| ---
|
| 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
|
|
|
| ```bibtex
|
| @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}
|
| }
|
| ```
|
|
|
