Datasets:

l3lab
/

miniCTX

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 record the version (git commit) of the repository.