README.md

metadata

license: apache-2.0

Example Entry

An entry in the miniCTX dataset consists of the theorem statement, preceding file contents, and metadata information. For example, given the following theorem s_eq_pow_two in context:

import Mathlib.Data.Real.Basic

/-!
# Square function
We define the squaring function `s : ℝ → ℝ` to be `s x := x * x`.
-/

def s (x : ℝ) : ℝ := x * x

lemma s_eq_pow_two {x : ℝ} : s x = x ^ 2 := by
  rw [s, pow_two]

The problem is formatted in JSON as follows:

{
  "srcContext": "import Mathlib.Data.Real.Basic\n\n/-!\n# Square function\nWe define the squaring function `s : ℝ → ℝ` to be `s x := x * x`.\n-/\n\ndef s (x : ℝ) : ℝ := x * x\n\n",
  "theoremStatement": "lemma s_eq_pow_two {x : ℝ} : s x = x ^ 2",
  "theoremName": "s_eq_pow_two",
  "fileCreated": "(git commit)",
  "theoremCreated": "(git commit)",
  "file": "(file name)",
  "positionMetadata": {
    "lineInFile": 10,
    "tokenPositionInFile": 152,
    "theoremPositionInFile": 1
  },
  "dependencyMetadata": {
    "inFilePremises": true,
    "repositoryPremises": false
  },
  "proofMetadata": {
    "hasProof": true,
    "proof": "by\n  rw [s, pow_two]",
    "proofType": "tactic",
    "proofLengthLines": 2,
    "proofLengthTokens": 20
  }
}

Description of Each Entry

• srcContext: The context of the source file preceding the theorem, including imports and relevant definitions. This provides necessary background to understand the theorem.
• theoremStatement: The statement of the theorem being proved.
• theoremName: The name of the theorem.
• fileCreated: The git commit hash indicating when the file was created.
• theoremCreated: The git commit hash indicating when the theorem was added.
• file: The name of the file containing the theorem.
• positionMetadata:
  • lineInFile: The line number in the file where the theorem is located.
  • tokenPositionInFile: The number of tokens in the file before the theorem starts.
  • theoremPositionInFile: The number of premises (definitions, theorems) before the theorem in the file.
• dependencyMetadata:
  • inFilePremises: Indicates whether the theorem uses definitions or lemmas defined in the same file.
  • repositoryPremises: Indicates whether the theorem uses definitions or lemmas defined in another file within the same repository.
• proofMetadata:
  • hasProof: Indicates whether the theorem has a proof.
  • proof: The proof of the theorem.
  • proofType: The type of proof, term proof or tactic proof.
  • proofLengthLines: The length of the proof in lines.
  • proofLengthTokens: The length of the proof in tokens.

In addition to individual entries, we also provide the link and git commit version of each split for evaluation:

• PrimeNumberTheoremAnd: https://github.com/AlexKontorovich/PrimeNumberTheoremAnd, commit 23650db830a45c227bd85d25d520725545192333
• PFR: https://github.com/teorth/pfr, commit 6aeed6ddf7dd02470b3196e44527a6f3d32e54cf
• Mathlib: https://github.com/leanprover-community/mathlib4, commit f4b4298bd76b82f7b28f0fb6b5ab92bdf5e5634d
• HTPI: We use the fork https://github.com/hanwenzhu/HTPILeanPackage4.7, commit 8eeebaec8d7fa17b5fe9d97589839ca2560e3ce2

Citation

Please cite:

@misc{hu2024minictx,
  title={miniCTX: Neural Theorem Proving with (Long-)Contexts}, 
  author={Jiewen Hu and Thomas Zhu and Sean Welleck},
  year={2024},
  eprint={2408.03350},
  archivePrefix={arXiv},
  primaryClass={cs.AI},
  url={https://arxiv.org/abs/2408.03350}, 
}