CoqGym and ASTactic scale learning-based interaction with the Coq proof assistant

CoqGym extracted proof states, environments, goals, tactics and proof trees from open-source Coq projects and exposed them through a programmatic interaction layer.

What happened?

Kaiyu Yang and Jia Deng released CoqGym, a dataset and interactive environment built from 71,000 human-written proofs across 123 Coq projects, together with ASTactic, a deep-learning model that generates tactics as abstract syntax trees and was reported to prove held-out theorems beyond the reach of the compared built-in automated tactics.

CoqGym extracted proof states, environments, goals, tactics and proof trees from open-source Coq projects and exposed them through a programmatic interaction layer. ASTactic learned proof-step generation from this corpus and composed tactics from runtime syntax rather than relying only on a predetermined list of complete tactics.

Why it matters

CoqGym made learning-based theorem proving on a mature interactive proof assistant substantially more data-rich and reproducible. Its environment-and-corpus design anticipated later projects such as LeanDojo that similarly expose large proof-assistant libraries as reusable machine-learning infrastructure.

Significance rationale: CoqGym turned a large collection of real Coq developments into an interactive machine-learning environment containing tens of thousands of human proofs, while ASTactic generated structured tactics rather than choosing only from a fixed tactic vocabulary. The environment became an important early template for later proof-assistant learning infrastructure.

Historical context

Primary evidence

Evidence & status at a glance

Significance
H2 · Field milestone
Verification
Paper released
Evidence level
E3 · Inspectable artifact
AI role
Autonomous primary role
Formal assurance
Machine-checked

How should these labels be read? →

Contribution & verification

Mathematical novelty
Tooling only
Interface
Formal, Symbolic
AI contribution
ASTactic generated structured Coq tactics from proof states and searched for proof scripts, while Coq checked whether generated tactic sequences produced valid formal proofs.
Human contribution
Researchers assembled and instrumented the Coq projects, designed the data extraction and interaction environment, defined train/validation/test splits, built ASTactic and evaluated it against automated tactics and theorem provers.
Verification
Paper released · E3 · Inspectable artifact · Machine-checked
Last reviewed
2026-09-15

Technical details

Systems
coqgym, astactic, coq
Organizations
princeton-university
Problems
coq-theorem-proving
Methods
tactic-generation, abstract-syntax-tree-generation, interactive-theorem-proving, supervised-learning, benchmarking

Sources & artifacts

Verification history

  • 2019-05-21 · Paper released · E2 · Research record

    The arXiv and ICML research records establish CoqGym, ASTactic, the dataset scale and the reported held-out theorem-proving experiments. Machine checking refers to proofs accepted by Coq and does not imply independent reproduction of the reported success rates.

  • 2026-09-15 · Paper released · E3 · Inspectable artifact

    The public CoqGym repository exposes the interaction environment, extraction pipeline, proof corpus tooling and ASTactic implementation. E3 denotes artifact-level inspectability rather than independent verification of every experimental claim.

Corrections

No corrections recorded.