HOL4

A structured dataset of theorems and definitions from HOL4, a mature theorem prover for higher-order logic.

Source

• Repository: https://github.com/HOL-Theorem-Prover/HOL
• Commit: ab6450c497d986a09043c9e930c36841ba93fbdb
• Files: 2940
• 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: 73,139
• With proof: 59,646 (81.6%)
• With docstring: 0 (0.0%)
• Libraries: 345

By type

Type	Count
Theorem	54,501
Definition	11,867
prove	4,610
Define	601
TAC_PROOF	507
store_thm	404
new_definition	379
Inductive	144
tDefine	70
new_recursive_definition	22
xDefine	15
CoInductive	12
zDefine	5
Triviality	2

Example

DIVIDES_TRANS :
 !a b c. a divides b /\ b divides c ==> a divides c
Proof
  metis_tac [divides_def,MULT_ASSOC]

• type: Theorem | symbolic_name: DIVIDES_TRANS | examples/euclid.sml

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{hol4_dataset,
  title  = {HOL4},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/HOL-Theorem-Prover/HOL, commit ab6450c497d9},
  url    = {https://huggingface.co/datasets/phanerozoic/HOL4}
}