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tomdif / eml-lean

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Lean 4 formalization of arXiv:2603.21852 — All elementary functions from a single binary operator eml(x,y) = exp(x) - ln(y)

19
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100% credibility
Found Apr 19, 2026 at 19 stars -- GitGems finds repos before they trend. Get early access to the next one.
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AI Analysis
Lean
AI Summary

Formal verification project proving that a single binary operator combined with the constant 1 can generate all standard elementary mathematical functions.

How It Works

1
🔍 Discover the math magic

You hear about a fascinating idea where one simple math operation can create every function on your calculator, and find this project to explore it.

2
📖 Read the story

You dive into the guide, learning how the EML operator plus the number 1 builds addition, logs, trig functions, and more.

3
✨ Wow, it all connects!

You see proofs showing exp, ln, pi, even imaginary numbers emerge from nesting this one operation—mind blown!

4
🛠️ Set up your math playground

You prepare the special tools needed to check these math claims yourself.

5
🔬 Run the treasure hunt

You launch a search to rediscover the shortest ways to build operations like subtraction or multiplication using EML trees.

6
✅ Verify the wonders

You confirm all the theorems hold true, with no gaps or errors.

🎉 Mastered the EML universe

Now you understand and trust this breakthrough: all basic math from one operator, ready to share or build upon.

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AI-Generated Review

What is eml-lean?

This Lean 4 formalization verifies a wild claim from arXiv:2603.21852: all elementary functions—exp, ln, trig, hyperbolic, powers, constants like π and i—emerge from a single binary operator eml(x,y) = exp(x) - ln(y) plus the constant 1. Built on Mathlib, it delivers 160 machine-checked theorems across arithmetic, transcendentals, and complex numbers, with zero gaps. Developers get a rock-solid proof library for exploring this "NAND gate for continuous math," plus a reproducible search script for minimal expression trees.

Why is it gaining traction?

Unlike informal papers or partial proofs, this Lean 4 formalization covers the full paper plus original extensions like eml's algebraic structure, calculus derivatives, and fixed-point analysis—letting users trust and extend it instantly. The exhaustive brute-force search for optimal trees stands out for reproducibility, and Lean GitHub Actions make builds seamless. It's a hook for anyone chasing lean math formalization projects, blending deep theory with practical verification.

Who should use this?

Lean theorem provers formalizing real analysis or scientific computing primitives, like researchers bounding generalization error via Rademacher complexity or quant devs modeling exp-log chains. Math educators demonstrating functional completeness in continuous domains. Lean GitHub dataset curators seeking verified math libraries.

Verdict

Grab it if you're deep into Lean proof formalization—docs are thorough, proofs complete, and extensions add real value despite 19 stars and 1.0% credibility score signaling early maturity. Skip for production unless verifying calculator ops is your niche.

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