# Values and Types

Values are objects, like for example booleans, integers, or arrays. Values are typed.

## Booleans

The two boolean values `true`

and `false`

have the type `Bool`

.

## Numeric Literals

Numbers can be written in various bases. Numbers are assumed to be decimal by default. Non-decimal literals have a specific prefix.

Numeral system | Prefix | Characters |
---|---|---|

Decimal | None | one or more numbers (`0` to `9` ) |

Binary | `0b` | one or more zeros or ones (`0` or `1` ) |

Octal | `0o` | one or more numbers in the range `0` to `7` |

Hexadecimal | `0x` | one or more numbers, or characters `a` to `f` , lowercase or uppercase |

```
// A decimal number
//
1234567890 // is `1234567890`
// A binary number
//
0b101010 // is `42`
// An octal number
//
0o12345670 // is `2739128`
// A hexadecimal number
//
0x1234567890ABCabc // is `1311768467294898876`
// Invalid: unsupported prefix 0z
//
0z0
// A decimal number with leading zeros. Not an octal number!
00123 // is `123`
// A binary number with several trailing zeros.
0b001000 // is `8`
```

Decimal numbers may contain underscores (`_`

) to logically separate components.

```
let largeNumber = 1_000_000
// Invalid: Value is not a number literal, but a variable.
let notNumber = _123
```

Underscores are allowed for all numeral systems.

```
let binaryNumber = 0b10_11_01
```

## Integers

Integers are numbers without a fractional part.
They are either *signed* (positive, zero, or negative)
or *unsigned* (positive or zero).

Signed integer types which check for overflow and underflow have an `Int`

prefix
and can represent values in the following ranges:

: −2^7 through 2^7 − 1 (-128 through 127)`Int8`

: −2^15 through 2^15 − 1 (-32768 through 32767)`Int16`

: −2^31 through 2^31 − 1 (-2147483648 through 2147483647)`Int32`

: −2^63 through 2^63 − 1 (-9223372036854775808 through 9223372036854775807)`Int64`

: −2^127 through 2^127 − 1`Int128`

: −2^255 through 2^255 − 1`Int256`

Unsigned integer types which check for overflow and underflow have a `UInt`

prefix
and can represent values in the following ranges:

: 0 through 2^8 − 1 (255)`UInt8`

: 0 through 2^16 − 1 (65535)`UInt16`

: 0 through 2^32 − 1 (4294967295)`UInt32`

: 0 through 2^64 − 1 (18446744073709551615)`UInt64`

: 0 through 2^128 − 1`UInt128`

: 0 through 2^256 − 1`UInt256`

Unsigned integer types which do **not** check for overflow and underflow,
i.e. wrap around, have the `Word`

prefix
and can represent values in the following ranges:

: 0 through 2^8 − 1 (255)`Word8`

: 0 through 2^16 − 1 (65535)`Word16`

: 0 through 2^32 − 1 (4294967295)`Word32`

: 0 through 2^64 − 1 (18446744073709551615)`Word64`

The types are independent types, i.e. not subtypes of each other.

See the section about arithmetic operators for further information about the behavior of the different integer types.

```
// Declare a constant that has type `UInt8` and the value 10.
let smallNumber: UInt8 = 10
```

```
// Invalid: negative literal cannot be used as an unsigned integer
//
let invalidNumber: UInt8 = -10
```

In addition, the arbitrary precision integer type `Int`

is provided.

```
let veryLargeNumber: Int = 10000000000000000000000000000000
```

Integer literals are inferred to have type `Int`

,
or if the literal occurs in a position that expects an explicit type,
e.g. in a variable declaration with an explicit type annotation.

```
let someNumber = 123
// `someNumber` has type `Int`
```

Negative integers are encoded in two's complement representation.

Integer types are not converted automatically. Types must be explicitly converted, which can be done by calling the constructor of the type with the integer type.

```
let x: Int8 = 1
let y: Int16 = 2
// Invalid: the types of the operands, `Int8` and `Int16` are incompatible.
let z = x + y
// Explicitly convert `x` from `Int8` to `Int16`.
let a = Int16(x) + y
// `a` has type `Int16`
// Invalid: The integer literal is expected to be of type `UInt8`,
// but the large integer literal does not fit in the range of `UInt8`.
//
let b = x + 1000000000000000000000000
```

### Integer Functions

Integers have multiple built-in functions you can use.

`fun toString(): String`

Returns the string representation of the integer.

`let answer = 42 answer.toString() // is "42"`

`fun toBigEndianBytes(): [UInt8]`

Returns the byte array representation (

`[UInt8]`

) in big-endian order of the integer.`let largeNumber = 1234567890 largeNumber.toBigEndianBytes() // is `[73, 150, 2, 210]``

## Fixed-Point Numbers

🚧 Status: Currently only the 64-bit wide `Fix64`

and `UFix64`

types are available.
More fixed-point number types will be added in a future release.

Fixed-point numbers are useful for representing fractional values. They have a fixed number of digits after decimal point.

They are essentially integers which are scaled by a factor. For example, the value 1.23 can be represented as 1230 with a scaling factor of 1/1000. The scaling factor is the same for all values of the same type and stays the same during calculations.

Fixed-point numbers in Cadence have a scaling factor with a power of 10, instead of a power of 2, i.e. they are decimal, not binary.

Signed fixed-point number types have the prefix `Fix`

,
have the following factors, and can represent values in the following ranges:

: Factor 1/100,000,000; -92233720368.54775808 through 92233720368.54775807`Fix64`

Unsigned fixed-point number types have the prefix `UFix`

,
have the following factors, and can represent values in the following ranges:

: Factor 1/100,000,000; 0.0 through 184467440737.09551615`UFix64`

### Fixed-Point Number Functions

Fixed-Point numbers have multiple built-in functions you can use.

`fun toString(): String`

Returns the string representation of the fixed-point number.

`let fix = 1.23 fix.toString() // is "1.23000000"`

`fun toBigEndianBytes(): [UInt8]`

Returns the byte array representation (

`[UInt8]`

) in big-endian order of the fixed-point number.`let fix = 1.23 fix.toBigEndianBytes() // is `[0, 0, 0, 0, 7, 84, 212, 192]``

## Minimum and maximum values

The minimum and maximum values for all integer and fixed-point number types are available through the fields `min`

and `max`

.

For example:

```
let max = UInt8.max
// `max` is 255, the maximum value of the type `UInt8`
```

```
let max = UFix64.max
// `max` is 184467440737.09551615, the maximum value of the type `UFix64`
```

## Saturation Arithmetic

Integers and fixed-point numbers support saturation arithmetic: Arithmetic operations, such as addition or multiplications, are saturating at the numeric bounds instead of overflowing.

If the result of an operation is greater than the maximum value of the operands' type, the maximum is returned. If the result is lower than the minimum of the operands' type, the minimum is returned.

Saturating addition, subtraction, multiplication, and division are provided as functions with the prefix `saturating`

:

`Int8`

,`Int16`

,`Int32`

,`Int64`

,`Int128`

,`Int256`

,`Fix64`

:`saturatingAdd`

`saturatingSubtract`

`saturatingMultiply`

`saturatingDivide`

`Int`

:- none

`UInt8`

,`UInt16`

,`UInt32`

,`UInt64`

,`UInt128`

,`UInt256`

,`UFix64`

:`saturatingAdd`

`saturatingSubtract`

`saturatingMultiply`

`UInt`

:`saturatingSubtract`

```
let a: UInt8 = 200
let b: UInt8 = 100
let result = a.saturatingAdd(b)
// `result` is 255, the maximum value of the type `UInt8`
```

## Floating-Point Numbers

There is **no** support for floating point numbers.

Smart Contracts are not intended to work with values with error margins and therefore floating point arithmetic is not appropriate here.

Instead, consider using fixed point numbers.

## Addresses

The type `Address`

represents an address.
Addresses are unsigned integers with a size of 64 bits (8 bytes).
Hexadecimal integer literals can be used to create address values.

```
// Declare a constant that has type `Address`.
//
let someAddress: Address = 0x436164656E636521
// Invalid: Initial value is not compatible with type `Address`,
// it is not a number.
//
let notAnAddress: Address = ""
// Invalid: Initial value is not compatible with type `Address`.
// The integer literal is valid, however, it is larger than 64 bits.
//
let alsoNotAnAddress: Address = 0x436164656E63652146757265766572
```

Integer literals are not inferred to be an address.

```
// Declare a number. Even though it happens to be a valid address,
// it is not inferred as it.
//
let aNumber = 0x436164656E636521
// `aNumber` has type `Int`
```

### Address Functions

Addresses have multiple built-in functions you can use.

`fun toString(): String`

Returns the string representation of the address.

`let someAddress: Address = 0x436164656E636521 someAddress.toString() // is "0x436164656E636521"`

`fun toBytes(): [UInt8]`

Returns the byte array representation (

`[UInt8]`

) of the address.`let someAddress: Address = 0x436164656E636521 someAddress.toBytes() // is `[67, 97, 100, 101, 110, 99, 101, 33]``

## AnyStruct and AnyResource

`AnyStruct`

is the top type of all non-resource types,
i.e., all non-resource types are a subtype of it.

`AnyResource`

is the top type of all resource types.

```
// Declare a variable that has the type `AnyStruct`.
// Any non-resource typed value can be assigned to it, for example an integer,
// but not resource-typed values.
//
var someStruct: AnyStruct = 1
// Assign a value with a different non-resource type, `Bool`.
someStruct = true
// Declare a structure named `TestStruct`, create an instance of it,
// and assign it to the `AnyStruct`-typed variable
//
struct TestStruct {}
let testStruct = TestStruct()
someStruct = testStruct
// Declare a resource named `TestResource`
resource Test {}
// Declare a variable that has the type `AnyResource`.
// Any resource-typed value can be assigned to it,
// but not non-resource typed values.
//
var someResource: @AnyResource <- create Test()
// Invalid: Resource-typed values can not be assigned
// to `AnyStruct`-typed variables
//
someStruct <- create Test()
// Invalid: Non-resource typed values can not be assigned
// to `AnyResource`-typed variables
//
someResource = 1
```

However, using `AnyStruct`

and `AnyResource`

does not opt-out of type checking.
It is invalid to access fields and call functions on these types,
as they have no fields and functions.

```
// Declare a variable that has the type `AnyStruct`.
// The initial value is an integer,
// but the variable still has the explicit type `AnyStruct`.
//
let a: AnyStruct = 1
// Invalid: Operator cannot be used for an `AnyStruct` value (`a`, left-hand side)
// and an `Int` value (`2`, right-hand side).
//
a + 2
```

`AnyStruct`

and `AnyResource`

may be used like other types,
for example, they may be the element type of arrays
or be the element type of an optional type.

```
// Declare a variable that has the type `[AnyStruct]`,
// i.e. an array of elements of any non-resource type.
//
let anyValues: [AnyStruct] = [1, "2", true]
// Declare a variable that has the type `AnyStruct?`,
// i.e. an optional type of any non-resource type.
//
var maybeSomething: AnyStruct? = 42
maybeSomething = "twenty-four"
maybeSomething = nil
```

`AnyStruct`

is also the super-type of all non-resource optional types,
and `AnyResource`

is the super-type of all resource optional types.

```
let maybeInt: Int? = 1
let anything: AnyStruct = maybeInt
```

Conditional downcasting allows coercing
a value which has the type `AnyStruct`

or `AnyResource`

back to its original type.

## Optionals

Optionals are values which can represent the absence of a value. Optionals have two cases: either there is a value, or there is nothing.

An optional type is declared using the `?`

suffix for another type.
For example, `Int`

is a non-optional integer, and `Int?`

is an optional integer,
i.e. either nothing, or an integer.

The value representing nothing is `nil`

.

```
// Declare a constant which has an optional integer type,
// with nil as its initial value.
//
let a: Int? = nil
// Declare a constant which has an optional integer type,
// with 42 as its initial value.
//
let b: Int? = 42
// Invalid: `b` has type `Int?`, which does not support arithmetic.
b + 23
// Invalid: Declare a constant with a non-optional integer type `Int`,
// but the initial value is `nil`, which in this context has type `Int?`.
//
let x: Int = nil
```

Optionals can be created for any value, not just for literals.

```
// Declare a constant which has a non-optional integer type,
// with 1 as its initial value.
//
let x = 1
// Declare a constant which has an optional integer type.
// An optional with the value of `x` is created.
//
let y: Int? = x
// Declare a variable which has an optional any type, i.e. the variable
// may be `nil`, or any other value.
// An optional with the value of `x` is created.
//
var z: AnyStruct? = x
```

A non-optional type is a subtype of its optional type.

```
var a: Int? = nil
let b = 2
a = b
// `a` is `2`
```

Optional types may be contained in other types, for example arrays or even optionals.

```
// Declare a constant which has an array type of optional integers.
let xs: [Int?] = [1, nil, 2, nil]
// Declare a constant which has a double optional type.
//
let doubleOptional: Int?? = nil
```

### Nil-Coalescing Operator

The nil-coalescing operator `??`

returns
the value inside an optional if it contains a value,
or returns an alternative value if the optional has no value,
i.e., the optional value is `nil`

.

If the left-hand side is non-nil, the right-hand side is not evaluated.

```
// Declare a constant which has an optional integer type
//
let a: Int? = nil
// Declare a constant with a non-optional integer type,
// which is initialized to `a` if it is non-nil, or 42 otherwise.
//
let b: Int = a ?? 42
// `b` is 42, as `a` is nil
```

The nil-coalescing operator can only be applied to values which have an optional type.

```
// Declare a constant with a non-optional integer type.
//
let a = 1
// Invalid: nil-coalescing operator is applied to a value which has a non-optional type
// (a has the non-optional type `Int`).
//
let b = a ?? 2
```

```
// Invalid: nil-coalescing operator is applied to a value which has a non-optional type
// (the integer literal is of type `Int`).
//
let c = 1 ?? 2
```

The type of the right-hand side of the operator (the alternative value) must be a subtype of the type of left-hand side, i.e. the right-hand side of the operator must be the non-optional or optional type matching the type of the left-hand side.

```
// Declare a constant with an optional integer type.
//
let a: Int? = nil
let b: Int? = 1
let c = a ?? b
// `c` is `1` and has type `Int?`
// Invalid: nil-coalescing operator is applied to a value of type `Int?`,
// but the alternative has type `Bool`.
//
let d = a ?? false
```

### Force Unwrap (`!`

)

The force-unwrap operator (`!`

) returns
the value inside an optional if it contains a value,
or panics and aborts the execution if the optional has no value,
i.e., the optional value is `nil`

.

```
// Declare a constant which has an optional integer type
//
let a: Int? = nil
// Declare a constant with a non-optional integer type,
// which is initialized to `a` if `a` is non-nil.
// If `a` is nil, the program aborts.
//
let b: Int = a!
// The program aborts because `a` is nil.
// Declare another optional integer constant
let c: Int? = 3
// Declare a non-optional integer
// which is initialized to `c` if `a` is non-nil.
// If `c` is nil, the program aborts.
let d: Int = c!
// `d` is initialized to 3 because c isn't nil.
```

The force-unwrap operator can only be applied to values which have an optional type.

```
// Declare a constant with a non-optional integer type.
//
let a = 1
// Invalid: force-unwrap operator is applied to a value which has a
// non-optional type (`a` has the non-optional type `Int`).
//
let b = a!
```

```
// Invalid: The force-unwrap operator is applied
// to a value which has a non-optional type
// (the integer literal is of type `Int`).
//
let c = 1!
```

### Force-assignment operator (`<-!`

)

The force-assignment operator (`<-!`

) assigns a resource-typed value to an
optional-typed variable if the variable is nil.
If the variable being assigned to is non-nil,
the execution of the program aborts.

The force-assignment operator is only used for
resource types and the move operator (`<-`

),
which are covered in the resources section of this document.

### Conditional Downcasting Operator

🚧 Status: The conditional downcasting operator `as?`

is implemented,
but it only supports values that have the type `AnyStruct`

and `AnyResource`

.

The conditional downcasting operator `as?`

can be used to type cast a value to a type.
The operator returns an optional.
If the value has a type that is a subtype
of the given type that should be casted to,
the operator returns the value as the given type,
otherwise the result is `nil`

.

The cast and check is performed at run-time, i.e. when the program is executed, not statically, i.e. when the program is checked.

```
// Declare a constant named `something` which has type `AnyStruct`,
// with an initial value which has type `Int`.
//
let something: AnyStruct = 1
// Conditionally downcast the value of `something` to `Int`.
// The cast succeeds, because the value has type `Int`.
//
let number = something as? Int
// `number` is `1` and has type `Int?`
// Conditionally downcast the value of `something` to `Bool`.
// The cast fails, because the value has type `Int`,
// and `Bool` is not a subtype of `Int`.
//
let boolean = something as? Bool
// `boolean` is `nil` and has type `Bool?`
```

Downcasting works for nested types (e.g. arrays), interfaces (if a resource interface not to a concrete resource), and optionals.

```
// Declare a constant named `values` which has type `[AnyStruct]`,
// i.e. an array of arbitrarily typed values.
//
let values: [AnyStruct] = [1, true]
let first = values[0] as? Int
// `first` is `1` and has type `Int?`
let second = values[1] as? Bool
// `second` is `true` and has type `Bool?`
```

## Never

`Never`

is the bottom type, i.e., it is a subtype of all types.
There is no value that has type `Never`

.
`Never`

can be used as the return type for functions that never return normally.
For example, it is the return type of the function `panic`

.

```
// Declare a function named `crashAndBurn` which will never return,
// because it calls the function named `panic`, which never returns.
//
fun crashAndBurn(): Never {
panic("An unrecoverable error occurred")
}
// Invalid: Declare a constant with a `Never` type, but the initial value is an integer.
//
let x: Never = 1
// Invalid: Declare a function which returns an invalid return value `nil`,
// which is not a value of type `Never`.
//
fun returnNever(): Never {
return nil
}
```

## Strings and Characters

Strings are collections of characters.
Strings have the type `String`

, and characters have the type `Character`

.
Strings can be used to work with text in a Unicode-compliant way.
Strings are immutable.

String and character literals are enclosed in double quotation marks (`"`

).

```
let someString = "Hello, world!"
```

String literals may contain escape sequences. An escape sequence starts with a backslash (`\`

):

`\0`

: Null character`\\`

: Backslash`\t`

: Horizontal tab`\n`

: Line feed`\r`

: Carriage return`\"`

: Double quotation mark`\'`

: Single quotation mark`\u`

: A Unicode scalar value, written as`\u{x}`

, where`x`

is a 1–8 digit hexadecimal number which needs to be a valid Unicode scalar value, i.e., in the range 0 to 0xD7FF and 0xE000 to 0x10FFFF inclusive

```
// Declare a constant which contains two lines of text
// (separated by the line feed character `\n`), and ends
// with a thumbs up emoji, which has code point U+1F44D (0x1F44D).
//
let thumbsUpText =
"This is the first line.\nThis is the second line with an emoji: \u{1F44D}"
```

The type `Character`

represents a single, human-readable character.
Characters are extended grapheme clusters,
which consist of one or more Unicode scalars.

For example, the single character `ü`

can be represented
in several ways in Unicode.
First, it can be represented by a single Unicode scalar value `ü`

("LATIN SMALL LETTER U WITH DIAERESIS", code point U+00FC).
Second, the same single character can be represented
by two Unicode scalar values:
`u`

("LATIN SMALL LETTER U", code point U+0075),
and "COMBINING DIAERESIS" (code point U+0308).
The combining Unicode scalar value is applied to the scalar before it,
which turns a `u`

into a `ü`

.

Still, both variants represent the same human-readable character `ü`

.

```
let singleScalar: Character = "\u{FC}"
// `singleScalar` is `ü`
let twoScalars: Character = "\u{75}\u{308}"
// `twoScalars` is `ü`
```

Another example where multiple Unicode scalar values are rendered as a single, human-readable character is a flag emoji. These emojis consist of two "REGIONAL INDICATOR SYMBOL LETTER" Unicode scalar values.

```
// Declare a constant for a string with a single character, the emoji
// for the Canadian flag, which consists of two Unicode scalar values:
// - REGIONAL INDICATOR SYMBOL LETTER C (U+1F1E8)
// - REGIONAL INDICATOR SYMBOL LETTER A (U+1F1E6)
//
let canadianFlag: Character = "\u{1F1E8}\u{1F1E6}"
// `canadianFlag` is `🇨🇦`
```

### String Fields and Functions

Strings have multiple built-in functions you can use.

`let length: Int`

Returns the number of characters in the string as an integer.

`let example = "hello" // Find the number of elements of the string. let length = example.length // `length` is `5``

`fun concat(_ other: String): String`

Concatenates the string

`other`

to the end of the original string, but does not modify the original string. This function creates a new string whose length is the sum of the lengths of the string the function is called on and the string given as a parameter.`let example = "hello" let new = "world" // Concatenate the new string onto the example string and return thenew string. let helloWorld = example.concat(new) // `helloWorld` is now `"helloworld"``

`fun slice(from: Int, upTo: Int): String`

Returns a string slice of the characters in the given string from start index

`from`

up to, but not including, the end index`upTo`

. This function creates a new string whose length is`upTo - from`

. It does not modify the original string. If either of the parameters are out of the bounds of the string, the function will fail.`let example = "helloworld" // Create a new slice of part of the original string. let slice = example.slice(from: 3, upTo: 6) // `slice` is now `"lowo"` // Run-time error: Out of bounds index, the program aborts. let outOfBounds = example.slice(from: 2, upTo: 10)`

`fun decodeHex(): [UInt8]`

Returns an array containing the bytes represented by the given hexadecimal string.

The given string must only contain hexadecimal characters and must have an even length. If the string is malformed, the program aborts

`let example = "436164656e636521" example.decodeHex() // is `[67, 97, 100, 101, 110, 99, 101, 33]``

## Arrays

Arrays are mutable, ordered collections of values.
All values in an array must have the same type.
Arrays may contain a value multiple times.
Array literals start with an opening square bracket `[`

and end with a closing square bracket `]`

.

```
// An empty array
//
[]
// An array with integers
//
[1, 2, 3]
// Invalid: mixed types
//
[1, true, 2, false]
```

### Array Types

Arrays either have a fixed size or are variably sized, i.e., elements can be added and removed.

Fixed-size arrays have the form `[T; N]`

, where `T`

is the element type,
and `N`

is the size of the array. `N`

has to be statically known, meaning
that it needs to be an integer literal.
For example, a fixed-size array of 3 `Int8`

elements has the type `[Int8; 3]`

.

Variable-size arrays have the form `[T]`

, where `T`

is the element type.
For example, the type `[Int16]`

specifies a variable-size array of elements that have type `Int16`

.

It is important to understand that arrays are value types and are only ever copied when used as an initial value for a constant or variable, when assigning to a variable, when used as function argument, or when returned from a function call.

```
let size = 2
// Invalid: Array-size must be an integer literal
let numbers: [Int; size] = []
// Declare a fixed-sized array of integers
// which always contains exactly two elements.
//
let array: [Int8; 2] = [1, 2]
// Declare a fixed-sized array of fixed-sized arrays of integers.
// The inner arrays always contain exactly three elements,
// the outer array always contains two elements.
//
let arrays: [[Int16; 3]; 2] = [
[1, 2, 3],
[4, 5, 6]
]
// Declare a variable length array of integers
var variableLengthArray: [Int] = []
```

Array types are covariant in their element types.
For example, `[Int]`

is a subtype of `[AnyStruct]`

.
This is safe because arrays are value types and not reference types.

### Array Indexing

To get the element of an array at a specific index, the indexing syntax can be used:
The array is followed by an opening square bracket `[`

, the indexing value,
and ends with a closing square bracket `]`

.

Indexes start at 0 for the first element in the array.

Accessing an element which is out of bounds results in a fatal error at run-time and aborts the program.

```
// Declare an array of integers.
let numbers = [42, 23]
// Get the first number of the array.
//
numbers[0] // is `42`
// Get the second number of the array.
//
numbers[1] // is `23`
// Run-time error: Index 2 is out of bounds, the program aborts.
//
numbers[2]
```

```
// Declare an array of arrays of integers, i.e. the type is `[[Int]]`.
let arrays = [[1, 2], [3, 4]]
// Get the first number of the second array.
//
arrays[1][0] // is `3`
```

To set an element of an array at a specific index, the indexing syntax can be used as well.

```
// Declare an array of integers.
let numbers = [42, 23]
// Change the second number in the array.
//
// NOTE: The declaration `numbers` is constant, which means that
// the *name* is constant, not the *value* – the value, i.e. the array,
// is mutable and can be changed.
//
numbers[1] = 2
// `numbers` is `[42, 2]`
```

### Array Fields and Functions

Arrays have multiple built-in fields and functions that can be used to get information about and manipulate the contents of the array.

The field `length`

, and the functions `concat`

, and `contains`

are available for both variable-sized and fixed-sized or variable-sized arrays.

`let length: Int`

The number of elements in the array.

`// Declare an array of integers. let numbers = [42, 23, 31, 12] // Find the number of elements of the array. let length = numbers.length // `length` is `4``

`fun concat(_ array: T): T`

Concatenates the parameter

`array`

to the end of the array the function is called on, but does not modify that array.Both arrays must be the same type

`T`

.This function creates a new array whose length is the sum of the length of the array the function is called on and the length of the array given as the parameter.

`// Declare two arrays of integers. let numbers = [42, 23, 31, 12] let moreNumbers = [11, 27] // Concatenate the array `moreNumbers` to the array `numbers` // and declare a new variable for the result. // let allNumbers = numbers.concat(moreNumbers) // `allNumbers` is `[42, 23, 31, 12, 11, 27]` // `numbers` is still `[42, 23, 31, 12]` // `moreNumbers` is still `[11, 27]``

`fun contains(_ element: T): Bool`

Returns true if the given element of type

`T`

is in the array.`// Declare an array of integers. let numbers = [42, 23, 31, 12] // Check if the array contains 11. let containsEleven = numbers.contains(11) // `containsEleven` is `false` // Check if the array contains 12. let containsTwelve = numbers.contains(12) // `containsTwelve` is `true` // Invalid: Check if the array contains the string "Kitty". // This results in a type error, as the array only contains integers. // let containsKitty = numbers.contains("Kitty")`

#### Variable-size Array Functions

The following functions can only be used on variable-sized arrays. It is invalid to use one of these functions on a fixed-sized array.

`fun append(_ element: T): Void`

Adds the new element

`element`

of type`T`

to the end of the array.The new element must be the same type as all the other elements in the array.

`// Declare an array of integers. let numbers = [42, 23, 31, 12] // Add a new element to the array. numbers.append(20) // `numbers` is now `[42, 23, 31, 12, 20]` // Invalid: The parameter has the wrong type `String`. numbers.append("SneakyString")`

`fun appendAll(_ array: T): Void`

Adds all the elements from

`array`

to the end of the array the function is called on.Both arrays must be the same type

`T`

.`// Declare an array of integers. let numbers = [42, 23] // Add new elements to the array. numbers.appendAll([31, 12, 20]) // `numbers` is now `[42, 23, 31, 12, 20]` // Invalid: The parameter has the wrong type `[String]`. numbers.appendAll(["Sneaky", "String"])`

`fun insert(at index: Int, _ element: T): Void`

Inserts the new element

`element`

of type`T`

at the given`index`

of the array.The new element must be of the same type as the other elements in the array.

The

`index`

must be within the bounds of the array. If the index is outside the bounds, the program aborts.The existing element at the supplied index is not overwritten.

All the elements after the new inserted element are shifted to the right by one.

`// Declare an array of integers. let numbers = [42, 23, 31, 12] // Insert a new element at position 1 of the array. numbers.insert(at: 1, 20) // `numbers` is now `[42, 20, 23, 31, 12]` // Run-time error: Out of bounds index, the program aborts. numbers.insert(at: 12, 39)`

`fun remove(at index: Int): T`

Removes the element at the given

`index`

from the array and returns it.The

`index`

must be within the bounds of the array. If the index is outside the bounds, the program aborts.`// Declare an array of integers. let numbers = [42, 23, 31] // Remove element at position 1 of the array. let twentyThree = numbers.remove(at: 1) // `numbers` is now `[42, 31]` // `twentyThree` is `23` // Run-time error: Out of bounds index, the program aborts. numbers.remove(at: 19)`

`fun removeFirst(): T`

Removes the first element from the array and returns it.

The array must not be empty. If the array is empty, the program aborts.

`// Declare an array of integers. let numbers = [42, 23] // Remove the first element of the array. let fortytwo = numbers.removeFirst() // `numbers` is now `[23]` // `fortywo` is `42` // Remove the first element of the array. let twentyThree = numbers.removeFirst() // `numbers` is now `[]` // `twentyThree` is `23` // Run-time error: The array is empty, the program aborts. numbers.removeFirst()`

`fun removeLast(): T`

Removes the last element from the array and returns it.

The array must not be empty. If the array is empty, the program aborts.

`// Declare an array of integers. let numbers = [42, 23] // Remove the last element of the array. let twentyThree = numbers.removeLast() // `numbers` is now `[42]` // `twentyThree` is `23` // Remove the last element of the array. let fortyTwo = numbers.removeLast() // `numbers` is now `[]` // `fortyTwo` is `42` // Run-time error: The array is empty, the program aborts. numbers.removeLast()`

## Dictionaries

Dictionaries are mutable, unordered collections of key-value associations. In a dictionary, all keys must have the same type, and all values must have the same type. Dictionaries may contain a key only once and may contain a value multiple times.

Dictionary literals start with an opening brace `{`

and end with a closing brace `}`

.
Keys are separated from values by a colon,
and key-value associations are separated by commas.

```
// An empty dictionary
//
{}
// A dictionary which associates integers with booleans
//
{
1: true,
2: false
}
// Invalid: mixed types
//
{
1: true,
false: 2
}
```

### Dictionary Types

Dictionaries have the form `{K: V}`

,
where `K`

is the type of the key,
and `V`

is the type of the value.
For example, a dictionary with `Int`

keys and `Bool`

values has type `{Int: Bool}`

.

```
// Declare a constant that has type `{Int: Bool}`,
// a dictionary mapping integers to booleans.
//
let booleans = {
1: true,
0: false
}
// Declare a constant that has type `{Bool: Int}`,
// a dictionary mapping booleans to integers.
//
let integers = {
true: 1,
false: 0
}
```

Dictionary types are covariant in their key and value types.
For example, `{Int: String}`

is a subtype of `{AnyStruct: String}`

and also a subtype of `{Int: AnyStruct}`

.
This is safe because dictionaries are value types and not reference types.

### Dictionary Access

To get the value for a specific key from a dictionary,
the access syntax can be used:
The dictionary is followed by an opening square bracket `[`

, the key,
and ends with a closing square bracket `]`

.

Accessing a key returns an optional:
If the key is found in the dictionary, the value for the given key is returned,
and if the key is not found, `nil`

is returned.

```
// Declare a constant that has type `{Int: Bool}`,
// a dictionary mapping integers to booleans.
//
let booleans = {
1: true,
0: false
}
// The result of accessing a key has type `Bool?`.
//
booleans[1] // is `true`
booleans[0] // is `false`
booleans[2] // is `nil`
// Invalid: Accessing a key which does not have type `Int`.
//
booleans["1"]
```

```
// Declare a constant that has type `{Bool: Int}`,
// a dictionary mapping booleans to integers.
//
let integers = {
true: 1,
false: 0
}
// The result of accessing a key has type `Int?`
//
integers[true] // is `1`
integers[false] // is `0`
```

To set the value for a key of a dictionary, the access syntax can be used as well.

```
// Declare a constant that has type `{Int: Bool}`,
// a dictionary mapping booleans to integers.
//
let booleans = {
1: true,
0: false
}
// Assign new values for the keys `1` and `0`.
//
booleans[1] = false
booleans[0] = true
// `booleans` is `{1: false, 0: true}`
```

### Dictionary Fields and Functions

`let length: Int`

The number of entries in the dictionary.

`// Declare a dictionary mapping strings to integers. let numbers = {"fortyTwo": 42, "twentyThree": 23} // Find the number of entries of the dictionary. let length = numbers.length // `length` is `2``

`fun insert(key: K, _ value: V): V?`

Inserts the given value of type

`V`

into the dictionary under the given`key`

of type`K`

.Returns the previous value as an optional if the dictionary contained the key, otherwise

`nil`

.`// Declare a dictionary mapping strings to integers. let numbers = {"twentyThree": 23} // Insert the key `"fortyTwo"` with the value `42` into the dictionary. // The key did not previously exist in the dictionary, // so the result is `nil` // let old = numbers.insert(key: "fortyTwo", 42) // `old` is `nil` // `numbers` is `{"twentyThree": 23, "fortyTwo": 42}``

`fun remove(key: K): V?`

Removes the value for the given

`key`

of type`K`

from the dictionary.Returns the value of type

`V`

as an optional if the dictionary contained the key, otherwise`nil`

.`// Declare a dictionary mapping strings to integers. let numbers = {"fortyTwo": 42, "twentyThree": 23} // Remove the key `"fortyTwo"` from the dictionary. // The key exists in the dictionary, // so the value associated with the key is returned. // let fortyTwo = numbers.remove(key: "fortyTwo") // `fortyTwo` is `42` // `numbers` is `{"twentyThree": 23}` // Remove the key `"oneHundred"` from the dictionary. // The key does not exist in the dictionary, so `nil` is returned. // let oneHundred = numbers.remove(key: "oneHundred") // `oneHundred` is `nil` // `numbers` is `{"twentyThree": 23}``

`let keys: [K]`

Returns an array of the keys of type

`K`

in the dictionary. This does not modify the dictionary, just returns a copy of the keys as an array. If the dictionary is empty, this returns an empty array.`// Declare a dictionary mapping strings to integers. let numbers = {"fortyTwo": 42, "twentyThree": 23} // Find the keys of the dictionary. let keys = numbers.keys // `keys` has type `[String]` and is `["fortyTwo","twentyThree"]``

`let values: [V]`

Returns an array of the values of type

`V`

in the dictionary. This does not modify the dictionary, just returns a copy of the values as an array. If the dictionary is empty, this returns an empty array.This field is not available if

`V`

is a resource type.`// Declare a dictionary mapping strings to integers. let numbers = {"fortyTwo": 42, "twentyThree": 23} // Find the values of the dictionary. let values = numbers.values // `values` has type [Int] and is `[42, 23]``

`fun containsKey(key: K): Bool`

Returns true if the given key of type

`K`

is in the dictionary.`// Declare a dictionary mapping strings to integers. let numbers = {"fortyTwo": 42, "twentyThree": 23} // Check if the dictionary contains the key "twentyFive". let containsKeyTwentyFive = numbers.containsKey("twentyFive") // `containsKeyTwentyFive` is `false` // Check if the dictionary contains the key "fortyTwo". let containsKeyFortyTwo = numbers.containsKey("fortyTwo") // `containsKeyFortyTwo` is `true` // Invalid: Check if the dictionary contains the key 42. // This results in a type error, as the key type of the dictionary is `String`. // let containsKey42 = numbers.containsKey(42)`

### Dictionary Keys

Dictionary keys must be hashable and equatable,
i.e., must implement the `Hashable`

and `Equatable`

interfaces.

Most of the built-in types, like booleans and integers, are hashable and equatable, so can be used as keys in dictionaries.