.
• In the current 6-category evaluation, a category prompt expects YES iff error_primary equals the queried category; otherwise NO.

Normalization Policy

This exported release is intentionally normalized:

• lean_code is the single canonical code field.
• ProofNet examples are normalized from original_lean_code to lean_code.
• fixed_lean_code and lean_code_fixed are not included in this release bundle.
• error_secondary, error_tags, and meta_tags are always lists.

Example

{
  "id": "example_id",
  "source": "FormalMath",
  "problem_nl": "...",
  "lean_code": "theorem ... := by",
  "expected_verdict": "YES",
  "error_primary": "definition_mismatch",
  "error_secondary": [],
  "error_tags": ["wrong_operator"],
  "meta_tags": [],
  "gold_explanation": "The Lean operator does not match the intended informal notion."
}