A constant-product AMM in Solidity

#Brief

Automated market makers are the core of DeFi. Implementing one and checking it against an independent model teaches the maths and the rounding far better than reading about them. Study the Uniswap v2 design, then write your own simplified version. Use a local Anvil chain and, when you deploy publicly, a testnet such as Sepolia with free test ether from a faucet. Never use real funds or a wallet that holds any, and never paste a private key into code or a website.

#What to build

1. Implement a pool for two ERC-20 tokens that mints liquidity shares on deposit and burns them on withdrawal

2. Implement swaps with the constant-product formula and a 0.30% fee, with amountOutMin and deadline parameters

3. Write a Python model of the same maths, starting from the DeFi shelf example

4. Write differential fuzz tests: random sequences of deposits, swaps and withdrawals must match the model within one unit of rounding

5. Document rounding decisions, why spot price must not be used as an oracle, and other design risks

#Deliverables

• Repository with src/, test/, model/ and DESIGN.md

#How it is graded

Reviewers run the differential tests with more fuzz runs and check that k never decreases across swaps.

#Stretch

Add a time-weighted average price accumulator and explain why it is harder to move than the spot price.