Coq-Stdlib

Structured dataset of definitions and theorems from the Coq standard library.

Source

• Repository: https://github.com/rocq-prover/stdlib
• Commit: f76a666b0b2c28c671d4fdf6dd25bcab865b9c36
• Files: 583
• License: lgpl-2.1

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: 18,419
• With proof: 17,842 (96.9%)
• With docstring: 2,948 (16.0%)
• Libraries: 44

By type

Type	Count
Lemma	10,045
Definition	2,527
Notation	1,550
Theorem	1,386
Instance	736
Ltac	597
Fixpoint	512
Parameter	305
Inductive	182
Axiom	127
Hypothesis	107
Let	105
Record	60
Class	45
Example	42
Corollary	24
Fact	17
Coercion	12
Remark	11
Scheme	10
Parameters	6
CoFixpoint	5
Variant	3
CoInductive	3
Proposition	1
Structure	1

Example

gt_pred_stt : forall n m, m > S n -> pred m > n
:= fun n m Hgt => proj1 (Nat.lt_succ_lt_pred n m) Hgt.

• type: Definition | symbolic_name: gt_pred_stt | theories/Arith/Arith_base.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_stdlib_dataset,
  title  = {Coq-Stdlib},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/rocq-prover/stdlib, commit f76a666b0b2c},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Stdlib}
}