README.md

metadata

license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - cooltt
  - cubical-type-theory
size_categories:
  - 10K<n<100K
dataset_info:
  features:
    - name: fact
      dtype: string
    - 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: line_start
      dtype: int64
    - name: line_end
      dtype: int64
    - name: has_proof
      dtype: bool
    - name: source_url
      dtype: string
    - name: commit
      dtype: string
  splits:
    - name: train
      num_examples: 235
  config_name: default
configs:
  - config_name: default
    data_files:
      - split: train
        path: data/train-*

cooltt

Declarations from cooltt, a cubical/computational type theory system.

Source

• Repository: https://github.com/RedPRL/cooltt
• Commit: b39bf29900451cb43ae6fbd9af5aa33d59e18935
• Files: 32
• License: other

Schema

Column	Type	Description
fact	string	Verbatim declaration with the leading keyword removed: signature and body/proof joined
statement	string	Signature with the leading keyword removed (verbatim slice)
proof	string	Verbatim proof/body, empty if 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 import modules
deps	list[string]	Intra-corpus identifiers referenced
docstring	string	Preceding documentation comment, null if absent
line_start	int	First source line
line_end	int	Last source line
has_proof	bool	Whether a proof block was captured
source_url	string	Upstream repository
commit	string	Upstream commit extracted

Statistics

• Entries: 235
• With proof: 228 (97.0%)
• With docstring: 32 (13.6%)
• Libraries: 1

By type

Type	Count
def	228
axiom	7

Example

+0R : (x : nat) → path nat {+ x 0} x :=
  elim [
  | zero => +0L 0
  | suc {x => ih} =>
    equation nat begin
      + {suc x} 0 =[ +SL x 0 ]
      suc {+ x 0} =[ i => suc {ih i} ]
      suc x
    end
  ]

• type: def | symbolic_name: +0R | test/abstract.cooltt:23

Use

Statement and proof are available both joined (fact) and split (statement, proof) for proof-term modeling, autoformalization, retrieval, and dependency analysis via deps.

Citation

@misc{cooltt_dataset,
  title  = {cooltt},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/RedPRL/cooltt, commit b39bf2990045},
  url    = {https://huggingface.co/datasets/phanerozoic/cooltt}
}