Intro

Purpose

1. Understanding the mathematical principles behind Uniswap V2.
2. A thorough examination of Uniswap V2 contracts.
3. Building defi-swap-demo with Foundry on Uniswap V2 Core fork.

Uniswap V2 Overview

Uniswap V2 is a foundational protocol in DeFi, serving as the basis for countless other AMMs (Automated Market Makers).

Decentralized exchange that allows users to buy and sell tokens without an order book.

Operations

• Liquidity provider
  • Deposit tokens
• Trader
  • Swap tokens with liquidity pool
• AMM
  • Execute trades
  • Maintain liquidity pool
  • Give swap fees to liquidity providers

Pros and Cons

Pros	Cons
Permissionless	Impermanent loss
No order book	Slippage
Low fees	Front-running
Decentralized	Smart contract risk

How an AMM Works

x * y = k

Where:

• x: amount of Token A in the pool
• y: amount of Token B in the pool
• k: liquidity constant

Example:

If we start with an AMM where x = 1 ETH and y = 4000 USDC, then k = 4000, after that if one user wants to swap 0.1 x(ETH) for y(USDC). in this case, the amount of token y(USDC) that the user will receive can be calculated as follows:

(x + Δx) * (y - Δy) = k
(1 + 0.1) * (4000 - Δy) = 4000
Δy = 363.64 USDC

We can see that 0.1 ETH can be swapped for 363.64 USDC. As more users swap USDC for ETH, the price of ETH in terms of USDC increases. Eventually, the price of ETH reaches a new balance point.

Contracts

• Factory
  • Create new pairs
• Pair
  • Lock up the tokens
  • Trade tokens
• Router
  • Interact with the pairs

Swap Fees

• 0.30% fee on each trade

// balance0Adjusted = balance0 * 1000 - amount0In * 3
uint balance0Adjusted = balance0.mul(1000).sub(amount0In.mul(3));
// balance1Adjusted = balance1 * 1000 - amount1In * 3
uint balance1Adjusted = balance1.mul(1000).sub(amount1In.mul(3));
// Why need this requirement?
// To ensure that after accounting for fees the invariant x * y >= k still holds true.
require(balance0Adjusted.mul(balance1Adjusted) >= uint(_reserve0).mul(_reserve1).mul(1000**2), 'UniswapV2: K');

How to deploy locally Uniswap V2 Contracts

1. Compile Uniswap V2 Contracts

npx hardhat compile

2. Calculate Hash for UniswapV2Pair contract

npm run keccak256

3. Replace the hex string in UniswapV2Library.sol

// ... existing code ...
function pairFor(address factory, address tokenA, address tokenB) internal pure returns (address pair) {
    (address token0, address token1) = sortTokens(tokenA, tokenB);
    pair = address(uint(keccak256(abi.encodePacked(
            hex'ff',
            factory,
            keccak256(abi.encodePacked(token0, token1)),
            hex'??????' // init code hash(uniswapV2Pair)
        ))));
}

4. Run a local Ethereum node through Hardhat

npx hardhat node

5. Test setup liquidity script

forge script script/SetupLiquidity.sol -vvv

Test Cases

• Swap between two tokens
• Add liquidity to a pool
• Remove liquidity from a pool
• Code walkthrough IUniswapV2Pair interface
• Flash swap
• TWAP
• Flash swap arbitrage