Ethereum Builder's Guide

Solidity Tutorials

Solidity is a high-level language whose syntax is similar to that of JavaScript and it is designed to compile to code for the Ethereum Virtual Machine. This tutorial provides a basic introduction to Solidity and assumes some knowledge of the Ethereum Virtual Machine and programming in general. For more details, please see the Solidity specficiation (yet to be written). This tutorial does not cover features like the natural language documentation or formal verification and is also not meant as a final specification of the language.

You can start using Solidity in your browser, with no need to download or compile anything. This application only supports compilation - if you want to run the code or inject it into the blockchain, you have to use a client like AlethZero.

Simple Example

contract SimpleStorage {
    uint storedData;
    function set(uint x) {
        storedData = x;
    function get() constant returns (uint retVal) {
        return storedData;

uint storedData declares a state variable called storedData of type uint (unsigned integer of 256 bits) whose position in storage is automatically allocated by the compiler. The functions set and get can be used to modify or retrieve the value of the variable.

Subcurrency Example

contract Coin {
    address minter;
    mapping (address => uint) balances;
    function Coin() {
        minter = msg.sender;
    function mint(address owner, uint amount) {
        if (msg.sender != minter) return;
        balances[owner] += amount;
    function send(address receiver, uint amount) {
        if (balances[msg.sender] < amount) return;
        balances[msg.sender] -= amount;
        balances[receiver] += amount;
    function queryBalance(address addr) constant returns (uint balance) {
        return balances[addr];

This contract introduces some new concepts. One of them is the address type, which is a 160 bit value that does not allow any arithmetic operations. Furthermore, the state variable balance is of a complex datatype that maps addresses to unsigned integers. Mappings can be seen as hashtables which are virtually initialized such that every possible key exists and is mapped to a value whose byte-representation is all zeros. The special function Coin is the constructor which is run during creation of the contract and cannot be called afterwards. It permanently stores the address of the person creating the contract: Together with tx and block, msg is a magic global variable that contains some properties which allow access to the world outside of the contract. The function queryBalance is declared constant and thus is not allowed to modify the state of the contract (note that this is not yet enforced, though). In Solidity, return "parameters" are named and essentially create a local variable. So to return the balance, we could also just use balance = balances[addr]; without any return statement.


Single-line comments (//) and multi-line comments (/*...*/) are possible, while triple-slash comments (///) right in front of function declarations introduce NatSpec comments (which are not covered here).


The currently implemented (elementary) types are booleans (bool), integer and fixed-length string/byte array (bytes0 to bytes32) types. The integer types are signed and unsigned integers of various bit widths (int8/uint8 to int256/uint256 in steps of 8 bits, where uint/int are aliases for uint256/int256) and addresses (of 160 bits).

Comparisons (<=, !=, ==, etc.) always yield booleans which can be combined using &&, || and !. Note that the usual short-circuiting rules apply for && and ||, which means that for expressions of the form (0 < 1 || fun()), the function is actually never called.

If an operator is applied to different types, the compiler tries to implicitly convert one of the operands to the type of the other (the same is true for assignments). In general, an implicit conversion is possible if it makes sense semantically and no information is lost: uint8 is convertible to uint16 and int120 to int256, but int8 is not convertible to uint256. Furthermore, unsigned integers can be converted to bytes of the same or larger size, but not vice-versa. Any type that can be converted to uint160 can also be converted to address.

If the compiler does not allow implicit conversion but you know what you are doing, an explicit type conversion is sometimes possible:

int8 y = -3;
uint x = uint(y);

At the end of this code snippet, x will have the value 0xfffff..fd (64 hex characters), which is -3 in two's complement representation of 256 bits.

For convenience, it is not always necessary to explicitly specify the type of a variable, the compiler automatically infers it from the type of the first expression that is assigned to the variable:

uint20 x = 0x123;
var y = x;

Here, the type of y will be uint20. Using var is not possible for function parameters or return parameters. State variables of integer and bytesXX types can be declared as constant.

uint constant x = 32;
bytes3 constant text = "abc";

Integer Literals

The type of integer literals is not determined as long as integer literals are combined with themselves. This is probably best explained with examples:

var x = 1 - 2;

The value of 1 - 2 is -1, which is assigned to x and thus x receives the type int8 -- the smallest type that contains -1. The following code snippet behaves differently, though:

var one = 1;
var two = 2;
var x = one - two;

Here, one and two both have type uint8 which is also propagated to x. The subtraction inside the type uint8 causes wrapping and thus the value of x will be 255.

It is even possible to temporarily exceed the maximum of 256 bits as long as only integer literals are used for the computation:

var x = (0xffffffffffffffffffff * 0xffffffffffffffffffff) * 0;

Here, x will have the value 0 and thus the type uint8.

Ether and Time Units

A literal number can take a suffix of wei, finney, szabo or ether to convert between the subdenominations of ether, where Ether currency numbers without a postfix are assumed to be "wei", e.g. 2 ether == 2000 finney evaluates to true.

Furthermore, suffixes of seconds, minutes, hours, days, weeks and years can be used to convert between units of time where seconds are the base unit and units are converted naively (i.e. a year is always exactly 365 days, etc.).

Control Structures

Most of the control structures from C/JavaScript are available in Solidity except for switch (not planned) and goto (note that it's called Solidity). So there is: if, else, while, for, break, continue, return. Note that there is no type conversion from non-boolean to boolean types as there is in C and JavaScript, so if (1) { ... } is not valid Solidity.

Function Calls

Functions of the current contract can be called directly, also recursively, as seen in this nonsensical example:

contract c {
  function g(uint a) returns (uint ret) { return f(); }
  function f() returns (uint ret) { return g(7) + f(); }

The expression this.g(8); is also a valid function call, but this time, the function will be called via a message call and not directly via jumps. When calling functions of other contracts, the amount of Wei sent with the call and the gas can be specified:

contract InfoFeed {
  function info() returns (uint ret) { return 42; }
contract Consumer {
  InfoFeed feed;
  function setFeed(address addr) { feed = InfoFeed(addr); }
  function callFeed() {; }

Note that the expression InfoFeed(addr) performs an explicit type conversion stating that "we know that the type of the contract at the given address is InfoFeed" and this does not execute a constructor. Be careful in that only (locally) set the value and amount of gas sent with the function call and only the parentheses at the end perform the actual call.

Function call arguments can also be given by name, in any order:

contract c {
function f(uint key, uint value) { ... }
function g() {
  f({value: 2, key: 3});

The names for function parameters and return parameters are optional.

contract test {
  function func(uint k, uint) returns(uint){
    return k;

Special Variables and Functions

There are special variables and functions which always exist in the global namespace.

Block and Transaction Properties

  • block.coinbase (address): current block miner's address
  • block.difficulty (uint): current block difficulty
  • block.gaslimit (uint): current block gaslimit
  • block.number (uint): current block number
  • block.blockhash (function(uint) returns (bytes32)): hash of the given block
  • block.timestamp (uint): current block timestamp
  • (bytes): complete calldata
  • msg.gas (uint): remaining gas
  • msg.sender (address): sender of the message (current call)
  • msg.value (uint): number of wei sent with the message
  • now (uint): current block timestamp (alias for block.timestamp)
  • tx.gasprice (uint): gas price of the transaction
  • tx.origin (address): sender of the transaction (full call chain)

Cryptographic Functions

  • sha3(...) returns (bytes32): compute the SHA3 hash of the (tightly packed) arguments
  • sha256(...) returns (bytes32): compute the SHA256 hash of the (tightly packed) arguments
  • ripemd160(...) returns (bytes20): compute RIPEMD of 256 the (tightly packed) arguments
  • ecrecover(bytes32, byte, bytes32, bytes32) returns (address): recover public key from elliptic curve signature

In the above, "tightly packed" means that the arguments are concatenated without padding, i.e. sha3("ab", "c") == sha3("abc") == sha3(0x616263) == sha3(6382179) = sha3(97, 98, 99). If padding is needed, explicit type conversions can be used.

  • this (current contract's type): the current contract, explicitly convertible to address
  • suicide(address): suicide the current contract, sending its funds to the given address

Furthermore, all functions of the current contract are callable directly including the current function.

Functions on addresses

It is possible to query the balance of an address using the property balance and to send Ether (in units of wei) to an address using the send function:

address x = 0x123;
if (x.balance < 10 && address(this).balance >= 10) x.send(10);

Furthermore, to interface with contracts that do not adhere to the ABI (like the classic NameReg contract), the function call is provided which takes an arbitrary number of arguments of any type. These arguments are ABI-serialized (i.e. also padded to 32 bytes). One exception is the case where the first argument is encoded to exactly four bytes. In this case, it is not padded to allow the use of function signatures here.

address nameReg = 0x72ba7d8e73fe8eb666ea66babc8116a41bfb10e2;"register", "MyName");"fun(uint256)")), a);

Note that contracts inherit all members of address, so it is possible to query the balance of the current contract using this.balance.

Order of Evaluation of Expressions

The evaluation order of expressions is not specified (more formally, the order in which the children of one node in the expression tree are evaluated is not specified, but they are of course evaluated before the node itself). It is only guaranteed that statements are executed in order and short-circuiting for boolean expressions is done.


Both variably and fixed size arrays are supported in storage and as parameters of external functions:

contract ArrayContract {
  uint[2**20] m_aLotOfIntegers;
  bool[2][] m_pairsOfFlags;
  function setAllFlagPairs(bool[2][] newPairs) {
    // assignment to array replaces the complete array
    m_pairsOfFlags = newPairs;
  function setFlagPair(uint index, bool flagA, bool flagB) {
    // access to a non-existing index will stop execution
    m_pairsOfFlags[index][0] = flagA;
    m_pairsOfFlags[index][1] = flagB;
  function changeFlagArraySize(uint newSize) {
    // if the new size is smaller, removed array elements will be cleared
    m_pairsOfFlags.length = newSize;
  function clear() {
    // these clear the arrays completely
    delete m_pairsOfFlags;
    delete m_aLotOfIntegers;
    // identical effect here
    m_pairsOfFlags.length = 0;
  bytes m_byteData;
  function byteArrays(bytes data) external {
    // byte arrays ("bytes") are different as they are stored without padding,
    // but can be treated identical to "uint8[]"
    m_byteData = data;
    m_byteData.length += 7;
    m_byteData[3] = 8;
    delete m_byteData[2];


Solidity provides a way to define new types in the form of structs, which is shown in the following example:

contract CrowdFunding {
  struct Funder {
    address addr;
    uint amount;
  struct Campaign {
    address beneficiary;
    uint fundingGoal;
    uint numFunders;
    uint amount;
    mapping (uint => Funder) funders;
  uint numCampaigns;
  mapping (uint => Campaign) campaigns;
  function newCampaign(address beneficiary, uint goal) returns (uint campaignID) {
    campaignID = numCampaigns++; // campaignID is return variable
    Campaign c = campaigns[campaignID];  // assigns reference
    c.beneficiary = beneficiary;
    c.fundingGoal = goal;
  function contribute(uint campaignID) {
    Campaign c = campaigns[campaignID];
    Funder f = c.funders[c.numFunders++];
    f.addr = msg.sender;
    f.amount = msg.value;
    c.amount += f.amount;
  function checkGoalReached(uint campaignID) returns (bool reached) {
    Campaign c = campaigns[campaignID];
    if (c.amount < c.fundingGoal)
      return false;
    c.amount = 0;
    return true;

The contract does not provide the full functionality of a crowdfunding contract, but it contains the basic concepts necessary to understand structs. Struct types can be used as value types for mappings and they can itself contain mappings (even the struct itself can be the value type of the mapping, although it is not possible to include a struct as is inside of itself). Note how in all the functions, a struct type is assigned to a local variable. This does not copy the struct but only store a reference so that assignments to members of the local variable actually write to the state.


Enums are another way to create a user-defined type in Solidity. They are explicitly convertible to and from all integer types but implicit conversion is not allowed. The variable of enum type can be declared as constant.

contract test {
    enum ActionChoices { GoLeft, GoRight, GoStraight, SitStill }
    ActionChoices choices;
    ActionChoices constant defaultChoice = ActionChoices.GoStraight;
    function setGoStraight()
        choices = ActionChoices.GoStraight;
    function getChoice() returns (uint)
        return uint(choices);
    function getDefaultChoice() returns (uint)
        return uint(defaultChoice);

Interfacing with other Contracts

There are two ways to interface with other contracts: Either call a method of a contract whose address is known or create a new contract. Both uses are shown in the example below. Note that (obviously) the source code of a contract to be created needs to be known, which means that it has to come before the contract that creates it (and cyclic dependencies are not possible since the bytecode of the new contract is actually contained in the bytecode of the creating contract).

contract OwnedToken {
  // TokenCreator is a contract type that is defined below. It is fine to reference it
  // as long as it is not used to create a new contract.
  TokenCreator creator;
  address owner;
  bytes32 name;
  function OwnedToken(bytes32 _name) {
    address nameReg = 0x72ba7d8e73fe8eb666ea66babc8116a41bfb10e2;"register", _name);
    owner = msg.sender;
    // We do an explicit type conversion from `address` to `TokenCreator` and assume that the type of
    // the calling contract is TokenCreator, there is no real way to check.
    creator = TokenCreator(msg.sender);
    name = _name;
  function changeName(bytes32 newName) {
    // Only the creator can alter the name -- contracts are explicitly convertible to addresses.
    if (msg.sender == address(creator)) name = newName;
  function transfer(address newOwner) {
    // Only the current owner can transfer the token.
    if (msg.sender != owner) return;
    // We also want to ask the creator if the transfer is fine.
    // Note that this calls a function of the contract defined below.
    // If the call fails (e.g. due to out-of-gas), the execution here stops
    // immediately (the ability to catch this will be added later).
    if (creator.isTokenTransferOK(owner, newOwner))
      owner = newOwner;
contract TokenCreator {
  function createToken(bytes32 name) returns (address tokenAddress) {
    // Create a new Token contract and return its address.
    return address(new OwnedToken(name));
  function changeName(address tokenAddress, bytes32 name) {
    // We need an explicit type conversion because contract types are not part of the ABI.
    OwnedToken token = OwnedToken(tokenAddress);
  function isTokenTransferOK(address currentOwner, address newOwner) returns (bool ok) {
    // Check some arbitrary condition.
    address tokenAddress = msg.sender;
    return (sha3(newOwner) & 0xff) == (bytes20(tokenAddress) & 0xff);

Constructor Arguments

A Solidity contract expects constructor arguments after the end of the contract data itself. This means that you pass the arguments to a contract by putting them after the compiled bytes as returned by the compiler in the usual ABI format.

Contract Inheritance

Solidity supports multiple inheritance by copying code including polymorphism. Details are given in the following example.

contract owned {
    function owned() { owner = msg.sender; }
    address owner;

// Use "is" to derive from another contract. Derived contracts can access all members
// including private functions and storage variables.
contract mortal is owned {
    function kill() { if (msg.sender == owner) suicide(owner); }

// These are only provided to make the interface known to the compiler.
contract Config { function lookup(uint id) returns (address adr) {} }
contract NameReg { function register(bytes32 name) {} function unregister() {} }

// Multiple inheritance is possible. Note that "owned" is also a base class of
// "mortal", yet there is only a single instance of "owned" (as for virtual
// inheritance in C++).
contract named is owned, mortal {
    function named(bytes32 name) {
        address ConfigAddress = 0xd5f9d8d94886e70b06e474c3fb14fd43e2f23970;

// Functions can be overridden, both local and message-based function calls take
// these overrides into account.
    function kill() {
        if (msg.sender == owner) {
            address ConfigAddress = 0xd5f9d8d94886e70b06e474c3fb14fd43e2f23970;
// It is still possible to call a specific overridden function. 

// If a constructor takes an argument, it needs to be provided in the header.
contract PriceFeed is owned, mortal, named("GoldFeed") {
   function updateInfo(uint newInfo) {
      if (msg.sender == owner) info = newInfo;

   function get() constant returns(uint r) { return info; }

   uint info;

Note that above, we call mortal.kill() to "forward" the destruction request. The way this is done is problematic, as seen in the following example:

contract mortal is owned {
    function kill() { if (msg.sender == owner) suicide(owner); }
contract Base1 is mortal {
    function kill() { /* do cleanup 1 */ mortal.kill(); }
contract Base2 is mortal {
    function kill() { /* do cleanup 2 */ mortal.kill(); }
contract Final is Base1, Base2 {

A call to Final.kill() will call Base2.kill as the most derived override, but this function will bypass Base1.kill, basically because it does not even know about Base1. The way around this is to use super:

contract mortal is owned {
    function kill() { if (msg.sender == owner) suicide(owner); }
contract Base1 is mortal {
    function kill() { /* do cleanup 1 */ super.kill(); }
contract Base2 is mortal {
    function kill() { /* do cleanup 2 */ super.kill(); }
contract Final is Base1, Base2 {

If Base1 calls a function of super, it does not simply call this function on one of its base contracts, it rather calls this function on the next base contract in the final inheritance graph, so it will call Base2.kill(). Note that the actual function that is called when using super is not known in the context of the class where it is used, although its type is known. This is similar for ordinary virtual method lookup.

Multiple Inheritance and Linearization

Languages that allow multiple inheritance have to deal with several problems, one of them being the Diamond Problem. Solidity follows the path of Python and uses "C3 Linearization" to force a specific order in the DAG of base classes. This results in the desirable property of monotonicity but disallows some inheritance graphs. Especially, the order in which the base classes are given in the is directive is important. In the following code, Solidity will give the error "Linearization of inheritance graph impossible".

contract X {}
contract A is X {}
contract C is A, X {}

The reason for this is that C requests X to override A (by specifying A, X in this order), but A itself requests to override X, which is a contradiction that cannot be resolved.

A simple rule to remember is to specify the base classes in the order from "most base-like" to "most derived".

Abstract Contracts

Contract functions can lack an implementation as in the following example (note that the function declaration header is terminated by ;).

contract feline {
  function utterance() returns (bytes32);

Such contracts cannot be compiled (even if they contain implemented functions alongside non-implemented functions), but they can be used as base contracts:

contract Cat is feline {
  function utterance() returns (bytes32) { return "miaow"; }

If a contract inherits from an abstract contract and does not implement all non-implemented functions by overriding, it will itself be abstract.

Visibility Specifiers

Functions and storage variables can be specified as being public, internal or private, where the default for functions is public and internal for storage variables. In addition, functions can also be specified as external.

External: External functions are part of the contract interface and they can be called from other contracts and via transactions. An external function f cannot be called internally (i.e. f() does not work, but this.f() works). Furthermore, all function parameters are immutable.

Public: Public functions are part of the contract interface and can be either called internally or via messages. For public storage variables, an automatic accessor function (see below) is generated.

Inherited: Those functions and storage variables can only be accessed internally.

Private: Private functions and storage variables are only visible for the contract they are defined in and not in derived contracts.

contract c {
  function f(uint a) private returns (uint b) { return a + 1; }
  function setData(uint a) inherited { data = a; }
  uint public data;

Other contracts can call to retrieve the value of data in storage, but are not able to call f. Contracts derived from c can call setData to alter the value of data (but only in their own storage).

Accessor Functions

The compiler automatically creates accessor functions for all public state variables. The contract given below will have a function called data that does not take any arguments and returns a uint, the value of the state variable data. The initialization of state variables can be done at declaration.

contract test {
     uint public data = 42;

The next example is a bit more complex:

contract complex {
  struct Data { uint a; bytes3 b; mapping(uint => uint) map; }
  mapping(uint => mapping(bool => Data[])) public data;

It will generate a function of the following form:

function data(uint arg1, bool arg2, uint arg3) returns (uint a, bytes3 b)
  a = data[arg1][arg2][arg3].a;
  b = data[arg1][arg2][arg3].b;

Note that the mapping in the struct is omitted because there is no good way to provide the key for the mapping.

Fallback Functions

A contract can have exactly one unnamed function. This function cannot have arguments and is executed on a call to the contract if none of the other functions matches the given function identifier (or if no data was supplied at all).

contract Test {
  function() { x = 1; }
  uint x;

contract Caller {
  function callTest(address testAddress) {
    // results in Test(testAddress).x becoming == 1.

Function Modifiers

Modifiers can be used to easily change the behaviour of functions, for example to automatically check a condition prior to executing the function. They are inheritable properties of contracts and may be overridden by derived contracts.

contract owned {
  function owned() { owner = msg.sender; }
  address owner;

  // This contract only defines a modifier but does not use it - it will
  // be used in derived contracts.
  // The function body is inserted where the special symbol "_" in the
  // definition of a modifier appears.
  modifier onlyowner { if (msg.sender == owner) _ }
contract mortal is owned {
  // This contract inherits the "onlyowner"-modifier from "owned" and
  // applies it to the "kill"-function, which causes that calls to "kill"
  // only have an effect if they are made by the stored owner.
  function kill() onlyowner {
contract priced {
  // Modifiers can receive arguments:
  modifier costs(uint price) { if (msg.value >= price) _ }
contract Register is priced, owned {
  mapping (address => bool) registeredAddresses;
  uint price;
  function Register(uint initialPrice) { price = initialPrice; }
  function register() costs(price) {
    registeredAddresses[msg.sender] = true;
  function changePrice(uint _price) onlyowner {
    price = _price;

Multiple modifiers can be applied to a function by specifying them in a whitespace-separated list and will be evaluated in order. Explicit returns from a modifier or function body immediately leave the whole function, while control flow reaching the end of a function or modifier body continues after the "_" in the preceding modifier. Arbitrary expressions are allowed for modifier arguments and in this context, all symbols visible from the function are visible in the modifier. Symbols introduced in the modifier are not visible in the function (as they might change by overriding).


Events allow the convenient usage of the EVM logging facilities. Events are inheritable members of contracts. When they are called, they cause the arguments to be stored in the transaction's log. Up to three parameters can receive the attribute indexed which will cause the respective arguments to be treated as log topics instead of data. The hash of the signature of the event is one of the topics except you declared the event with anonymous specifier. All non-indexed arguments will be stored in the data part of the log. Example:

contract ClientReceipt {
  event Deposit(address indexed _from, bytes32 indexed _id, uint _value);
  function deposit(bytes32 _id) {
    Deposit(msg.sender, _id, msg.value);

Here, the call to Deposit will behave identical to log3(msg.value, 0x50cb9fe53daa9737b786ab3646f04d0150dc50ef4e75f59509d83667ad5adb20, sha3(msg.sender), _id);. Note that the large hex number is equal to the sha3-hash of "Deposit(address,bytes32,uint256)", the event's signature.

Layout of Storage

Statically-sized variables (everything except mapping and dynamically-sized array types) are laid out contiguously in storage starting from position 0. Multiple items that need less than 32 bytes are packed into a single storage slot if possible, according to the following rules:

  • The first item in a storage slot is stored lower-order aligned.
  • Elementary types use only that many bytes that are necessary to store them.
  • If an elementary type does not fit the remaining part of a storage slot, it is moved to the next storage slot.
  • Structs and array data always start a new slot and occupy whole slots (but items inside a struct or array are packed tightly according to these rules).

The elements of structs and arrays are stored after each other, just as if they were given explicitly.

Due to their unpredictable size, mapping and dynamically-sized array types use a sha3 computation to find the starting position of the value or the array data. These starting positions are always full stack slots.

The mapping or the dynamic array itself occupies an (unfilled) slot in storage at some position p according to the above rule (or by recursively applying this rule for mappings to mappings or arrays of arrays). For a dynamic array, this slot stores the number of elements in the array. For a mapping, the slot is unused (but it is needed so that two equal mappings after each other will use a different hash distribution). Array data is located at sha3(p) and the value corresponding to a mapping key k is located at sha3(k . p) where . is concatenation. If the value is again a non-elementary type, the positions are found by adding an offset of sha3(k . p).

So for the following contract snippet:

contract c {
  struct S { uint a; uint b; }
  uint x;
  mapping(uint => mapping(uint => S)) data;

The position of data[4][9].b is at sha3(uint256(9) . sha3(uint256(4) . uint(256(1))) + 1.

Esoteric Features

There are some types in Solidity's type system that have no counterpart in the syntax. One of these types are the types of functions. But still, using var it is possible to have local variables of these types:

contract FunctionSelector {
  function select(bool useB, uint x) returns (uint z) {
    var f = a;
    if (useB) f = b;
    return f(x);
  function a(uint x) returns (uint z) {
    return x * x;
  function b(uint x) returns (uint z) {
    return 2 * x;

Calling select(false, x) will compute x * x and select(true, x) will compute 2 * x.

Internals - the Optimizer

The Solidity optimizer operates on assembly, so it can be and also is used by other languages. It splits the sequence of instructions into basic blocks at points that are hard to move. These are basically all instructions that modify change the control flow (jumps, calls, etc), instructions that have side effects apart from MSTORE and SSTORE (like LOGi, EXTCODECOPY, but also CALLDATALOAD and others). Inside of such a block, the instructions are analysed and every modification to the stack, to memory or storage is recorded as an expression which consists of an instruction and a list of arguments which are essentially pointers to other expressions. The main idea is now to find expressions that are always equal (or every input) and combine them into an expression class. The optimizer first tries to find each new expression in a list of already known expressions. If this does not work, the expression is simplified according to rules like constant + constant = sum_of_constants or X * 1 = X. Since this is done recursively, we can also apply the latter rule if the second factor is a more complex expression where we know that it will always evaluate to one. Modifications to storage and memory locations have to erase knowledge about storage and memory locations which are not known to be different: If we first write to location x and then to location y and both are input variables, the second could overwrite the first, so we actually do not know what is stored at x after we wrote to y. On the other hand, if a simplification of the expression x - y evaluates to a non-zero constant, we know that we can keep our knowledge about what is stored at x.

At the end of this process, we know which expressions have to be on the stack in the end and have list of modifications to memory and storage. From these expressions which are actually needed, a dependency graph is created and every operation that is not part of this graph is essentially dropped. Now new code is generated that applies the modifications to memory and storage in the order they were made in the original code (dropping modifications which were found not to be needed) and finally, generates all values that are required to be on the stack in the correct place.

These steps are applied to each basic block and the newly generated code is used as replacement if it is smaller. If a basic block is split at a JUMPI and during the analysis, the condition evaluates to a constant, the JUMPI is replaced depending on the value of the constant, and thus code like

var x = 7;
data[7] = 9;
if (data[x] != x + 2) 
  return 2;
  return 1;

is simplified to code which can also be compiled from

data[7] = 9;
return 1;

even though the instructions contained a jump in the beginning.