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NumpySpec

numpy -> lean 4 through ai

NumpySpec

NumpySpec is a formally verified numpy-compatible library for Lean 4, providing mathematically proven implementations of matrix operations with numpy-style APIs.

Overview

This project aims to port essential numpy functionality to Lean 4 with formal verification, starting with core matrix operations. Unlike traditional numpy implementations, every operation comes with mathematical proofs of correctness.

The core specification is found in NumpySpec.lean:

  • Matrix.add: Element-wise matrix addition with type-safe dimensions
  • Matrix.multiply: Matrix multiplication with dimension checking
  • Matrix.transpose: Matrix transposition preserving mathematical properties
  • Future: Broadcasting, linear algebra decompositions, and advanced operations

Key Features

  • Formal Verification: Every operation is mathematically proven correct
  • Numpy Compatibility: Familiar API design for numpy users
  • Type Safety: Lean's type system prevents dimension mismatches
  • Cloud-Native: Compilation and verification offloaded to Pantograph servers
  • RL Training: Reinforcement learning agents for automated theorem proving

Dependencies

Local machine only needs:

  • Python ≥ 3.12 with uv (see Justfile)

Installation

git clone https://github.com/Beneficial-AI-Foundation/NumpySpec.git
cd NumpySpec
just sync   # installs all Python deps (Pantograph, LeanTool, …)

Everything else (Elan, Lean toolchain) is provisioned automatically in the remote Pantograph snapshot when you invoke any just pipeline target.

Build

This project uses just.

Cloud Compilation

The project supports remote compilation via Pantograph servers. First run provisions a snapshot (≈ 5 min). Subsequent runs reuse the warmed snapshot/instance.

Numpy Port Roadmap

1. Core Matrix Operations (Current Focus)

  • ✅ Basic matrix types with fixed dimensions
  • 🚧 Matrix addition, multiplication, transpose
  • 📋 Element access and slicing
  • 📋 Broadcasting support

2. Linear Algebra

  • 📋 LU decomposition
  • 📋 Matrix inversion
  • 📋 Eigenvalue computation
  • 📋 SVD decomposition

3. Advanced Features

  • 📋 Sparse matrix support
  • 📋 Batch operations
  • 📋 GPU computation integration
  • 📋 Performance optimization

4. Verification Strategy

  • Spec vs. Exec separation: Pure mathematical specifications with efficient implementations
  • Refinement proofs: Each executable function proven correct against its specification
  • Property-based testing: Integration with Lean's testing framework

Automated Agent System

NumpySpec includes RL-powered agents for automated development:

Multi-Agent Architecture

Core Agents:

  • LeanEditSubagent: Applies edits to Lean files with error handling
  • LeanBuildSubagent: Runs local lake build and parses output
  • LeanRemoteBuildSubagent: Cloud compilation via Pantograph
  • FeedbackParseSubagent: Extracts actionable information from build output
  • LakeProjectInitSubagent: Project initialization and dependency management

RL Training:

  • PPO-based theorem proving agent
  • Custom Lean environment for proof search
  • Integration with state-of-the-art language models

Usage

from numpyspec.rl_env import LeanEnv
from numpyspec.rl_trainer import train_agent

# Train an RL agent for theorem proving
train_agent(steps=10000)

# Use subagents for development automation
from numpyspec.subagents import LeanEditSubagent, LeanBuildSubagent

edit_agent = LeanEditSubagent()
build_agent = LeanBuildSubagent()

Contributing

Contributions welcome! Focus areas:

  1. Core Operations: Implement matrix operations with formal proofs
  2. API Design: Ensure numpy compatibility while maintaining mathematical rigor
  3. Performance: Optimize implementations without sacrificing correctness
  4. Documentation: Examples showing numpy-to-Lean translation

Research Applications

NumpySpec enables:

  • Verified Scientific Computing: Mathematical guarantees for numerical algorithms
  • Educational Tool: Learn formal methods through familiar numpy operations
  • AI Safety Research: Provably correct implementations for safety-critical applications
  • Automated Theorem Proving: RL agents learning to prove mathematical properties

License

This project is licensed under the Apache-2.0 license - see the LICENSE file for details.

Related Projects

  • FuncTracker: ASCII table parsing for development progress tracking (separate module)
  • NDArray: NumPy-compatible n-dimensional arrays with formal verification
  • LeanTool: Integration utilities for Lean development workflows