README.md

metadata

license: other
license_name: cecill-b
license_link: https://cecill.info/licences/Licence_CeCILL-B_V1-en.html
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - coq
  - mathcomp
  - algebra
  - mathematics
size_categories:
  - 10K<n<100K
dataset_info:
  features:
    - name: fact
      dtype: string
    - name: statement
      dtype: string
    - name: proof
      dtype: string
    - name: type
      dtype: string
    - name: symbolic_name
      dtype: string
    - name: library
      dtype: string
    - name: filename
      dtype: string
    - name: imports
      list: string
    - name: deps
      list: string
    - name: docstring
      dtype: string
    - name: line_start
      dtype: int64
    - name: line_end
      dtype: int64
    - name: has_proof
      dtype: bool
    - name: source_url
      dtype: string
    - name: commit
      dtype: string
  splits:
    - name: train
      num_examples: 23813
  config_name: default
configs:
  - config_name: default
    data_files:
      - split: train
        path: data/train-*

Coq-MathComp

Structured dataset from the Mathematical Components library (MathComp) for Coq.

Source

• Repository: https://github.com/math-comp/math-comp
• Commit: 91d97df9cf3204b4dab84f4e24bc633e84b6473d
• Files: 139
• License: other

Schema

Column	Type	Description
fact	string	Verbatim declaration with the leading keyword removed: signature and body/proof joined
statement	string	Signature with the leading keyword removed (verbatim slice)
proof	string	Verbatim proof/body, empty if none
type	string	Declaration keyword
symbolic_name	string	Declaration identifier
library	string	Sub-library
filename	string	Repository-relative source path
imports	list[string]	File-level Require/Import modules
deps	list[string]	Intra-corpus identifiers referenced
docstring	string	Preceding documentation comment, null if absent
line_start	int	First source line
line_end	int	Last source line
has_proof	bool	Whether a proof block was captured
source_url	string	Upstream repository
commit	string	Upstream commit extracted

Statistics

• Entries: 23,813
• With proof: 23,468 (98.6%)
• With docstring: 847 (3.6%)
• Libraries: 10

By type

Type	Count
Lemma	15,224
Notation	3,122
Definition	2,907
Fact	737
Let	557
Canonical	407
Hypothesis	202
Fixpoint	149
Coercion	119
Variant	116
Theorem	63
Hypotheses	51
Inductive	38
Ltac	26
Structure	24
Record	23
Corollary	18
Example	7
Parameter	5
Proposition	5
Axiom	4
Instance	3
Remark	3
Class	2
Scheme	1

Example

floor_subproof n :
  if n \is real_num then n%:~R <= n < (n + 1)%:~R else n == 0.
Proof. by rewrite num_real !intz ltzD1 lexx. Qed.

• type: Fact | symbolic_name: floor_subproof | algebra/archimedean.v:163

Use

Statement and proof are available both joined (fact) and split (statement, proof) for proof-term modeling, autoformalization, retrieval, and dependency analysis via deps.

Citation

@misc{coq_mathcomp_dataset,
  title  = {Coq-MathComp},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/math-comp/math-comp, commit 91d97df9cf32},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-MathComp}
}