Coq-Paco

Structured declarations from the Paco library - a Coq library for parameterized coinduction. Source: github.com/snu-sf/paco

Source

• Repository: https://github.com/snu-sf/paco
• Commit: d0561bf7f0a96cac486ba3bd8ca0b72ce01fb9cf
• Files: 42
• License: bsd-3-clause

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: 2,114
• With proof: 2,099 (99.3%)
• With docstring: 92 (4.4%)
• Libraries: 1

By type

Type	Count
Lemma	1,304
Definition	202
Theorem	188
Ltac	126
Notation	83
Structure	75
Inductive	45
Variant	16
Corollary	16
Hypothesis	15
Instance	15
Record	15
CoInductive	8
CoFixpoint	5
Class	1

Example

id_match_stream {A} (s:stream A) : stream A
:=
  match s with
  | snil => snil
  | scons x t => scons x t
  end.

• type: Definition | symbolic_name: id_match_stream | src/examples.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_paco_dataset,
  title  = {Coq-Paco},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/snu-sf/paco, commit d0561bf7f0a9},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Paco}
}