Leanstral: Automating Formal Proofs with AI-Powered Code Generation

Formal verification is having a moment. As software systems grow more critical—from blockchain protocols to autonomous systems—the need for mathematically proven correctness has never been greater. Enter Leanstral, an exciting open-source project that combines AI agents with formal proof engineering to automatically generate verified code.

What Makes Leanstral Significant

Leanstral bridges a gap that's plagued developers for years: the tedious, error-prone process of writing formal proofs. By leveraging language models as intelligent agents, it can:

• Generate code in Lean (a proof assistant language) from natural language specifications
• Automatically construct formal proofs alongside implementation
• Verify correctness before code reaches production
• Reduce the expertise barrier for formal methods adoption

This matters because traditional formal verification requires specialized knowledge. Leanstral democratizes it by letting developers describe what their code should do, while AI handles the how of formal proof construction.

The Developer Challenge

Building trustworthy code at scale is expensive. Security audits, formal verification consultants, and proof engineers command premium salaries. For startups and teams building critical infrastructure, cost is a real barrier to adopting formal methods.

Leanstral agents solve this by automating the grunt work—iterating on proof strategies, handling tedious lemma proofs, and suggesting improvements. Developers can focus on high-level logic while the agent handles formal rigor.

Powering Leanstral with AiPayGen

If you're building tools like Leanstral or integrating formal verification into your development pipeline, you need reliable, cost-effective API access to powerful language models. That's where AiPayGen comes in.

AiPayGen provides pay-per-use access to Claude, perfect for agent-based workflows where API calls scale with complexity. Here's how you might use it to generate Lean proofs:

import requests
import json

# Use AiPayGen to generate a Lean proof
response = requests.post(
    "https://api.aipaygen.com/v1/messages",
    headers={
        "x-api-key": "YOUR_AIPAYGEN_KEY",
        "content-type": "application/json"
    },
    json={
        "model": "claude-3-5-sonnet-20241022",
        "max_tokens": 2048,
        "messages": [
            {
                "role": "user",
                "content": """Generate a Lean 4 proof that the sum of 
                two even numbers is even. Include the theorem statement 
                and complete proof."""
            }
        ]
    }
)

proof = response.json()["content"][0]["text"]
print("Generated Lean proof:")
print(proof)
  

Or via curl:

curl https://api.aipaygen.com/v1/messages \
  -H "x-api-key: YOUR_AIPAYGEN_KEY" \
  -H "content-type: application/json" \
  -d '{
    "model": "claude-3-5-sonnet-20241022",
    "max_tokens": 2048,
    "messages": [{
      "role": "user",
      "content": "Write a Lean proof that list append is associative"
    }]
  }'
  

Why AiPayGen for Formal Verification

Claude excels at reasoning tasks—exactly what formal proof generation demands. AiPayGen's pay-per-use model means you only pay for the complexity you need. Experimenting with proof strategies? Running batch verification? AiPayGen scales with you without fixed monthly costs.

For teams building the next generation of trustworthy software, combining Leanstral's formal verification capabilities with AiPayGen's flexible API access creates a powerful development experience.

Try it free at https://api.aipaygen.com — 3 calls/day, no credit card.