Coq-UniMath

Structured dataset of formalizations from the UniMath library (Univalent Mathematics in Coq).

Source

• Repository: https://github.com/UniMath/UniMath
• Commit: fa8f7d65ac96baddca8614f1c7bdfa73f043aef5
• Files: 1617
• 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: 51,194
• With proof: 50,466 (98.6%)
• With docstring: 7,116 (13.9%)
• Libraries: 189

By type

Type	Count
Definition	30,696
Lemma	10,022
Proposition	4,557
Let	2,476
Coercion	1,269
Notation	1,223
Theorem	356
Ltac	229
Corollary	179
Ltac2	98
Hypothesis	49
Fixpoint	21
Inductive	7
Example	6
Axiom	5
Record	1

Example

abgrconstr (X : abmonoid) (inv0 : X → X) (is : isinv (@op X) 0 inv0) : abgr.
Proof.
  use make_abgr.
  - exact X.
  - use make_isabgrop.
    + use make_isgrop.
      * apply (make_ismonoidop (assocax X)).
        exact (make_isunital (unel X) (unax X)).
      * exact (make_invstruct inv0 is).
    + exact (commax X).
Defined.

• type: Definition | symbolic_name: abgrconstr | UniMath/Algebra/AbelianGroups.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_unimath_dataset,
  title  = {Coq-UniMath},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/UniMath/UniMath, commit fa8f7d65ac96},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-UniMath}
}