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: 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: 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
statement	string	Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof
proof	string	Verbatim proof/body, empty if the declaration has 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, empty if absent
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

Use

Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint and together form the complete declaration, for proof 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}
}