Solidity is a statically typed language, which means that the type of each variable (state and local) needs to be specified. Solidity provides several elementary types which can be combined to form complex types.

In addition, types can interact with each other in expressions containing operators. For a quick reference of the various operators, see Order of Precedence of Operators.

The concept of “undefined” or “null” values does not exist in Solidity, but newly declared variables always have a default value dependent on its type. To handle any unexpected values, you should use the revert function to revert the whole transaction, or return a tuple with a second bool value denoting success.

Value Types

The following types are also called value types because variables of these types will always be passed by value, i.e. they are always copied when they are used as function arguments or in assignments.


bool: The possible values are constants true and false.


  • ! (logical negation)
  • && (logical conjunction, “and”)
  • || (logical disjunction, “or”)
  • == (equality)
  • != (inequality)

The operators || and && apply the common short-circuiting rules. This means that in the expression f(x) || g(y), if f(x) evaluates to true, g(y) will not be evaluated even if it may have side-effects.


int / uint: Signed and unsigned integers of various sizes. Keywords uint8 to uint256 in steps of 8 (unsigned of 8 up to 256 bits) and int8 to int256. uint and int are aliases for uint256 and int256, respectively.


  • Comparisons: <=, <, ==, !=, >=, > (evaluate to bool)
  • Bit operators: &, |, ^ (bitwise exclusive or), ~ (bitwise negation)
  • Shift operators: << (left shift), >> (right shift)
  • Arithmetic operators: +, -, unary -, *, /, % (modulo), ** (exponentiation)


Integers in Solidity are restricted to a certain range. For example, with uint32, this is 0 up to 2**32 - 1. If the result of some operation on those numbers does not fit inside this range, it is truncated. These truncations can have serious consequences that you should be aware of and mitigate against.


The value of a comparison is the one obtained by comparing the integer value.

Bit operations

Bit operations are performed on the two’s complement representation of the number. This means that, for example ~int256(0) == int256(-1).


The result of a shift operation has the type of the left operand, truncating the result to match the type.

  • For positive and negative x values, x << y is equivalent to x * 2**y.
  • For positive x values, x >> y is equivalent to x / 2**y.
  • For negative x values, x >> y is equivalent to (x + 1) / 2**y - 1 (which is the same as dividing x by 2**y while rounding down towards negative infinity).
  • In all cases, shifting by a negative y throws a runtime exception.


Before version 0.5.0 a right shift x >> y for negative x was equivalent to x / 2**y, i.e., right shifts used rounding up (towards zero) instead of rounding down (towards negative infinity).

Addition, Subtraction and Multiplication

Addition, subtraction and multiplication have the usual semantics. They wrap in two’s complement representation, meaning that for example uint256(0) - uint256(1) == 2**256 - 1. You have to take these overflows into account when designing safe smart contracts.

The expression -x is equivalent to (T(0) - x) where T is the type of x. This means that -x will not be negative if the type of x is an unsigned integer type. Also, -x can be positive if x is negative. There is another caveat also resulting from two’s complement representation:

int x = -2**255;
assert(-x == x);

This means that even if a number is negative, you cannot assume that its negation will be positive.


Since the type of the result of an operation is always the type of one of the operands, division on integers always results in an integer. In Solidity, division rounds towards zero. This mean that int256(-5) / int256(2) == int256(-2).

Note that in contrast, division on literals results in fractional values of arbitrary precision.


Division by zero causes a failing assert.


The modulo operation a % n yields the remainder r after the division of the operand a by the operand n, where q = int(a / n) and r = a - (n * q). This means that modulo results in the same sign as its left operand (or zero) and a % n == -(-a % n) holds for negative a:

  • int256(5) % int256(2) == int256(1)
  • int256(5) % int256(-2) == int256(1)
  • int256(-5) % int256(2) == int256(-1)
  • int256(-5) % int256(-2) == int256(-1)


Modulo with zero causes a failing assert.


Exponentiation is only available for unsigned types in the exponent. The resulting type of an exponentiation is always equal to the type of the base. Please take care that it is large enough to hold the result and prepare for potential wrapping behaviour.


Note that 0**0 is defined by the EVM as 1.

Fixed Point Numbers


Fixed point numbers are not fully supported by Solidity yet. They can be declared, but cannot be assigned to or from.

fixed / ufixed: Signed and unsigned fixed point number of various sizes. Keywords ufixedMxN and fixedMxN, where M represents the number of bits taken by the type and N represents how many decimal points are available. M must be divisible by 8 and goes from 8 to 256 bits. N must be between 0 and 80, inclusive. ufixed and fixed are aliases for ufixed128x18 and fixed128x18, respectively.


  • Comparisons: <=, <, ==, !=, >=, > (evaluate to bool)
  • Arithmetic operators: +, -, unary -, *, /, % (modulo)


The main difference between floating point (float and double in many languages, more precisely IEEE 754 numbers) and fixed point numbers is that the number of bits used for the integer and the fractional part (the part after the decimal dot) is flexible in the former, while it is strictly defined in the latter. Generally, in floating point almost the entire space is used to represent the number, while only a small number of bits define where the decimal point is.


The address type comes in two flavours, which are largely identical:

  • address: Holds a 20 byte value (size of an Ethereum address).
  • address payable: Same as address, but with the additional members transfer and send.

The idea behind this distinction is that address payable is an address you can send Ether to, while a plain address cannot be sent Ether.

Type conversions:

Implicit conversions from address payable to address are allowed, whereas conversions from address to address payable must be explicit via payable(<address>).

Address literals can be implicitly converted to address payable.

Explicit conversions to and from address are allowed for integers, integer literals, bytes20 and contract types with the following caveat: The result of a conversion of the form address(x) has the type address payable, if x is of integer or fixed bytes type, a literal or a contract with a receive or payable fallback function. If x is a contract without a receive or payable fallback function, then address(x) will be of type address. In external function signatures address is used for both the address and the address payable type.

Only expressions of type address can be converted to type address payable via payable(<address>).


It might very well be that you do not need to care about the distinction between address and address payable and just use address everywhere. For example, if you are using the withdrawal pattern, you can (and should) store the address itself as address, because you invoke the transfer function on msg.sender, which is an address payable.


  • <=, <, ==, !=, >= and >


If you convert a type that uses a larger byte size to an address, for example bytes32, then the address is truncated. To reduce conversion ambiguity version 0.4.24 and higher of the compiler force you make the truncation explicit in the conversion. Take for example the 32-byte value 0x111122223333444455556666777788889999AAAABBBBCCCCDDDDEEEEFFFFCCCC.

You can use address(uint160(bytes20(b))), which results in 0x111122223333444455556666777788889999aAaa, or you can use address(uint160(uint256(b))), which results in 0x777788889999AaAAbBbbCcccddDdeeeEfFFfCcCc.


The distinction between address and address payable was introduced with version 0.5.0. Also starting from that version, contracts do not derive from the address type, but can still be explicitly converted to address or to address payable, if they have a receive or payable fallback function.

Members of Addresses

For a quick reference of all members of address, see Members of Address Types.

  • balance and transfer

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

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

The transfer function fails if the balance of the current contract is not large enough or if the Ether transfer is rejected by the receiving account. The transfer function reverts on failure.


If x is a contract address, its code (more specifically: its Receive Ether Function, if present, or otherwise its Fallback Function, if present) will be executed together with the transfer call (this is a feature of the EVM and cannot be prevented). If that execution runs out of gas or fails in any way, the Ether transfer will be reverted and the current contract will stop with an exception.

  • send

Send is the low-level counterpart of transfer. If the execution fails, the current contract will not stop with an exception, but send will return false.


There are some dangers in using send: The transfer fails if the call stack depth is at 1024 (this can always be forced by the caller) and it also fails if the recipient runs out of gas. So in order to make safe Ether transfers, always check the return value of send, use transfer or even better: use a pattern where the recipient withdraws the money.

  • call, delegatecall and staticcall

In order to interface with contracts that do not adhere to the ABI, or to get more direct control over the encoding, the functions call, delegatecall and staticcall are provided. They all take a single bytes memory parameter and return the success condition (as a bool) and the returned data (bytes memory). The functions abi.encode, abi.encodePacked, abi.encodeWithSelector and abi.encodeWithSignature can be used to encode structured data.


bytes memory payload = abi.encodeWithSignature("register(string)", "MyName");
(bool success, bytes memory returnData) = address(nameReg).call(payload);


All these functions are low-level functions and should be used with care. Specifically, any unknown contract might be malicious and if you call it, you hand over control to that contract which could in turn call back into your contract, so be prepared for changes to your state variables when the call returns. The regular way to interact with other contracts is to call a function on a contract object (x.f()).


Previous versions of Solidity allowed these functions to receive arbitrary arguments and would also handle a first argument of type bytes4 differently. These edge cases were removed in version 0.5.0.

It is possible to adjust the supplied gas with the .gas() modifier:

address(nameReg).call.gas(1000000)(abi.encodeWithSignature("register(string)", "MyName"));

Similarly, the supplied Ether value can be controlled too:

address(nameReg).call.value(1 ether)(abi.encodeWithSignature("register(string)", "MyName"));

Lastly, these modifiers can be combined. Their order does not matter:

address(nameReg).call.gas(1000000).value(1 ether)(abi.encodeWithSignature("register(string)", "MyName"));

In a similar way, the function delegatecall can be used: the difference is that only the code of the given address is used, all other aspects (storage, balance, …) are taken from the current contract. The purpose of delegatecall is to use library code which is stored in another contract. The user has to ensure that the layout of storage in both contracts is suitable for delegatecall to be used.


Prior to homestead, only a limited variant called callcode was available that did not provide access to the original msg.sender and msg.value values. This function was removed in version 0.5.0.

Since byzantium staticcall can be used as well. This is basically the same as call, but will revert if the called function modifies the state in any way.

All three functions call, delegatecall and staticcall are very low-level functions and should only be used as a last resort as they break the type-safety of Solidity.

The .gas() option is available on all three methods, while the .value() option is not supported for delegatecall.


All contracts can be converted to address type, so it is possible to query the balance of the current contract using address(this).balance.

Contract Types

Every contract defines its own type. You can implicitly convert contracts to contracts they inherit from. Contracts can be explicitly converted to and from the address type.

Explicit conversion to and from the address payable type is only possible if the contract type has a receive or payable fallback function. The conversion is still performed using address(x). If the contract type does not have a receive or payable fallback function, the conversion to address payable can be done using payable(address(x)). You can find more information in the section about the address type.


Before version 0.5.0, contracts directly derived from the address type and there was no distinction between address and address payable.

If you declare a local variable of contract type (MyContract c), you can call functions on that contract. Take care to assign it from somewhere that is the same contract type.

You can also instantiate contracts (which means they are newly created). You can find more details in the ‘Contracts via new’ section.

The data representation of a contract is identical to that of the address type and this type is also used in the ABI.

Contracts do not support any operators.

The members of contract types are the external functions of the contract including any state variables marked as public.

For a contract C you can use type(C) to access type information about the contract.

Fixed-size byte arrays

The value types bytes1, bytes2, bytes3, …, bytes32 hold a sequence of bytes from one to up to 32. byte is an alias for bytes1.


  • Comparisons: <=, <, ==, !=, >=, > (evaluate to bool)
  • Bit operators: &, |, ^ (bitwise exclusive or), ~ (bitwise negation)
  • Shift operators: << (left shift), >> (right shift)
  • Index access: If x is of type bytesI, then x[k] for 0 <= k < I returns the k th byte (read-only).

The shifting operator works with any integer type as right operand (but returns the type of the left operand), which denotes the number of bits to shift by. Shifting by a negative amount causes a runtime exception.


  • .length yields the fixed length of the byte array (read-only).


The type byte[] is an array of bytes, but due to padding rules, it wastes 31 bytes of space for each element (except in storage). It is better to use the bytes type instead.

Dynamically-sized byte array

Dynamically-sized byte array, see Arrays. Not a value-type!
Dynamically-sized UTF-8-encoded string, see Arrays. Not a value-type!

Address Literals

Hexadecimal literals that pass the address checksum test, for example 0xdCad3a6d3569DF655070DEd06cb7A1b2Ccd1D3AF are of address payable type. Hexadecimal literals that are between 39 and 41 digits long and do not pass the checksum test produce an error. You can prepend (for integer types) or append (for bytesNN types) zeros to remove the error.


The mixed-case address checksum format is defined in EIP-55.

Rational and Integer Literals

Integer literals are formed from a sequence of numbers in the range 0-9. They are interpreted as decimals. For example, 69 means sixty nine. Octal literals do not exist in Solidity and leading zeros are invalid.

Decimal fraction literals are formed by a . with at least one number on one side. Examples include 1., .1 and 1.3.

Scientific notation is also supported, where the base can have fractions and the exponent cannot. Examples include 2e10, -2e10, 2e-10, 2.5e1.

Underscores can be used to separate the digits of a numeric literal to aid readability. For example, decimal 123_000, hexadecimal 0x2eff_abde, scientific decimal notation 1_2e345_678 are all valid. Underscores are only allowed between two digits and only one consecutive underscore is allowed. There is no additional semantic meaning added to a number literal containing underscores, the underscores are ignored.

Number literal expressions retain arbitrary precision until they are converted to a non-literal type (i.e. by using them together with a non-literal expression or by explicit conversion). This means that computations do not overflow and divisions do not truncate in number literal expressions.

For example, (2**800 + 1) - 2**800 results in the constant 1 (of type uint8) although intermediate results would not even fit the machine word size. Furthermore, .5 * 8 results in the integer 4 (although non-integers were used in between).

Any operator that can be applied to integers can also be applied to number literal expressions as long as the operands are integers. If any of the two is fractional, bit operations are disallowed and exponentiation is disallowed if the exponent is fractional (because that might result in a non-rational number).


Division on integer literals used to truncate in Solidity prior to version 0.4.0, but it now converts into a rational number, i.e. 5 / 2 is not equal to 2, but to 2.5.


Solidity has a number literal type for each rational number. Integer literals and rational number literals belong to number literal types. Moreover, all number literal expressions (i.e. the expressions that contain only number literals and operators) belong to number literal types. So the number literal expressions 1 + 2 and 2 + 1 both belong to the same number literal type for the rational number three.


Number literal expressions are converted into a non-literal type as soon as they are used with non-literal expressions. Disregarding types, the value of the expression assigned to b below evaluates to an integer. Because a is of type uint128, the expression 2.5 + a has to have a proper type, though. Since there is no common type for the type of 2.5 and uint128, the Solidity compiler does not accept this code.

uint128 a = 1;
uint128 b = 2.5 + a + 0.5;

String Literals and Types

String literals are written with either double or single-quotes ("foo" or 'bar'), and they can also be split into multiple consecutive parts ("foo" "bar" is equivalent to "foobar") which can be helpful when dealing with long strings. They do not imply trailing zeroes as in C; "foo" represents three bytes, not four. As with integer literals, their type can vary, but they are implicitly convertible to bytes1, …, bytes32, if they fit, to bytes and to string.

For example, with bytes32 samevar = "stringliteral" the string literal is interpreted in its raw byte form when assigned to a bytes32 type.

String literals support the following escape characters:

  • \<newline> (escapes an actual newline)
  • \\ (backslash)
  • \' (single quote)
  • \" (double quote)
  • \b (backspace)
  • \f (form feed)
  • \n (newline)
  • \r (carriage return)
  • \t (tab)
  • \v (vertical tab)
  • \xNN (hex escape, see below)
  • \uNNNN (unicode escape, see below)

\xNN takes a hex value and inserts the appropriate byte, while \uNNNN takes a Unicode codepoint and inserts an UTF-8 sequence.

The string in the following example has a length of ten bytes. It starts with a newline byte, followed by a double quote, a single quote a backslash character and then (without separator) the character sequence abcdef.


Any unicode line terminator which is not a newline (i.e. LF, VF, FF, CR, NEL, LS, PS) is considered to terminate the string literal. Newline only terminates the string literal if it is not preceded by a \.

Hexadecimal Literals

Hexadecimal literals are prefixed with the keyword hex and are enclosed in double or single-quotes (hex"001122FF", hex'0011_22_FF'). Their content must be hexadecimal digits which can optionally use a single underscore as separator between byte boundaries. The value of the literal will be the binary representation of the hexadecimal sequence.

Multiple hexadecimal literals separated by whitespace are concatenated into a single literal: hex"00112233" hex"44556677" is equivalent to hex"0011223344556677"

Hexadecimal literals behave like string literals and have the same convertibility restrictions.


Enums are one 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 explicit conversion from integer checks at runtime that the value lies inside the range of the enum and causes a failing assert otherwise. Enums require at least one member, and its default value when declared is the first member.

The data representation is the same as for enums in C: The options are represented by subsequent unsigned integer values starting from 0.

pragma solidity >=0.4.16 <0.7.0;

contract test {
    enum ActionChoices { GoLeft, GoRight, GoStraight, SitStill }
    ActionChoices choice;
    ActionChoices constant defaultChoice = ActionChoices.GoStraight;

    function setGoStraight() public {
        choice = ActionChoices.GoStraight;

    // Since enum types are not part of the ABI, the signature of "getChoice"
    // will automatically be changed to "getChoice() returns (uint8)"
    // for all matters external to Solidity. The integer type used is just
    // large enough to hold all enum values, i.e. if you have more than 256 values,
    // `uint16` will be used and so on.
    function getChoice() public view returns (ActionChoices) {
        return choice;

    function getDefaultChoice() public pure returns (uint) {
        return uint(defaultChoice);


Enums can also be declared on the file level, outside of contract or library definitions.

Function Types

Function types are the types of functions. Variables of function type can be assigned from functions and function parameters of function type can be used to pass functions to and return functions from function calls. Function types come in two flavours - internal and external functions:

Internal functions can only be called inside the current contract (more specifically, inside the current code unit, which also includes internal library functions and inherited functions) because they cannot be executed outside of the context of the current contract. Calling an internal function is realized by jumping to its entry label, just like when calling a function of the current contract internally.

External functions consist of an address and a function signature and they can be passed via and returned from external function calls.

Function types are notated as follows:

function (<parameter types>) {internal|external} [pure|view|payable] [returns (<return types>)]

In contrast to the parameter types, the return types cannot be empty - if the function type should not return anything, the whole returns (<return types>) part has to be omitted.

By default, function types are internal, so the internal keyword can be omitted. Note that this only applies to function types. Visibility has to be specified explicitly for functions defined in contracts, they do not have a default.


A function type A is implicitly convertible to a function type B if and only if their parameter types are identical, their return types are identical, their internal/external property is identical and the state mutability of A is not more restrictive than the state mutability of B. In particular:

  • pure functions can be converted to view and non-payable functions
  • view functions can be converted to non-payable functions
  • payable functions can be converted to non-payable functions

No other conversions between function types are possible.

The rule about payable and non-payable might be a little confusing, but in essence, if a function is payable, this means that it also accepts a payment of zero Ether, so it also is non-payable. On the other hand, a non-payable function will reject Ether sent to it, so non-payable functions cannot be converted to payable functions.

If a function type variable is not initialised, calling it results in a failed assertion. The same happens if you call a function after using delete on it.

If external function types are used outside of the context of Solidity, they are treated as the function type, which encodes the address followed by the function identifier together in a single bytes24 type.

Note that public functions of the current contract can be used both as an internal and as an external function. To use f as an internal function, just use f, if you want to use its external form, use this.f.


External (or public) functions have the following members:

  • .address returns the address of the contract of the function.
  • .selector returns the ABI function selector
  • .gas(uint) returns a callable function object which, when called, will send the specified amount of gas to the target function. See External Function Calls for more information.
  • .value(uint) returns a callable function object which, when called, will send the specified amount of wei to the target function. See External Function Calls for more information.

Example that shows how to use the members:

pragma solidity >=0.4.16 <0.7.0;

contract Example {
    function f() public payable returns (bytes4) {
        assert(this.f.address == address(this));
        return this.f.selector;

    function g() public {

Example that shows how to use internal function types:

pragma solidity >=0.4.16 <0.7.0;

library ArrayUtils {
    // internal functions can be used in internal library functions because
    // they will be part of the same code context
    function map(uint[] memory self, function (uint) pure returns (uint) f)
        returns (uint[] memory r)
        r = new uint[](self.length);
        for (uint i = 0; i < self.length; i++) {
            r[i] = f(self[i]);

    function reduce(
        uint[] memory self,
        function (uint, uint) pure returns (uint) f
        returns (uint r)
        r = self[0];
        for (uint i = 1; i < self.length; i++) {
            r = f(r, self[i]);

    function range(uint length) internal pure returns (uint[] memory r) {
        r = new uint[](length);
        for (uint i = 0; i < r.length; i++) {
            r[i] = i;

contract Pyramid {
    using ArrayUtils for *;

    function pyramid(uint l) public pure returns (uint) {
        return ArrayUtils.range(l).map(square).reduce(sum);

    function square(uint x) internal pure returns (uint) {
        return x * x;

    function sum(uint x, uint y) internal pure returns (uint) {
        return x + y;

Another example that uses external function types:

pragma solidity >=0.4.22 <0.7.0;

contract Oracle {
    struct Request {
        bytes data;
        function(uint) external callback;

    Request[] private requests;
    event NewRequest(uint);

    function query(bytes memory data, function(uint) external callback) public {
        requests.push(Request(data, callback));
        emit NewRequest(requests.length - 1);

    function reply(uint requestID, uint response) public {
        // Here goes the check that the reply comes from a trusted source

contract OracleUser {
    Oracle constant private ORACLE_CONST = Oracle(0x1234567); // known contract
    uint private exchangeRate;

    function buySomething() public {
        ORACLE_CONST.query("USD", this.oracleResponse);

    function oracleResponse(uint response) public {
            msg.sender == address(ORACLE_CONST),
            "Only oracle can call this."
        exchangeRate = response;


Lambda or inline functions are planned but not yet supported.

Reference Types

Values of reference type can be modified through multiple different names. Contrast this with value types where you get an independent copy whenever a variable of value type is used. Because of that, reference types have to be handled more carefully than value types. Currently, reference types comprise structs, arrays and mappings. If you use a reference type, you always have to explicitly provide the data area where the type is stored: memory (whose lifetime is limited to an external function call), storage (the location where the state variables are stored, where the lifetime is limited to the lifetime of a contract) or calldata (special data location that contains the function arguments, only available for external function call parameters).

An assignment or type conversion that changes the data location will always incur an automatic copy operation, while assignments inside the same data location only copy in some cases for storage types.

Data location

Every reference type has an additional annotation, the “data location”, about where it is stored. There are three data locations: memory, storage and calldata. Calldata is only valid for parameters of external contract functions and is required for this type of parameter. Calldata is a non-modifiable, non-persistent area where function arguments are stored, and behaves mostly like memory.


Prior to version 0.5.0 the data location could be omitted, and would default to different locations depending on the kind of variable, function type, etc., but all complex types must now give an explicit data location.

Data location and assignment behaviour

Data locations are not only relevant for persistency of data, but also for the semantics of assignments:

  • Assignments between storage and memory (or from calldata) always create an independent copy.
  • Assignments from memory to memory only create references. This means that changes to one memory variable are also visible in all other memory variables that refer to the same data.
  • Assignments from storage to a local storage variable also only assign a reference.
  • All other assignments to storage always copy. Examples for this case are assignments to state variables or to members of local variables of storage struct type, even if the local variable itself is just a reference.
pragma solidity >=0.4.0 <0.7.0;

contract C {
    // The data location of x is storage.
    // This is the only place where the
    // data location can be omitted.
    uint[] x;

    // The data location of memoryArray is memory.
    function f(uint[] memory memoryArray) public {
        x = memoryArray; // works, copies the whole array to storage
        uint[] storage y = x; // works, assigns a pointer, data location of y is storage
        y[7]; // fine, returns the 8th element
        y.pop(); // fine, modifies x through y
        delete x; // fine, clears the array, also modifies y
        // The following does not work; it would need to create a new temporary /
        // unnamed array in storage, but storage is "statically" allocated:
        // y = memoryArray;
        // This does not work either, since it would "reset" the pointer, but there
        // is no sensible location it could point to.
        // delete y;
        g(x); // calls g, handing over a reference to x
        h(x); // calls h and creates an independent, temporary copy in memory

    function g(uint[] storage) internal pure {}
    function h(uint[] memory) public pure {}


Arrays can have a compile-time fixed size, or they can have a dynamic size.

The type of an array of fixed size k and element type T is written as T[k], and an array of dynamic size as T[].

For example, an array of 5 dynamic arrays of uint is written as uint[][5]. The notation is reversed compared to some other languages. In Solidity, X[3] is always an array containing three elements of type X, even if X is itself an array. This is not the case in other languages such as C.

Indices are zero-based, and access is in the opposite direction of the declaration.

For example, if you have a variable uint[][5] memory x, you access the second uint in the third dynamic array using x[2][1], and to access the third dynamic array, use x[2]. Again, if you have an array T[5] a for a type T that can also be an array, then a[2] always has type T.

Array elements can be of any type, including mapping or struct. The general restrictions for types apply, in that mappings can only be stored in the storage data location and publicly-visible functions need parameters that are ABI types.

It is possible to mark state variable arrays public and have Solidity create a getter. The numeric index becomes a required parameter for the getter.

Accessing an array past its end causes a failing assertion. Methods .push() and .push(value) can be used to append a new element at the end of the array, where .push() appends a zero-initialized element and returns a reference to it.

bytes and strings as Arrays

Variables of type bytes and string are special arrays. A bytes is similar to byte[], but it is packed tightly in calldata and memory. string is equal to bytes but does not allow length or index access.

Solidity does not have string manipulation functions, but there are third-party string libraries. You can also compare two strings by their keccak256-hash using keccak256(abi.encodePacked(s1)) == keccak256(abi.encodePacked(s2)) and concatenate two strings using abi.encodePacked(s1, s2).

You should use bytes over byte[] because it is cheaper, since byte[] adds 31 padding bytes between the elements. As a general rule, use bytes for arbitrary-length raw byte data and string for arbitrary-length string (UTF-8) data. If you can limit the length to a certain number of bytes, always use one of the value types bytes1 to bytes32 because they are much cheaper.


If you want to access the byte-representation of a string s, use bytes(s).length / bytes(s)[7] = 'x';. Keep in mind that you are accessing the low-level bytes of the UTF-8 representation, and not the individual characters.

Allocating Memory Arrays

Memory arrays with dynamic length can be created using the new operator. As opposed to storage arrays, it is not possible to resize memory arrays (e.g. the .push member functions are not available). You either have to calculate the required size in advance or create a new memory array and copy every element.

pragma solidity >=0.4.16 <0.7.0;

contract C {
    function f(uint len) public pure {
        uint[] memory a = new uint[](7);
        bytes memory b = new bytes(len);
        assert(a.length == 7);
        assert(b.length == len);
        a[6] = 8;

Array Literals

An array literal is a comma-separated list of one or more expressions, enclosed in square brackets ([...]). For example [1, a, f(3)]. There must be a common type all elements can be implicitly converted to. This is the elementary type of the array.

Array literals are always statically-sized memory arrays.

In the example below, the type of [1, 2, 3] is uint8[3] memory. Because the type of each of these constants is uint8, if you want the result to be a uint[3] memory type, you need to convert the first element to uint.

pragma solidity >=0.4.16 <0.7.0;

contract C {
    function f() public pure {
        g([uint(1), 2, 3]);
    function g(uint[3] memory) public pure {
        // ...

Fixed size memory arrays cannot be assigned to dynamically-sized memory arrays, i.e. the following is not possible:

pragma solidity >=0.4.0 <0.7.0;

// This will not compile.
contract C {
    function f() public {
        // The next line creates a type error because uint[3] memory
        // cannot be converted to uint[] memory.
        uint[] memory x = [uint(1), 3, 4];

It is planned to remove this restriction in the future, but it creates some complications because of how arrays are passed in the ABI.

Array Members

Arrays have a length member that contains their number of elements. The length of memory arrays is fixed (but dynamic, i.e. it can depend on runtime parameters) once they are created.
Dynamic storage arrays and bytes (not string) have a member function called push() that you can use to append a zero-initialised element at the end of the array. It returns a reference to the element, so that it can be used like x.push().t = 2 or x.push() = b.
Dynamic storage arrays and bytes (not string) have a member function called push(x) that you can use to append a given element at the end of the array. The function returns nothing.
Dynamic storage arrays and bytes (not string) have a member function called pop that you can use to remove an element from the end of the array. This also implicitly calls delete on the removed element.


Increasing the length of a storage array by calling push() has constant gas costs because storage is zero-initialised, while decreasing the length by calling pop() has a cost that depends on the “size” of the element being removed. If that element is an array, it can be very costly, because it includes explicitly clearing the removed elements similar to calling delete on them.


To use arrays of arrays in external (instead of public) functions, you need to activate ABIEncoderV2.


In EVM versions before Byzantium, it was not possible to access dynamic arrays return from function calls. If you call functions that return dynamic arrays, make sure to use an EVM that is set to Byzantium mode.

pragma solidity >=0.4.16 <0.7.0;

contract ArrayContract {
    uint[2**20] m_aLotOfIntegers;
    // Note that the following is not a pair of dynamic arrays but a
    // dynamic array of pairs (i.e. of fixed size arrays of length two).
    // Because of that, T[] is always a dynamic array of T, even if T
    // itself is an array.
    // Data location for all state variables is storage.
    bool[2][] m_pairsOfFlags;

    // newPairs is stored in memory - the only possibility
    // for public contract function arguments
    function setAllFlagPairs(bool[2][] memory newPairs) public {
        // assignment to a storage array performs a copy of ``newPairs`` and
        // replaces the complete array ``m_pairsOfFlags``.
        m_pairsOfFlags = newPairs;

    struct StructType {
        uint[] contents;
        uint moreInfo;
    StructType s;

    function f(uint[] memory c) public {
        // stores a reference to ``s`` in ``g``
        StructType storage g = s;
        // also changes ``s.moreInfo``.
        g.moreInfo = 2;
        // assigns a copy because ``g.contents``
        // is not a local variable, but a member of
        // a local variable.
        g.contents = c;

    function setFlagPair(uint index, bool flagA, bool flagB) public {
        // access to a non-existing index will throw an exception
        m_pairsOfFlags[index][0] = flagA;
        m_pairsOfFlags[index][1] = flagB;

    function changeFlagArraySize(uint newSize) public {
        // using push and pop is the only way to change the
        // length of an array
        if (newSize < m_pairsOfFlags.length) {
            while (m_pairsOfFlags.length > newSize)
        } else if (newSize > m_pairsOfFlags.length) {
            while (m_pairsOfFlags.length < newSize)

    function clear() public {
        // these clear the arrays completely
        delete m_pairsOfFlags;
        delete m_aLotOfIntegers;
        // identical effect here
        m_pairsOfFlags = new bool[2][](0);

    bytes m_byteData;

    function byteArrays(bytes memory data) public {
        // byte arrays ("bytes") are different as they are stored without padding,
        // but can be treated identical to "uint8[]"
        m_byteData = data;
        for (uint i = 0; i < 7; i++)
        m_byteData[3] = 0x08;
        delete m_byteData[2];

    function addFlag(bool[2] memory flag) public returns (uint) {
        return m_pairsOfFlags.length;

    function createMemoryArray(uint size) public pure returns (bytes memory) {
        // Dynamic memory arrays are created using `new`:
        uint[2][] memory arrayOfPairs = new uint[2][](size);

        // Inline arrays are always statically-sized and if you only
        // use literals, you have to provide at least one type.
        arrayOfPairs[0] = [uint(1), 2];

        // Create a dynamic byte array:
        bytes memory b = new bytes(200);
        for (uint i = 0; i < b.length; i++)
            b[i] = byte(uint8(i));
        return b;

Array Slices

Array slices are a view on a contiguous portion of an array. They are written as x[start:end], where start and end are expressions resulting in a uint256 type (or implicitly convertible to it). The first element of the slice is x[start] and the last element is x[end - 1].

If start is greater than end or if end is greater than the length of the array, an exception is thrown.

Both start and end are optional: start defaults
to 0 and end defaults to the length of the array.

Array slices do not have any members. They are implicitly convertible to arrays of their underlying type and support index access. Index access is not absolute in the underlying array, but relative to the start of the slice.

Array slices do not have a type name which means no variable can have an array slices as type, they only exist in intermediate expressions.


As of now, array slices are only implemented for calldata arrays.

Array slices are useful to ABI-decode secondary data passed in function parameters:

pragma solidity >=0.4.99 <0.7.0;

contract Proxy {
    /// Address of the client contract managed by proxy i.e., this contract
    address client;

    constructor(address _client) public {
        client = _client;

    /// Forward call to "setOwner(address)" that is implemented by client
    /// after doing basic validation on the address argument.
    function forward(bytes calldata _payload) external {
        bytes4 sig = abi.decode(_payload[:4], (bytes4));
        if (sig == bytes4(keccak256("setOwner(address)"))) {
            address owner = abi.decode(_payload[4:], (address));
            require(owner != address(0), "Address of owner cannot be zero.");
        (bool status,) = client.delegatecall(_payload);
        require(status, "Forwarded call failed.");


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

pragma solidity >=0.4.11 <0.7.0;

// Defines a new type with two fields.
// Declaring a struct outside of a contract allows
// it to be shared by multiple contracts.
// Here, this is not really needed.
struct Funder {
    address addr;
    uint amount;

contract CrowdFunding {
    // Structs can also be defined inside contracts, which makes them
    // visible only there and in derived contracts.
    struct Campaign {
        address payable beneficiary;
        uint fundingGoal;
        uint numFunders;
        uint amount;
        mapping (uint => Funder) funders;

    uint numCampaigns;
    mapping (uint => Campaign) campaigns;

    function newCampaign(address payable beneficiary, uint goal) public returns (uint campaignID) {
        campaignID = numCampaigns++; // campaignID is return variable
        // Creates new struct in memory and copies it to storage.
        // We leave out the mapping type, because it is not valid in memory.
        // If structs are copied (even from storage to storage),
        // types that are not valid outside of storage (ex. mappings and array of mappings)
        // are always omitted, because they cannot be enumerated.
        campaigns[campaignID] = Campaign(beneficiary, goal, 0, 0);

    function contribute(uint campaignID) public payable {
        Campaign storage c = campaigns[campaignID];
        // Creates a new temporary memory struct, initialised with the given values
        // and copies it over to storage.
        // Note that you can also use Funder(msg.sender, msg.value) to initialise.
        c.funders[c.numFunders++] = Funder({addr: msg.sender, amount: msg.value});
        c.amount += msg.value;

    function checkGoalReached(uint campaignID) public returns (bool reached) {
        Campaign storage c = campaigns[campaignID];
        if (c.amount < c.fundingGoal)
            return false;
        uint amount = c.amount;
        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 inside mappings and arrays and they can itself contain mappings and arrays.

It is not possible for a struct to contain a member of its own type, although the struct itself can be the value type of a mapping member or it can contain a dynamically-sized array of its type. This restriction is necessary, as the size of the struct has to be finite.

Note how in all the functions, a struct type is assigned to a local variable with data location storage. This does not copy the struct but only stores a reference so that assignments to members of the local variable actually write to the state.

Of course, you can also directly access the members of the struct without assigning it to a local variable, as in campaigns[campaignID].amount = 0.

Mapping Types

Mapping types use the syntax mapping(_KeyType => _ValueType) and variables of mapping type are declared using the syntax mapping(_KeyType => _ValueType) _VariableName. The _KeyType can be any built-in value type plus bytes and string. User-defined or complex types such as contract types, enums, mappings, structs or array types apart from bytes and string are not allowed. _ValueType can be any type, including mappings, arrays and structs.

You can think of mappings as hash tables, which are virtually initialised such that every possible key exists and is mapped to a value whose byte-representation is all zeros, a type’s default value. The similarity ends there, the key data is not stored in a mapping, only its keccak256 hash is used to look up the value.

Because of this, mappings do not have a length or a concept of a key or value being set, and therefore cannot be erased without extra information regarding the assigned keys (see Clearing Mappings).

Mappings can only have a data location of storage and thus are allowed for state variables, as storage reference types in functions, or as parameters for library functions. They cannot be used as parameters or return parameters of contract functions that are publicly visible.

You can mark state variables of mapping type as public and Solidity creates a getter for you. The _KeyType becomes a parameter for the getter. If _ValueType is a value type or a struct, the getter returns _ValueType. If _ValueType is an array or a mapping, the getter has one parameter for each _KeyType, recursively.

In the example below, the MappingExample contract defines a public balances mapping, with the key type an address, and a value type a uint, mapping an Ethereum address to an unsigned integer value. As uint is a value type, the getter returns a value that matches the type, which you can see in the MappingUser contract that returns the value at the specified address.

pragma solidity >=0.4.0 <0.7.0;

contract MappingExample {
    mapping(address => uint) public balances;

    function update(uint newBalance) public {
        balances[msg.sender] = newBalance;

contract MappingUser {
    function f() public returns (uint) {
        MappingExample m = new MappingExample();
        return m.balances(address(this));

The example below is a simplified version of an ERC20 token. _allowances is an example of a mapping type inside another mapping type. The example below uses _allowances to record the amount someone else is allowed to withdraw from your account.

pragma solidity >=0.4.0 <0.7.0;

contract MappingExample {

    mapping (address => uint256) private _balances;
    mapping (address => mapping (address => uint256)) private _allowances;

    event Transfer(address indexed from, address indexed to, uint256 value);
    event Approval(address indexed owner, address indexed spender, uint256 value);

    function allowance(address owner, address spender) public view returns (uint256) {
        return _allowances[owner][spender];

    function transferFrom(address sender, address recipient, uint256 amount) public returns (bool) {
        _transfer(sender, recipient, amount);
        approve(sender, msg.sender, amount);
        return true;

    function approve(address owner, address spender, uint256 amount) public returns (bool) {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
        return true;

    function _transfer(address sender, address recipient, uint256 amount) internal {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _balances[sender] -= amount;
        _balances[recipient] += amount;
        emit Transfer(sender, recipient, amount);

Iterable Mappings

You cannot iterate over mappings, i.e. you cannot enumerate their keys. It is possible, though, to implement a data structure on top of them and iterate over that. For example, the code below implements an IterableMapping library that the User contract then adds data too, and the sum function iterates over to sum all the values.

pragma solidity >=0.5.99 <0.7.0;

struct IndexValue { uint keyIndex; uint value; }
struct KeyFlag { uint key; bool deleted; }

struct itmap {
    mapping(uint => IndexValue) data;
    KeyFlag[] keys;
    uint size;

library IterableMapping {
    function insert(itmap storage self, uint key, uint value) internal returns (bool replaced) {
        uint keyIndex = self.data[key].keyIndex;
        self.data[key].value = value;
        if (keyIndex > 0)
            return true;
        else {
            keyIndex = self.keys.length;
            self.data[key].keyIndex = keyIndex + 1;
            self.keys[keyIndex].key = key;
            return false;

    function remove(itmap storage self, uint key) internal returns (bool success) {
        uint keyIndex = self.data[key].keyIndex;
        if (keyIndex == 0)
            return false;
        delete self.data[key];
        self.keys[keyIndex - 1].deleted = true;
        self.size --;

    function contains(itmap storage self, uint key) internal view returns (bool) {
        return self.data[key].keyIndex > 0;

    function iterate_start(itmap storage self) internal view returns (uint keyIndex) {
        return iterate_next(self, uint(-1));

    function iterate_valid(itmap storage self, uint keyIndex) internal view returns (bool) {
        return keyIndex < self.keys.length;

    function iterate_next(itmap storage self, uint keyIndex) internal view returns (uint r_keyIndex) {
        while (keyIndex < self.keys.length && self.keys[keyIndex].deleted)
        return keyIndex;

    function iterate_get(itmap storage self, uint keyIndex) internal view returns (uint key, uint value) {
        key = self.keys[keyIndex].key;
        value = self.data[key].value;

// How to use it
contract User {
    // Just a struct holding our data.
    itmap data;
    // Apply library functions to the data type.
    using IterableMapping for itmap;

    // Insert something
    function insert(uint k, uint v) public returns (uint size) {
        // This calls IterableMapping.insert(data, k, v)
        data.insert(k, v);
        // We can still access members of the struct,
        // but we should take care not to mess with them.
        return data.size;

    // Computes the sum of all stored data.
    function sum() public view returns (uint s) {
        for (
            uint i = data.iterate_start();
            i = data.iterate_next(i)
        ) {
            (, uint value) = data.iterate_get(i);
            s += value;

Operators Involving LValues

If a is an LValue (i.e. a variable or something that can be assigned to), the following operators are available as shorthands:

a += e is equivalent to a = a + e. The operators -=, *=, /=, %=, |=, &= and ^= are defined accordingly. a++ and a-- are equivalent to a += 1 / a -= 1 but the expression itself still has the previous value of a. In contrast, --a and ++a have the same effect on a but return the value after the change.


delete a assigns the initial value for the type to a. I.e. for integers it is equivalent to a = 0, but it can also be used on arrays, where it assigns a dynamic array of length zero or a static array of the same length with all elements set to their initial value. delete a[x] deletes the item at index x of the array and leaves all other elements and the length of the array untouched. This especially means that it leaves a gap in the array. If you plan to remove items, a mapping is probably a better choice.

For structs, it assigns a struct with all members reset. In other words, the value of a after delete a is the same as if a would be declared without assignment, with the following caveat:

delete has no effect on mappings (as the keys of mappings may be arbitrary and are generally unknown). So if you delete a struct, it will reset all members that are not mappings and also recurse into the members unless they are mappings. However, individual keys and what they map to can be deleted: If a is a mapping, then delete a[x] will delete the value stored at x.

It is important to note that delete a really behaves like an assignment to a, i.e. it stores a new object in a. This distinction is visible when a is reference variable: It will only reset a itself, not the value it referred to previously.

pragma solidity >=0.4.0 <0.7.0;

contract DeleteExample {
    uint data;
    uint[] dataArray;

    function f() public {
        uint x = data;
        delete x; // sets x to 0, does not affect data
        delete data; // sets data to 0, does not affect x
        uint[] storage y = dataArray;
        delete dataArray; // this sets dataArray.length to zero, but as uint[] is a complex object, also
        // y is affected which is an alias to the storage object
        // On the other hand: "delete y" is not valid, as assignments to local variables
        // referencing storage objects can only be made from existing storage objects.
        assert(y.length == 0);

Conversions between Elementary Types

Implicit Conversions

An implicit type conversion is automatically applied by the compiler in some cases during assignments, when passing arguments to functions and when applying operators. In general, an implicit conversion between value-types is possible if it makes sense semantically and no information is lost.

For example, uint8 is convertible to uint16 and int128 to int256, but int8 is not convertible to uint256, because uint256 cannot hold values such as -1.

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). This means that operations are always performed in the type of one of the operands.

For more details about which implicit conversions are possible, please consult the sections about the types themselves.

In the example below, y and z, the operands of the addition, do not have the same type, but uint8 can be implicitly converted to uint16 and not vice-versa. Because of that, y is converted to the type of z before the addition is performed in the uint16 type. The resulting type of the expression y + z is uint16`. Because it is assigned to a variable of type ``uint32 another implicit conversion is performed after the addition.

uint8 y;
uint16 z;
uint32 x = y + z;

Explicit Conversions

If the compiler does not allow implicit conversion but you are confident a conversion will work, an explicit type conversion is sometimes possible. This may result in unexpected behaviour and allows you to bypass some security features of the compiler, so be sure to test that the result is what you want and expect!

Take the following example that converts a negative int to a uint:

int  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 the two’s complement representation of 256 bits.

If an integer is explicitly converted to a smaller type, higher-order bits are cut off:

uint32 a = 0x12345678;
uint16 b = uint16(a); // b will be 0x5678 now

If an integer is explicitly converted to a larger type, it is padded on the left (i.e., at the higher order end). The result of the conversion will compare equal to the original integer:

uint16 a = 0x1234;
uint32 b = uint32(a); // b will be 0x00001234 now
assert(a == b);

Fixed-size bytes types behave differently during conversions. They can be thought of as sequences of individual bytes and converting to a smaller type will cut off the sequence:

bytes2 a = 0x1234;
bytes1 b = bytes1(a); // b will be 0x12

If a fixed-size bytes type is explicitly converted to a larger type, it is padded on the right. Accessing the byte at a fixed index will result in the same value before and after the conversion (if the index is still in range):

bytes2 a = 0x1234;
bytes4 b = bytes4(a); // b will be 0x12340000
assert(a[0] == b[0]);
assert(a[1] == b[1]);

Since integers and fixed-size byte arrays behave differently when truncating or padding, explicit conversions between integers and fixed-size byte arrays are only allowed, if both have the same size. If you want to convert between integers and fixed-size byte arrays of different size, you have to use intermediate conversions that make the desired truncation and padding rules explicit:

bytes2 a = 0x1234;
uint32 b = uint16(a); // b will be 0x00001234
uint32 c = uint32(bytes4(a)); // c will be 0x12340000
uint8 d = uint8(uint16(a)); // d will be 0x34
uint8 e = uint8(bytes1(a)); // e will be 0x12

Conversions between Literals and Elementary Types

Integer Types

Decimal and hexadecimal number literals can be implicitly converted to any integer type that is large enough to represent it without truncation:

uint8 a = 12; // fine
uint32 b = 1234; // fine
uint16 c = 0x123456; // fails, since it would have to truncate to 0x3456

Fixed-Size Byte Arrays

Decimal number literals cannot be implicitly converted to fixed-size byte arrays. Hexadecimal number literals can be, but only if the number of hex digits exactly fits the size of the bytes type. As an exception both decimal and hexadecimal literals which have a value of zero can be converted to any fixed-size bytes type:

bytes2 a = 54321; // not allowed
bytes2 b = 0x12; // not allowed
bytes2 c = 0x123; // not allowed
bytes2 d = 0x1234; // fine
bytes2 e = 0x0012; // fine
bytes4 f = 0; // fine
bytes4 g = 0x0; // fine

String literals and hex string literals can be implicitly converted to fixed-size byte arrays, if their number of characters matches the size of the bytes type:

bytes2 a = hex"1234"; // fine
bytes2 b = "xy"; // fine
bytes2 c = hex"12"; // not allowed
bytes2 d = hex"123"; // not allowed
bytes2 e = "x"; // not allowed
bytes2 f = "xyz"; // not allowed


As described in Address Literals, hex literals of the correct size that pass the checksum test are of address type. No other literals can be implicitly converted to the address type.

Explicit conversions from bytes20 or any integer type to address result in address payable.

An address a can be converted to address payable via payable(a).