# Formalizing Automated Market Makers in the Lean 4 Theorem Prover

arXiv: https://arxiv.org/abs/2402.06064 · HTML: https://mlsanity.com/paper/2402.06064/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2024.

## Built on by (most cited first, 3 of 3)

- [Type-Checked Compliance: Deterministic Guardrails for Agentic Financial Systems Using Lean 4 Theorem Proving](https://mlsanity.com/paper/2604.01483/) (2026)
- [Towards Automating Blockchain Consensus Verification with IsabeLLM](https://mlsanity.com/paper/2601.07654/) (2026)
- [IsabeLLM: Automated Theorem Proving Applied to Formally Verifying Consensus](https://mlsanity.com/paper/2606.18098/) (2026)

## Abstract (arXiv)

Automated Market Makers (AMMs) are an integral component of the decentralized finance (DeFi) ecosystem, as they allow users to exchange crypto-assets without the need for trusted authorities or external price oracles. Although these protocols are based on relatively simple mechanisms, e.g., to algorithmically determine the exchange rate between crypto-assets, they give rise to complex economic behaviours. This complexity is witnessed by the proliferation of models that study their structural and economic properties. Currently, most of theoretical results obtained on these models are supported by pen-and-paper proofs. This work proposes a formalization of constant-product AMMs in the Lean 4 Theorem Prover. To demonstrate the utility of our model, we provide mechanized proofs of key economic properties like arbitrage, that at the best of our knowledge have only been proved by pen-and-paper before.