# Essentials

## Introduction

Julia Base contains a range of functions and macros appropriate for performing scientific and numerical computing, but is also as broad as those of many general purpose programming languages. Additional functionality is available from a growing collection of available packages. Functions are grouped by topic below.

Some general notes:

- To use module functions, use `import Module` to import the module, and `Module.fn(x)` to use the functions.
- Alternatively, `using Module` will import all exported `Module` functions into the current namespace.
- By convention, function names ending with an exclamation point (`!`) modify their arguments. Some functions have both modifying (e.g., `sort!`) and non-modifying (`sort`) versions.

## Getting Around

`Base.exit` — Function

    exit(code=0)

Stop the program with an exit code. The default exit code is zero, indicating that the program completed successfully. In an interactive session, `exit()` can be called with the keyboard shortcut `^D`.

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`Base.atexit` — Function

    atexit(f)

Register a zero-argument function `f()` to be called at process exit. `atexit()` hooks are called in last in first out (LIFO) order and run before object finalizers.

Exit hooks are allowed to call `exit(n)`, in which case Julia will exit with exit code `n` (instead of the original exit code). If more than one exit hook calls `exit(n)`, then Julia will exit with the exit code corresponding to the last called exit hook that calls `exit(n)`. (Because exit hooks are called in LIFO order, "last called" is equivalent to "first registered".)

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`Base.isinteractive` — Function

    isinteractive() -> Bool

Determine whether Julia is running an interactive session.

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`Base.summarysize` — Function

    Base.summarysize(obj; exclude=Union{...}, chargeall=Union{...}) -> Int

Compute the amount of memory, in bytes, used by all unique objects reachable from the argument.

Keyword Arguments

- `exclude`: specifies the types of objects to exclude from the traversal.
- `chargeall`: specifies the types of objects to always charge the size of all of their fields, even if those fields would normally be excluded.

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`Base.require` — Function

    require(into::Module, module::Symbol)

This function is part of the implementation of `using` / `import`, if a module is not already defined in `Main`. It can also be called directly to force reloading a module, regardless of whether it has been loaded before (for example, when interactively developing libraries).

Loads a source file, in the context of the `Main` module, on every active node, searching standard locations for files. `require` is considered a top-level operation, so it sets the current `include` path but does not use it to search for files (see help for `include`). This function is typically used to load library code, and is implicitly called by `using` to load packages.

When searching for files, `require` first looks for package code in the global array `LOAD_PATH`. `require` is case-sensitive on all platforms, including those with case-insensitive filesystems like macOS and Windows.

For more details regarding code loading, see the manual sections on modules and parallel computing.

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`Base.compilecache` — Function

    Base.compilecache(module::PkgId)

Creates a precompiled cache file for a module and all of its dependencies. This can be used to reduce package load times. Cache files are stored in `DEPOT_PATH[1]/compiled`. See Module initialization and precompilation for important notes.

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`Base.__precompile__` — Function

    __precompile__(isprecompilable::Bool)

Specify whether the file calling this function is precompilable, defaulting to `true`. If a module or file is not safely precompilable, it should call `__precompile__(false)` in order to throw an error if Julia attempts to precompile it.

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`Base.include` — Function

    Base.include([mapexpr::Function,] [m::Module,] path::AbstractString)

Evaluate the contents of the input source file in the global scope of module `m`. Every module (except those defined with `baremodule`) has its own definition of `include` omitting the `m` argument, which evaluates the file in that module. Returns the result of the last evaluated expression of the input file. During including, a task-local include path is set to the directory containing the file. Nested calls to `include` will search relative to that path. This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files.

The optional first argument `mapexpr` can be used to transform the included code before it is evaluated: for each parsed expression `expr` in `path`, the `include` function actually evaluates `mapexpr(expr)`. If it is omitted, `mapexpr` defaults to `identity`.

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`Base.MainInclude.include` — Function

    include([mapexpr::Function,] path::AbstractString)

Evaluate the contents of the input source file in the global scope of the containing module. Every module (except those defined with `baremodule`) has its own definition of `include`, which evaluates the file in that module. Returns the result of the last evaluated expression of the input file. During including, a task-local include path is set to the directory containing the file. Nested calls to `include` will search relative to that path. This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files.

The optional first argument `mapexpr` can be used to transform the included code before it is evaluated: for each parsed expression `expr` in `path`, the `include` function actually evaluates `mapexpr(expr)`. If it is omitted, `mapexpr` defaults to `identity`.

Use `Base.include` to evaluate a file into another module.

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`Base.include_string` — Function

    include_string([mapexpr::Function,] m::Module, code::AbstractString, filename::AbstractString="string")

Like `include`, except reads code from the given string rather than from a file.

The optional first argument `mapexpr` can be used to transform the included code before it is evaluated: for each parsed expression `expr` in `code`, the `include_string` function actually evaluates `mapexpr(expr)`. If it is omitted, `mapexpr` defaults to `identity`.

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`Base.include_dependency` — Function

    include_dependency(path::AbstractString)

In a module, declare that the file specified by `path` (relative or absolute) is a dependency for precompilation; that is, the module will need to be recompiled if this file changes.

This is only needed if your module depends on a file that is not used via `include`. It has no effect outside of compilation.

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`Base.which` — Method

    which(f, types)

Returns the method of `f` (a `Method` object) that would be called for arguments of the given `types`.

If `types` is an abstract type, then the method that would be called by `invoke` is returned.

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`Base.methods` — Function

    methods(f, [types], [module])

Return the method table for `f`.

If `types` is specified, return an array of methods whose types match. If `module` is specified, return an array of methods defined in that module. A list of modules can also be specified as an array.

Julia 1.4

At least Julia 1.4 is required for specifying a module.

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`Base.@show` — Macro

    @show

Show an expression and result, returning the result. See also `show`.

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`ans` — Keyword

    ans

A variable referring to the last computed value, automatically set at the interactive prompt.

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`Base.active_project` — Function

    active_project()

Return the path of the active `Project.toml` file.

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## Keywords

This is the list of reserved keywords in Julia: `baremodule`, `begin`, `break`, `catch`, `const`, `continue`, `do`, `else`, `elseif`, `end`, `export`, `false`, `finally`, `for`, `function`, `global`, `if`, `import`, `let`, `local`, `macro`, `module`, `quote`, `return`, `struct`, `true`, `try`, `using`, `while`. Those keywords are not allowed to be used as variable names.

The following two-word sequences are reserved: `abstract type`, `mutable struct`, `primitive type`. However, you can create variables with names: `abstract`, `mutable`, `primitive` and `type`.

Finally, `where` is parsed as an infix operator for writing parametric method and type definitions. Also `in` and `isa` are parsed as infix operators. Creation of a variable named `where`, `in` or `isa` is allowed though.

`module` — Keyword

    module

`module` declares a `Module`, which is a separate global variable workspace. Within a module, you can control which names from other modules are visible (via importing), and specify which of your names are intended to be public (via exporting). Modules allow you to create top-level definitions without worrying about name conflicts when your code is used together with somebody else’s. See the manual section about modules for more details.

Examples

    module Foo
    import Base.show
    export MyType, foo

    struct MyType
        x
    end

    bar(x) = 2x
    foo(a::MyType) = bar(a.x) + 1
    show(io::IO, a::MyType) = print(io, "MyType $(a.x)")
    end

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`export` — Keyword

    export

`export` is used within modules to tell Julia which functions should be made available to the user. For example: `export foo` makes the name `foo` available when `using` the module. See the manual section about modules for details.

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`import` — Keyword

    import

`import Foo` will load the module or package `Foo`. Names from the imported `Foo` module can be accessed with dot syntax (e.g. `Foo.foo` to access the name `foo`). See the manual section about modules for details.

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`using` — Keyword

    using

`using Foo` will load the module or package `Foo` and make its `export`ed names available for direct use. Names can also be used via dot syntax (e.g. `Foo.foo` to access the name `foo`), whether they are `export`ed or not. See the manual section about modules for details.

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`baremodule` — Keyword

    baremodule

`baremodule` declares a module that does not contain `using Base` or local definitions of `eval` and `include`. It does still import `Core`. In other words,

    module Mod

    ...

    end

is equivalent to

    baremodule Mod

    using Base

    eval(x) = Core.eval(Mod, x)
    include(p) = Base.include(Mod, p)

    ...

    end

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`function` — Keyword

    function

Functions are defined with the `function` keyword:

    function add(a, b)
        return a + b
    end

Or the short form notation:

    add(a, b) = a + b

The use of the `return` keyword is exactly the same as in other languages, but is often optional. A function without an explicit `return` statement will return the last expression in the function body.

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`macro` — Keyword

    macro

`macro` defines a method for inserting generated code into a program. A macro maps a sequence of argument expressions to a returned expression, and the resulting expression is substituted directly into the program at the point where the macro is invoked. Macros are a way to run generated code without calling `eval`, since the generated code instead simply becomes part of the surrounding program. Macro arguments may include expressions, literal values, and symbols. Macros can be defined for variable number of arguments (varargs), but do not accept keyword arguments. Every macro also implicitly gets passed the arguments `__source__`, which contains the line number and file name the macro is called from, and `__module__`, which is the module the macro is expanded in.

Examples

    julia> macro sayhello(name)
               return :( println("Hello, ", $name, "!") )
           end
    @sayhello (macro with 1 method)

    julia> @sayhello "Charlie"
    Hello, Charlie!

    julia> macro saylots(x...)
               return :( println("Say: ", $(x...)) )
           end
    @saylots (macro with 1 method)

    julia> @saylots "hey " "there " "friend"
    Say: hey there friend

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`return` — Keyword

    return

`return x` causes the enclosing function to exit early, passing the given value `x` back to its caller. `return` by itself with no value is equivalent to `return nothing` (see `nothing`).

    function compare(a, b)
        a == b && return "equal to"
        a < b ? "less than" : "greater than"
    end

In general you can place a `return` statement anywhere within a function body, including within deeply nested loops or conditionals, but be careful with `do` blocks. For example:

    function test1(xs)
        for x in xs
            iseven(x) && return 2x
        end
    end

    function test2(xs)
        map(xs) do x
            iseven(x) && return 2x
            x
        end
    end

In the first example, the return breaks out of `test1` as soon as it hits an even number, so `test1([5,6,7])` returns `12`.

You might expect the second example to behave the same way, but in fact the `return` there only breaks out of the inner function (inside the `do` block) and gives a value back to `map`. `test2([5,6,7])` then returns `[5,12,7]`.

When used in a top-level expression (i.e. outside any function), `return` causes the entire current top-level expression to terminate early.

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`do` — Keyword

    do

Create an anonymous function and pass it as the first argument to a function call. For example:

    map(1:10) do x
        2x
    end

is equivalent to `map(x->2x, 1:10)`.

Use multiple arguments like so:

    map(1:10, 11:20) do x, y
        x + y
    end

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`begin` — Keyword

    begin

`begin...end` denotes a block of code.

    begin
        println("Hello, ")
        println("World!")
    end

Usually `begin` will not be necessary, since keywords such as `function` and `let` implicitly begin blocks of code. See also `;`.

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`end` — Keyword

    end

`end` marks the conclusion of a block of expressions, for example `module`, `struct`, `mutable struct`, `begin`, `let`, `for` etc. `end` may also be used when indexing into an array to represent the last index of a dimension.

Examples

    julia> A = [1 2; 3 4]
    2×2 Array{Int64, 2}:
     1  2
     3  4

    julia> A[end, :]
    2-element Array{Int64, 1}:
     3
     4

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`let` — Keyword

    let

`let` statements allocate new variable bindings each time they run. Whereas an assignment modifies an existing value location, `let` creates new locations. This difference is only detectable in the case of variables that outlive their scope via closures. The `let` syntax accepts a comma-separated series of assignments and variable names:

    let var1 = value1, var2, var3 = value3
        code
    end

The assignments are evaluated in order, with each right-hand side evaluated in the scope before the new variable on the left-hand side has been introduced. Therefore it makes sense to write something like `let x = x`, since the two `x` variables are distinct and have separate storage.

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`if` — Keyword

    if/elseif/else

`if`/`elseif`/`else` performs conditional evaluation, which allows portions of code to be evaluated or not evaluated depending on the value of a boolean expression. Here is the anatomy of the `if`/`elseif`/`else` conditional syntax:

    if x < y
        println("x is less than y")
    elseif x > y
        println("x is greater than y")
    else
        println("x is equal to y")
    end

If the condition expression `x < y` is true, then the corresponding block is evaluated; otherwise the condition expression `x > y` is evaluated, and if it is true, the corresponding block is evaluated; if neither expression is true, the `else` block is evaluated. The `elseif` and `else` blocks are optional, and as many `elseif` blocks as desired can be used.

In contrast to some other languages conditions must be of type `Bool`. It does not suffice for conditions to be convertible to `Bool`.

    julia> if 1 end
    ERROR: TypeError: non-boolean (Int64) used in boolean context

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`for` — Keyword

    for

`for` loops repeatedly evaluate a block of statements while iterating over a sequence of values.

Examples

    julia> for i in [1, 4, 0]
               println(i)
           end
    1
    4
    0

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`while` — Keyword

    while

`while` loops repeatedly evaluate a conditional expression, and continue evaluating the body of the while loop as long as the expression remains true. If the condition expression is false when the while loop is first reached, the body is never evaluated.

Examples

    julia> i = 1
    1

    julia> while i < 5
               println(i)
               global i += 1
           end
    1
    2
    3
    4

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`break` — Keyword

    break

Break out of a loop immediately.

Examples

    julia> i = 0
    0

    julia> while true
               global i += 1
               i > 5 && break
               println(i)
           end
    1
    2
    3
    4
    5

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`continue` — Keyword

    continue

Skip the rest of the current loop iteration.

Examples

    julia> for i = 1:6
               iseven(i) && continue
               println(i)
           end
    1
    3
    5

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`try` — Keyword

    try/catch

A `try`/`catch` statement allows intercepting errors (exceptions) thrown by `throw` so that program execution can continue. For example, the following code attempts to write a file, but warns the user and proceeds instead of terminating execution if the file cannot be written:

    try
        open("/danger", "w") do f
            println(f, "Hello")
        end
    catch
        @warn "Could not write file."
    end

or, when the file cannot be read into a variable:

    lines = try
        open("/danger", "r") do f
            readlines(f)
        end
    catch
        @warn "File not found."
    end

The syntax `catch e` (where `e` is any variable) assigns the thrown exception object to the given variable within the `catch` block.

The power of the `try`/`catch` construct lies in the ability to unwind a deeply nested computation immediately to a much higher level in the stack of calling functions.

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`finally` — Keyword

    finally

Run some code when a given block of code exits, regardless of how it exits. For example, here is how we can guarantee that an opened file is closed:

    f = open("file")
    try
        operate_on_file(f)
    finally
        close(f)
    end

When control leaves the `try` block (for example, due to a `return`, or just finishing normally), `close(f)` will be executed. If the `try` block exits due to an exception, the exception will continue propagating. A `catch` block may be combined with `try` and `finally` as well. In this case the `finally` block will run after `catch` has handled the error.

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`quote` — Keyword

    quote

`quote` creates multiple expression objects in a block without using the explicit `Expr` constructor. For example:

    ex = quote
        x = 1
        y = 2
        x + y
    end

Unlike the other means of quoting, `:( ... )`, this form introduces `QuoteNode` elements to the expression tree, which must be considered when directly manipulating the tree. For other purposes, `:( ... )` and `quote .. end` blocks are treated identically.

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`local` — Keyword

    local

`local` introduces a new local variable. See the manual section on variable scoping for more information.

Examples

    julia> function foo(n)
               x = 0
               for i = 1:n
                   local x # introduce a loop-local x
                   x = i
               end
               x
           end
    foo (generic function with 1 method)

    julia> foo(10)
    0

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`global` — Keyword

    global

`global x` makes `x` in the current scope and its inner scopes refer to the global variable of that name. See the manual section on variable scoping for more information.

Examples

    julia> z = 3
    3

    julia> function foo()
               global z = 6 # use the z variable defined outside foo
           end
    foo (generic function with 1 method)

    julia> foo()
    6

    julia> z
    6

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`const` — Keyword

    const

`const` is used to declare global variables whose values will not change. In almost all code (and particularly performance sensitive code) global variables should be declared constant in this way.

    const x = 5

Multiple variables can be declared within a single `const`:

    const y, z = 7, 11

Note that `const` only applies to one `=` operation, therefore `const x = y = 1` declares `x` to be constant but not `y`. On the other hand, `const x = const y = 1` declares both `x` and `y` constant.

Note that "constant-ness" does not extend into mutable containers; only the association between a variable and its value is constant. If `x` is an array or dictionary (for example) you can still modify, add, or remove elements.

In some cases changing the value of a `const` variable gives a warning instead of an error. However, this can produce unpredictable behavior or corrupt the state of your program, and so should be avoided. This feature is intended only for convenience during interactive use.

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`struct` — Keyword

    struct

The most commonly used kind of type in Julia is a struct, specified as a name and a set of fields.

    struct Point
        x
        y
    end

Fields can have type restrictions, which may be parameterized:

    struct Point{X}
        x::X
        y::Float64
    end

A struct can also declare an abstract super type via `<:` syntax:

    struct Point <: AbstractPoint
        x
        y
    end

`struct`s are immutable by default; an instance of one of these types cannot be modified after construction. Use `mutable struct` instead to declare a type whose instances can be modified.

See the manual section on Composite Types for more details, such as how to define constructors.

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`mutable struct` — Keyword

    mutable struct

`mutable struct` is similar to `struct`, but additionally allows the fields of the type to be set after construction. See the manual section on Composite Types for more information.

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`abstract type` — Keyword

    abstract type

`abstract type` declares a type that cannot be instantiated, and serves only as a node in the type graph, thereby describing sets of related concrete types: those concrete types which are their descendants. Abstract types form the conceptual hierarchy which makes Julia’s type system more than just a collection of object implementations. For example:

    abstract type Number end
    abstract type Real <: Number end

`Number` has no supertype, whereas `Real` is an abstract subtype of `Number`.

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`primitive type` — Keyword

    primitive type

`primitive type` declares a concrete type whose data consists only of a series of bits. Classic examples of primitive types are integers and floating-point values. Some example built-in primitive type declarations:

    primitive type Char 32 end
    primitive type Bool <: Integer 8 end

The number after the name indicates how many bits of storage the type requires. Currently, only sizes that are multiples of 8 bits are supported. The `Bool` declaration shows how a primitive type can be optionally declared to be a subtype of some supertype.

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`where` — Keyword

    where

The `where` keyword creates a type that is an iterated union of other types, over all values of some variable. For example `Vector{T} where T<:Real` includes all `Vector`s where the element type is some kind of `Real` number.

The variable bound defaults to `Any` if it is omitted:

    Vector{T} where T    # short for `where T<:Any`

Variables can also have lower bounds:

    Vector{T} where T>:Int
    Vector{T} where Int<:T<:Real

There is also a concise syntax for nested `where` expressions. For example, this:

    Pair{T, S} where S<:Array{T} where T<:Number

can be shortened to:

    Pair{T, S} where {T<:Number, S<:Array{T}}

This form is often found on method signatures.

Note that in this form, the variables are listed outermost-first. This matches the order in which variables are substituted when a type is "applied" to parameter values using the syntax `T{p1, p2, ...}`.

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`...` — Keyword

    ...

The "splat" operator, `...`, represents a sequence of arguments. `...` can be used in function definitions, to indicate that the function accepts an arbitrary number of arguments. `...` can also be used to apply a function to a sequence of arguments.

Examples

    julia> add(xs...) = reduce(+, xs)
    add (generic function with 1 method)

    julia> add(1, 2, 3, 4, 5)
    15

    julia> add([1, 2, 3]...)
    6

    julia> add(7, 1:100..., 1000:1100...)
    111107

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`;` — Keyword

    ;

`;` has a similar role in Julia as in many C-like languages, and is used to delimit the end of the previous statement. `;` is not necessary after new lines, but can be used to separate statements on a single line or to join statements into a single expression. `;` is also used to suppress output printing in the REPL and similar interfaces.

Examples

    julia> function foo()
               x = "Hello, "; x *= "World!"
               return x
           end
    foo (generic function with 1 method)

    julia> bar() = (x = "Hello, Mars!"; return x)
    bar (generic function with 1 method)

    julia> foo();

    julia> bar()
    "Hello, Mars!"

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`=` — Keyword

    =

`=` is the assignment operator.

- For variable `a` and expression `b`, `a = b` makes `a` refer to the value of `b`.
- For functions `f(x)`, `f(x) = x` defines a new function constant `f`, or adds a new method to `f` if `f` is already defined; this usage is equivalent to `function f(x); x; end`.
- `a[i] = v` calls `setindex!``(a,v,i)`.
- `a.b = c` calls `setproperty!``(a,:b,c)`.
- Inside a function call, `f(a=b)` passes `b` as the value of keyword argument `a`.
- Inside parentheses with commas, `(a=1,)` constructs a `NamedTuple`.

Examples

Assigning `a` to `b` does not create a copy of `b`; instead use `copy` or `deepcopy`.

    julia> b = [1]; a = b; b[1] = 2; a
    1-element Array{Int64, 1}:
     2

    julia> b = [1]; a = copy(b); b[1] = 2; a
    1-element Array{Int64, 1}:
     1

Collections passed to functions are also not copied. Functions can modify (mutate) the contents of the objects their arguments refer to. (The names of functions which do this are conventionally suffixed with '!'.)

    julia> function f!(x); x[:] .+= 1; end
    f! (generic function with 1 method)

    julia> a = [1]; f!(a); a
    1-element Array{Int64, 1}:
     2

Assignment can operate on multiple variables in parallel, taking values from an iterable:

    julia> a, b = 4, 5
    (4, 5)

    julia> a, b = 1:3
    1:3

    julia> a, b
    (1, 2)

Assignment can operate on multiple variables in series, and will return the value of the right-hand-most expression:

    julia> a = [1]; b = [2]; c = [3]; a = b = c
    1-element Array{Int64, 1}:
     3

    julia> b[1] = 2; a, b, c
    ([2], [2], [2])

Assignment at out-of-bounds indices does not grow a collection. If the collection is a `Vector` it can instead be grown with `push!` or `append!`.

    julia> a = [1, 1]; a[3] = 2
    ERROR: BoundsError: attempt to access 2-element Array{Int64, 1} at index [3]
    [...]

    julia> push!(a, 2, 3)
    4-element Array{Int64, 1}:
     1
     1
     2
     3

Assigning `[]` does not eliminate elements from a collection; instead use `filter!`.

    julia> a = collect(1:3); a[a .<= 1] = []
    ERROR: DimensionMismatch("tried to assign 0 elements to 1 destinations")
    [...]

    julia> filter!(x -> x > 1, a) # in-place & thus more efficient than a = a[a .> 1]
    2-element Array{Int64, 1}:
     2
     3

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`?:` — Keyword

    a ? b : c

Short form for conditionals; read "if `a`, evaluate `b` otherwise evaluate `c`". Also known as the ternary operator.

This syntax is equivalent to `if a; b else c end`, but is often used to emphasize the value `b`-or-`c` which is being used as part of a larger expression, rather than the side effects that evaluating `b` or `c` may have.

See the manual section on control flow for more details.

Examples

    julia> x = 1; y = 2;

    julia> println(x > y ? "x is larger" : "y is larger")
    y is larger

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## Standard Modules

`Main` — Module

    Main

`Main` is the top-level module, and Julia starts with `Main` set as the current module. Variables defined at the prompt go in `Main`, and `varinfo` lists variables in `Main`.

    julia> @__MODULE__
    Main

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`Core` — Module

    Core

`Core` is the module that contains all identifiers considered "built in" to the language, i.e. part of the core language and not libraries. Every module implicitly specifies `using Core`, since you can't do anything without those definitions.

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`Base` — Module

    Base

The base library of Julia. `Base` is a module that contains basic functionality (the contents of `base/`). All modules implicitly contain `using Base`, since this is needed in the vast majority of cases.

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## Base Submodules

`Base.Broadcast` — Module

    Base.Broadcast

Module containing the broadcasting implementation.

source
`Base.Docs` — Module

    Docs

The `Docs` module provides the `@doc` macro which can be used to set and retrieve documentation metadata for Julia objects.

Please see the manual section on documentation for more information.

source
`Base.Iterators` — Module

Methods for working with Iterators.

source
`Base.Libc` — Module

Interface to libc, the C standard library.

source
`Base.Meta` — Module

Convenience functions for metaprogramming.

source
`Base.StackTraces` — Module

Tools for collecting and manipulating stack traces. Mainly used for building errors.

source
`Base.Sys` — Module

Provide methods for retrieving information about hardware and the operating system.

source
`Base.Threads` — Module

Multithreading support.

source
`Base.GC` — Module

    Base.GC

Module with garbage collection utilities.

source

## All Objects

`Core.:===` — Function

    ===(x,y) -> Bool
    ≡(x,y) -> Bool

Determine whether `x` and `y` are identical, in the sense that no program could distinguish them. First the types of `x` and `y` are compared. If those are identical, mutable objects are compared by address in memory and immutable objects (such as numbers) are compared by contents at the bit level. This function is sometimes called "egal". It always returns a `Bool` value.

Examples

    julia> a = [1, 2]; b = [1, 2];

    julia> a == b
    true

    julia> a === b
    false

    julia> a === a
    true

source
`Core.isa` — Function

    isa(x, type) -> Bool

Determine whether `x` is of the given `type`. Can also be used as an infix operator, e.g. `x isa type`.

Examples

    julia> isa(1, Int)
    true

    julia> isa(1, Matrix)
    false

    julia> isa(1, Char)
    false

    julia> isa(1, Number)
    true

    julia> 1 isa Number
    true

source
`Base.isequal` — Function

    isequal(x, y)

Similar to `==`, except for the treatment of floating point numbers and of missing values. `isequal` treats all floating-point `NaN` values as equal to each other, treats `-0.0` as unequal to `0.0`, and `missing` as equal to `missing`. Always returns a `Bool` value.

Implementation

The default implementation of `isequal` calls `==`, so a type that does not involve floating-point values generally only needs to define `==`.

`isequal` is the comparison function used by hash tables (`Dict`). `isequal(x,y)` must imply that `hash(x) == hash(y)`.

This typically means that types for which a custom `==` or `isequal` method exists must implement a corresponding `hash` method (and vice versa). Collections typically implement `isequal` by calling `isequal` recursively on all contents.

Scalar types generally do not need to implement `isequal` separate from `==`, unless they represent floating-point numbers amenable to a more efficient implementation than that provided as a generic fallback (based on `isnan`, `signbit`, and `==`).

Examples

    julia> isequal([1., NaN], [1., NaN])
    true

    julia> [1., NaN] == [1., NaN]
    false

    julia> 0.0 == -0.0
    true

    julia> isequal(0.0, -0.0)
    false

source

    isequal(x)

Create a function that compares its argument to `x` using `isequal`, i.e. a function equivalent to `y -> isequal(y, x)`.

The returned function is of type `Base.Fix2{typeof(isequal)}`, which can be used to implement specialized methods.

source
`Base.isless` — Function

    isless(x, y)

Test whether `x` is less than `y`, according to a fixed total order. `isless` is not defined on all pairs of values `(x, y)`. However, if it is defined, it is expected to satisfy the following:

- If `isless(x, y)` is defined, then so is `isless(y, x)` and `isequal(x, y)`, and exactly one of those three yields `true`.
- The relation defined by `isless` is transitive, i.e., `isless(x, y) && isless(y, z)` implies `isless(x, z)`.

Values that are normally unordered, such as `NaN`, are ordered in an arbitrary but consistent fashion. `missing` values are ordered last.

This is the default comparison used by `sort`.

Implementation

Non-numeric types with a total order should implement this function. Numeric types only need to implement it if they have special values such as `NaN`. Types with a partial order should implement `<`. See the documentation on Alternate orderings for how to define alternate ordering methods that can be used in sorting and related functions.

Examples

    julia> isless(1, 3)
    true

    julia> isless("Red", "Blue")
    false

source
`Core.ifelse` — Function

    ifelse(condition::Bool, x, y)

Return `x` if `condition` is `true`, otherwise return `y`. This differs from `?` or `if` in that it is an ordinary function, so all the arguments are evaluated first. In some cases, using `ifelse` instead of an `if` statement can eliminate the branch in generated code and provide higher performance in tight loops.

Examples

    julia> ifelse(1 > 2, 1, 2)
    2

source
`Core.typeassert` — Function

    typeassert(x, type)

Throw a `TypeError` unless `x isa type`. The syntax `x::type` calls this function.

Examples

    julia> typeassert(2.5, Int)
    ERROR: TypeError: in typeassert, expected Int64, got a value of type Float64
    Stacktrace:
    [...]

source
`Core.typeof` — Function

    typeof(x)

Get the concrete type of `x`.

Examples

    julia> a = 1//2;

    julia> typeof(a)
    Rational{Int64}

    julia> M = [1 2; 3.5 4];

    julia> typeof(M)
    Matrix{Float64} (alias for Array{Float64, 2})

source
`Core.tuple` — Function

    tuple(xs...)

Construct a tuple of the given objects.

Examples

    julia> tuple(1, 'a', pi)
    (1, 'a', π)

source
`Base.ntuple` — Function

    ntuple(f::Function, n::Integer)

Create a tuple of length `n`, computing each element as `f(i)`, where `i` is the index of the element.

Examples

    julia> ntuple(i -> 2*i, 4)
    (2, 4, 6, 8)

source

    ntuple(f, ::Val{N})

Create a tuple of length `N`, computing each element as `f(i)`, where `i` is the index of the element. By taking a `Val(N)` argument, it is possible that this version of ntuple may generate more efficient code than the version taking the length as an integer. But `ntuple(f, N)` is preferable to `ntuple(f, Val(N))` in cases where `N` cannot be determined at compile time.

Examples

    julia> ntuple(i -> 2*i, Val(4))
    (2, 4, 6, 8)

source
`Base.objectid` — Function

    objectid(x) -> UInt

Get a hash value for `x` based on object identity. `objectid(x)==objectid(y)` if `x === y`.

source
`Base.hash` — Function

    hash(x[, h::UInt])

Compute an integer hash code such that `isequal(x,y)` implies `hash(x)==hash(y)`. The optional second argument `h` is a hash code to be mixed with the result.

New types should implement the 2-argument form, typically by calling the 2-argument `hash` method recursively in order to mix hashes of the contents with each other (and with `h`). Typically, any type that implements `hash` should also implement its own `==` (hence `isequal`) to guarantee the property mentioned above. Types supporting subtraction (operator `-`) should also implement `widen`, which is required to hash values inside heterogeneous arrays.

source
`Base.finalizer` — Function

    finalizer(f, x)

Register a function `f(x)` to be called when there are no program-accessible references to `x`, and return `x`. The type of `x` must be a `mutable struct`, otherwise the behavior of this function is unpredictable.

`f` must not cause a task switch, which excludes most I/O operations such as `println`. Using the `@async` macro (to defer context switching to outside of the finalizer) or `ccall` to directly invoke IO functions in C may be helpful for debugging purposes.

Examples

    finalizer(my_mutable_struct) do x
        @async println("Finalizing $x.")
    end

    finalizer(my_mutable_struct) do x
        ccall(:jl_safe_printf, Cvoid, (Cstring, Cstring), "Finalizing %s.", repr(x))
    end

A finalizer may be registered at object construction. In the following example note that we implicitly rely on the finalizer returning the newly created mutable struct `x`.

Example

    mutable struct MyMutableStruct
        bar
        function MyMutableStruct(bar)
            x = new(bar)
            f(t) = @async println("Finalizing $t.")
            finalizer(f, x)
        end
    end

source
`Base.finalize` — Function

    finalize(x)

Immediately run finalizers registered for object `x`.

source
`Base.copy` — Function

    copy(x)

Create a shallow copy of `x`: the outer structure is copied, but not all internal values. For example, copying an array produces a new array with identically-same elements as the original.

source
`Base.deepcopy` — Function

    deepcopy(x)

Create a deep copy of `x`: everything is copied recursively, resulting in a fully independent object. For example, deep-copying an array produces a new array whose elements are deep copies of the original elements. Calling `deepcopy` on an object should generally have the same effect as serializing and then deserializing it.

While it isn't normally necessary, user-defined types can override the default `deepcopy` behavior by defining a specialized version of the function `deepcopy_internal(x::T, dict::IdDict)` (which shouldn't otherwise be used), where `T` is the type to be specialized for, and `dict` keeps track of objects copied so far within the recursion. Within the definition, `deepcopy_internal` should be used in place of `deepcopy`, and the `dict` variable should be updated as appropriate before returning.

source
`Base.getproperty` — Function

    getproperty(value, name::Symbol)

The syntax `a.b` calls `getproperty(a, :b)`.

Examples

    julia> struct MyType
               x
           end

    julia> function Base.getproperty(obj::MyType, sym::Symbol)
               if sym === :special
                   return obj.x + 1
               else # fallback to getfield
                   return getfield(obj, sym)
               end
           end

    julia> obj = MyType(1);

    julia> obj.special
    2

    julia> obj.x
    1

See also `propertynames` and `setproperty!`.

source
`Base.setproperty!` — Function

    setproperty!(value, name::Symbol, x)

The syntax `a.b = c` calls `setproperty!(a, :b, c)`.

See also `propertynames` and `getproperty`.

source
`Base.propertynames` — Function

    propertynames(x, private=false)

Get a tuple or a vector of the properties (`x.property`) of an object `x`. This is typically the same as `fieldnames(typeof(x))`, but types that overload `getproperty` should generally overload `propertynames` as well to get the properties of an instance of the type.

`propertynames(x)` may return only "public" property names that are part of the documented interface of `x`. If you want it to also return "private" fieldnames intended for internal use, pass `true` for the optional second argument. REPL tab completion on `x.` shows only the `private=false` properties.

source
`Base.hasproperty` — Function

    hasproperty(x, s::Symbol)

Return a boolean indicating whether the object `x` has `s` as one of its own properties.

Julia 1.2

This function requires at least Julia 1.2.

source
`Core.getfield` — Function

    getfield(value, name::Symbol)
    getfield(value, i::Int)

Extract a field from a composite `value` by name or position. See also `getproperty` and `fieldnames`.

Examples

    julia> a = 1//2
    1//2

    julia> getfield(a, :num)
    1

    julia> a.num
    1

    julia> getfield(a, 1)
    1

source
`Core.setfield!` — Function

    setfield!(value, name::Symbol, x)

Assign `x` to a named field in `value` of composite type. The `value` must be mutable and `x` must be a subtype of `fieldtype(typeof(value), name)`. See also `setproperty!`.

Examples

    julia> mutable struct MyMutableStruct
               field::Int
           end

    julia> a = MyMutableStruct(1);

    julia> setfield!(a, :field, 2);

    julia> getfield(a, :field)
    2

    julia> a = 1//2
    1//2

    julia> setfield!(a, :num, 3);
    ERROR: setfield! immutable struct of type Rational cannot be changed

source
`Core.isdefined` — Function

    isdefined(m::Module, s::Symbol)
    isdefined(object, s::Symbol)
    isdefined(object, index::Int)

Tests whether a global variable or object field is defined. The arguments can be a module and a symbol or a composite object and field name (as a symbol) or index.

To test whether an array element is defined, use `isassigned` instead.

See also `@isdefined`.

Examples

    julia> isdefined(Base, :sum)
    true

    julia> isdefined(Base, :NonExistentMethod)
    false

    julia> a = 1//2;

    julia> isdefined(a, 2)
    true

    julia> isdefined(a, 3)
    false

    julia> isdefined(a, :num)
    true

    julia> isdefined(a, :numerator)
    false

source
`Base.@isdefined` — Macro

    @isdefined s -> Bool

Tests whether variable `s` is defined in the current scope.

See also `isdefined`.

Examples

    julia> @isdefined newvar
    false

    julia> newvar = 1
    1

    julia> @isdefined newvar
    true

    julia> function f()
               println(@isdefined x)
               x = 3
               println(@isdefined x)
           end
    f (generic function with 1 method)

    julia> f()
    false
    true

source
`Base.convert` — Function

    convert(T, x)

Convert `x` to a value of type `T`.

If `T` is an `Integer` type, an `InexactError` will be raised if `x` is not representable by `T`, for example if `x` is not integer-valued, or is outside the range supported by `T`.

Examples

    julia> convert(Int, 3.0)
    3

    julia> convert(Int, 3.5)
    ERROR: InexactError: Int64(3.5)
    Stacktrace:
    [...]

If `T` is a `AbstractFloat` or `Rational` type, then it will return the closest value to `x` representable by `T`.

    julia> x = 1/3
    0.3333333333333333

    julia> convert(Float32, x)
    0.33333334f0

    julia> convert(Rational{Int32}, x)
    1//3

    julia> convert(Rational{Int64}, x)
    6004799503160661//18014398509481984

If `T` is a collection type and `x` a collection, the result of `convert(T, x)` may alias all or part of `x`.

    julia> x = Int[1, 2, 3];

    julia> y = convert(Vector{Int}, x);

    julia> y === x
    true

source
`Base.promote` — Function

    promote(xs...)

Convert all arguments to a common type, and return them all (as a tuple). If no arguments can be converted, an error is raised.

Examples

    julia> promote(Int8(1), Float16(4.5), Float32(4.1))
    (1.0f0, 4.5f0, 4.1f0)

source
`Base.oftype` — Function

    oftype(x, y)

Convert `y` to the type of `x` (`convert(typeof(x), y)`).

Examples

    julia> x = 4;

    julia> y = 3.;

    julia> oftype(x, y)
    3

    julia> oftype(y, x)
    4.0

source
`Base.widen` — Function

    widen(x)

If `x` is a type, return a "larger" type, defined so that arithmetic operations `+` and `-` are guaranteed not to overflow nor lose precision for any combination of values that type `x` can hold.

For fixed-size integer types less than 128 bits, `widen` will return a type with twice the number of bits.

If `x` is a value, it is converted to `widen(typeof(x))`.

Examples

    julia> widen(Int32)
    Int64

    julia> widen(1.5f0)
    1.5

source
`Base.identity` — Function

    identity(x)

The identity function. Returns its argument.

Examples

    julia> identity("Well, what did you expect?")
    "Well, what did you expect?"

source

## Properties of Types

### Type relations

`Base.supertype` — Function

    supertype(T::DataType)

Return the supertype of DataType `T`.

Examples

    julia> supertype(Int32)
    Signed

source
`Core.Type` — Type

    Core.Type{T}

`Core.Type` is an abstract type which has all type objects as its instances. The only instance of the singleton type `Core.Type{T}` is the object `T`.

Examples

    julia> isa(Type{Float64}, Type)
    true

    julia> isa(Float64, Type)
    true

    julia> isa(Real, Type{Float64})
    false

    julia> isa(Real, Type{Real})
    true

source
`Core.DataType` — Type

    DataType <: Type{T}

`DataType` represents explicitly declared types that have names, explicitly declared supertypes, and, optionally, parameters. Every concrete value in the system is an instance of some `DataType`.

Examples

    julia> typeof(Real)
    DataType

    julia> typeof(Int)
    DataType

    julia> struct Point
               x::Int
               y
           end

    julia> typeof(Point)
    DataType

source
`Core.:<:` — Function

    <:(T1, T2)

Subtype operator: returns `true` if and only if all values of type `T1` are also of type `T2`.

Examples

    julia> Float64 <: AbstractFloat
    true

    julia> Vector{Int} <: AbstractArray
    true

    julia> Matrix{Float64} <: Matrix{AbstractFloat}
    false

source
`Base.:>:` — Function

    >:(T1, T2)

Supertype operator, equivalent to `T2 <: T1`.

source
`Base.typejoin` — Function

    typejoin(T, S)

Return the closest common ancestor of `T` and `S`, i.e. the narrowest type from which they both inherit.

source
`Base.typeintersect` — Function

    typeintersect(T, S)

Compute a type that contains the intersection of `T` and `S`. Usually this will be the smallest such type or one close to it.

source
`Base.promote_type` — Function

    promote_type(type1, type2)

Promotion refers to converting values of mixed types to a single common type. `promote_type` represents the default promotion behavior in Julia when operators (usually mathematical) are given arguments of differing types. `promote_type` generally tries to return a type which can at least approximate most values of either input type without excessively widening. Some loss is tolerated; for example, `promote_type(Int64, Float64)` returns `Float64` even though strictly, not all `Int64` values can be represented exactly as `Float64` values.

    julia> promote_type(Int64, Float64)
    Float64

    julia> promote_type(Int32, Int64)
    Int64

    julia> promote_type(Float32, BigInt)
    BigFloat

    julia> promote_type(Int16, Float16)
    Float16

    julia> promote_type(Int64, Float16)
    Float16

    julia> promote_type(Int8, UInt16)
    UInt16

source
`Base.promote_rule` — Function

    promote_rule(type1, type2)

Specifies what type should be used by `promote` when given values of types `type1` and `type2`. This function should not be called directly, but should have definitions added to it for new types as appropriate.

source
`Base.isdispatchtuple` — Function

    isdispatchtuple(T)

Determine whether type `T` is a tuple "leaf type", meaning it could appear as a type signature in dispatch and has no subtypes (or supertypes) which could appear in a call.

source

### Declared structure

`Base.ismutable` — Function

    ismutable(v) -> Bool

Return `true` iff value `v` is mutable. See Mutable Composite Types for a discussion of immutability. Note that this function works on values, so if you give it a type, it will tell you that a value of `DataType` is mutable.

Examples

    julia> ismutable(1)
    false

    julia> ismutable([1,2])
    true

Julia 1.5

This function requires at least Julia 1.5.

source
`Base.isimmutable` — Function

    isimmutable(v) -> Bool

Warning

Consider using `!ismutable(v)` instead, as `isimmutable(v)` will be replaced by `!ismutable(v)` in a future release. (Since Julia 1.5)

Return `true` iff value `v` is immutable. See Mutable Composite Types for a discussion of immutability. Note that this function works on values, so if you give it a type, it will tell you that a value of `DataType` is mutable.

Examples

    julia> isimmutable(1)
    true

    julia> isimmutable([1,2])
    false

source
`Base.isabstracttype` — Function

    isabstracttype(T)

Determine whether type `T` was declared as an abstract type (i.e. using the `abstract` keyword).

Examples

    julia> isabstracttype(AbstractArray)
    true

    julia> isabstracttype(Vector)
    false

source
`Base.isprimitivetype` — Function

    isprimitivetype(T) -> Bool

Determine whether type `T` was declared as a primitive type (i.e. using the `primitive` keyword).

source
`Base.issingletontype` — Function

    Base.issingletontype(T)

Determine whether type `T` has exactly one possible instance; for example, a struct type with no fields.

source
`Base.isstructtype` — Function

    isstructtype(T) -> Bool

Determine whether type `T` was declared as a struct type (i.e. using the `struct` or `mutable struct` keyword).

source
`Base.nameof` — Method

    nameof(t::DataType) -> Symbol

Get the name of a (potentially `UnionAll`-wrapped) `DataType` (without its parent module) as a symbol.

Examples

    julia> module Foo
               struct S{T}
               end
           end
    Foo

    julia> nameof(Foo.S{T} where T)
    :S

source
`Base.fieldnames` — Function

    fieldnames(x::DataType)

Get a tuple with the names of the fields of a `DataType`.

Examples

    julia> fieldnames(Rational)
    (:num, :den)

source
`Base.fieldname` — Function

    fieldname(x::DataType, i::Integer)

Get the name of field `i` of a `DataType`.

Examples

    julia> fieldname(Rational, 1)
    :num

    julia> fieldname(Rational, 2)
    :den

source
`Base.hasfield` — Function

    hasfield(T::Type, name::Symbol)

Return a boolean indicating whether `T` has `name` as one of its own fields.

Julia 1.2

This function requires at least Julia 1.2.

source

### Memory layout

`Base.sizeof` — Method

    sizeof(T::DataType)
    sizeof(obj)

Size, in bytes, of the canonical binary representation of the given `DataType` `T`, if any. Size, in bytes, of object `obj` if it is not `DataType`.

Examples

    julia> sizeof(Float32)
    4

    julia> sizeof(ComplexF64)
    16

    julia> sizeof(1.0)
    8

    julia> sizeof([1.0:10.0;])
    80

If `DataType` `T` does not have a specific size, an error is thrown.

    julia> sizeof(AbstractArray)
    ERROR: Abstract type AbstractArray does not have a definite size.
    Stacktrace:
    [...]

source
`Base.isconcretetype` — Function

    isconcretetype(T)

Determine whether type `T` is a concrete type, meaning it could have direct instances (values `x` such that `typeof(x) === T`).

Examples

    julia> isconcretetype(Complex)
    false

    julia> isconcretetype(Complex{Float32})
    true

    julia> isconcretetype(Vector{Complex})
    true

    julia> isconcretetype(Vector{Complex{Float32}})
    true

    julia> isconcretetype(Union{})
    false

    julia> isconcretetype(Union{Int,String})
    false

source
`Base.isbits` — Function

    isbits(x)

Return `true` if `x` is an instance of an `isbitstype` type.

source
`Base.isbitstype` — Function

    isbitstype(T)

Return `true` if type `T` is a "plain data" type, meaning it is immutable and contains no references to other values, only `primitive` types and other `isbitstype` types. Typical examples are numeric types such as `UInt8`, `Float64`, and `Complex{Float64}`. This category of types is significant since they are valid as type parameters, may not track `isdefined` / `isassigned` status, and have a defined layout that is compatible with C.

Examples

    julia> isbitstype(Complex{Float64})
    true

    julia> isbitstype(Complex)
    false

source
`Core.fieldtype` — Function

    fieldtype(T, name::Symbol | index::Int)

Determine the declared type of a field (specified by name or index) in a composite DataType `T`.

Examples

    julia> struct Foo
               x::Int64
               y::String
           end

    julia> fieldtype(Foo, :x)
    Int64

    julia> fieldtype(Foo, 2)
    String

source
`Base.fieldtypes` — Function

    fieldtypes(T::Type)

The declared types of all fields in a composite DataType `T` as a tuple.

Julia 1.1

This function requires at least Julia 1.1.

Examples

    julia> struct Foo
               x::Int64
               y::String
           end

    julia> fieldtypes(Foo)
    (Int64, String)

source
`Base.fieldcount` — Function

    fieldcount(t::Type)

Get the number of fields that an instance of the given type would have. An error is thrown if the type is too abstract to determine this.

source
`Base.fieldoffset` — Function

    fieldoffset(type, i)

The byte offset of field `i` of a type relative to the data start. For example, we could use it in the following manner to summarize information about a struct:

    julia> structinfo(T) = [(fieldoffset(T,i), fieldname(T,i), fieldtype(T,i)) for i = 1:fieldcount(T)];

    julia> structinfo(Base.Filesystem.StatStruct)
    12-element Vector{Tuple{UInt64, Symbol, DataType}}:
     (0x0000000000000000, :device, UInt64)
     (0x0000000000000008, :inode, UInt64)
     (0x0000000000000010, :mode, UInt64)
     (0x0000000000000018, :nlink, Int64)
     (0x0000000000000020, :uid, UInt64)
     (0x0000000000000028, :gid, UInt64)
     (0x0000000000000030, :rdev, UInt64)
     (0x0000000000000038, :size, Int64)
     (0x0000000000000040, :blksize, Int64)
     (0x0000000000000048, :blocks, Int64)
     (0x0000000000000050, :mtime, Float64)
     (0x0000000000000058, :ctime, Float64)

source
`Base.datatype_alignment` — Function

    Base.datatype_alignment(dt::DataType) -> Int

Memory allocation minimum alignment for instances of this type. Can be called on any `isconcretetype`.

source
`Base.datatype_haspadding` — Function

    Base.datatype_haspadding(dt::DataType) -> Bool

Return whether the fields of instances of this type are packed in memory, with no intervening padding bytes. Can be called on any `isconcretetype`.

source
`Base.datatype_pointerfree` — Function

    Base.datatype_pointerfree(dt::DataType) -> Bool

Return whether instances of this type can contain references to gc-managed memory. Can be called on any `isconcretetype`.

source

### Special values

`Base.typemin` — Function

    typemin(T)

The lowest value representable by the given (real) numeric DataType `T`.

Examples

    julia> typemin(Float16)
    -Inf16

    julia> typemin(Float32)
    -Inf32

source
`Base.typemax` — Function

    typemax(T)

The highest value representable by the given (real) numeric `DataType`.

Examples

    julia> typemax(Int8)
    127

    julia> typemax(UInt32)
    0xffffffff

source
`Base.floatmin` — Function

    floatmin(T = Float64)

Return the smallest positive normal number representable by the floating-point type `T`.

Examples

    julia> floatmin(Float16)
    Float16(6.104e-5)

    julia> floatmin(Float32)
    1.1754944f-38

    julia> floatmin()
    2.2250738585072014e-308

source
`Base.floatmax` — Function

    floatmax(T = Float64)

Return the largest finite number representable by the floating-point type `T`.

Examples

    julia> floatmax(Float16)
    Float16(6.55e4)

    julia> floatmax(Float32)
    3.4028235f38

    julia> floatmax()
    1.7976931348623157e308

source
`Base.maxintfloat` — Function

    maxintfloat(T=Float64)

The largest consecutive integer-valued floating-point number that is exactly represented in the given floating-point type `T` (which defaults to `Float64`).

That is, `maxintfloat` returns the smallest positive integer-valued floating-point number `n` such that `n+1` is not exactly representable in the type `T`.

When an `Integer`-type value is needed, use `Integer(maxintfloat(T))`.

source

    maxintfloat(T, S)

The largest consecutive integer representable in the given floating-point type `T` that also does not exceed the maximum integer representable by the integer type `S`. Equivalently, it is the minimum of `maxintfloat(T)` and `typemax(S)`.

source
`Base.eps` — Method

    eps(::Type{T}) where T<:AbstractFloat
    eps()

Return the machine epsilon of the floating point type `T` (`T = Float64` by default). This is defined as the gap between 1 and the next largest value representable by `typeof(one(T))`, and is equivalent to `eps(one(T))`. (Since `eps(T)` is a bound on the relative error of `T`, it is a "dimensionless" quantity like `one`.)

Examples

    julia> eps()
    2.220446049250313e-16

    julia> eps(Float32)
    1.1920929f-7

    julia> 1.0 + eps()
    1.0000000000000002

    julia> 1.0 + eps()/2
    1.0

source
`Base.eps` — Method

    eps(x::AbstractFloat)

Return the unit in last place (ulp) of `x`. This is the distance between consecutive representable floating point values at `x`. In most cases, if the distance on either side of `x` is different, then the larger of the two is taken, that is

    eps(x) == max(x-prevfloat(x), nextfloat(x)-x)

The exceptions to this rule are the smallest and largest finite values (e.g. `nextfloat(-Inf)` and `prevfloat(Inf)` for `Float64`), which round to the smaller of the values.

The rationale for this behavior is that `eps` bounds the floating point rounding error. Under the default `RoundNearest` rounding mode, if $y$ is a real number and $x$ is the nearest floating point number to $y$, then

\[|y-x| \leq \operatorname{eps}(x)/2.\]

Examples

    julia> eps(1.0)
    2.220446049250313e-16

    julia> eps(prevfloat(2.0))
    2.220446049250313e-16

    julia> eps(2.0)
    4.440892098500626e-16

    julia> x = prevfloat(Inf)      # largest finite Float64
    1.7976931348623157e308

    julia> x + eps(x)/2            # rounds up
    Inf

    julia> x + prevfloat(eps(x)/2) # rounds down
    1.7976931348623157e308

source
`Base.instances` — Function

    instances(T::Type)

Return a collection of all instances of the given type, if applicable. Mostly used for enumerated types (see `@enum`).

Example

    julia> @enum Color red blue green

    julia> instances(Color)
    (red, blue, green)

source

## Special Types

`Core.Any` — Type

    Any::DataType

`Any` is the union of all types. It has the defining property `isa(x, Any) == true` for any `x`. `Any` therefore describes the entire universe of possible values. For example `Integer` is a subset of `Any` that includes `Int`, `Int8`, and other integer types.

source
`Core.Union` — Type

    Union{Types...}

A type union is an abstract type which includes all instances of any of its argument types. The empty union `Union{}` is the bottom type of Julia.

Examples

    julia> IntOrString = Union{Int,AbstractString}
    Union{Int64, AbstractString}

    julia> 1 :: IntOrString
    1

    julia> "Hello!" :: IntOrString
    "Hello!"

    julia> 1.0 :: IntOrString
    ERROR: TypeError: in typeassert, expected Union{Int64, AbstractString}, got a value of type Float64

source
`Union{}` — Keyword

    Union{}

`Union{}`, the empty `Union` of types, is the type that has no values. That is, it has the defining property `isa(x, Union{}) == false` for any `x`. `Base.Bottom` is defined as its alias and the type of `Union{}` is `Core.TypeofBottom`.

Examples

    julia> isa(nothing, Union{})
    false

source
`Core.UnionAll` — Type

    UnionAll

A union of types over all values of a type parameter. `UnionAll` is used to describe parametric types where the values of some parameters are not known.

Examples

    julia> typeof(Vector)
    UnionAll

    julia> typeof(Vector{Int})
    DataType

source
`Core.Tuple` — Type

    Tuple{Types...}

Tuples are an abstraction of the arguments of a function – without the function itself. The salient aspects of a function's arguments are their order and their types. Therefore a tuple type is similar to a parameterized immutable type where each parameter is the type of one field. Tuple types may have any number of parameters.

Tuple types are covariant in their parameters: `Tuple{Int}` is a subtype of `Tuple{Any}`. Therefore `Tuple{Any}` is considered an abstract type, and tuple types are only concrete if their parameters are. Tuples do not have field names; fields are only accessed by index.

See the manual section on Tuple Types.

source
`Core.NamedTuple` — Type

    NamedTuple

`NamedTuple`s are, as their name suggests, named `Tuple`s. That is, they're a tuple-like collection of values, where each entry has a unique name, represented as a `Symbol`. Like `Tuple`s, `NamedTuple`s are immutable; neither the names nor the values can be modified in place after construction.

Accessing the value associated with a name in a named tuple can be done using field access syntax, e.g. `x.a`, or using `getindex`, e.g. `x[:a]`. A tuple of the names can be obtained using `keys`, and a tuple of the values can be obtained using `values`.

Note

Iteration over `NamedTuple`s produces the values without the names. (See example below.) To iterate over the name-value pairs, use the `pairs` function.

The `@NamedTuple` macro can be used for conveniently declaring `NamedTuple` types.

Examples

    julia> x = (a=1, b=2)
    (a = 1, b = 2)

    julia> x.a
    1

    julia> x[:a]
    1

    julia> keys(x)
    (:a, :b)

    julia> values(x)
    (1, 2)

    julia> collect(x)
    2-element Vector{Int64}:
     1
     2

    julia> collect(pairs(x))
    2-element Vector{Pair{Symbol, Int64}}:
     :a => 1
     :b => 2

In a similar fashion as to how one can define keyword arguments programmatically, a named tuple can be created by giving a pair `name::Symbol => value` or splatting an iterator yielding such pairs after a semicolon inside a tuple literal:

    julia> (; :a => 1)
    (a = 1,)

    julia> keys = (:a, :b, :c); values = (1, 2, 3);

    julia> (; zip(keys, values)...)
    (a = 1, b = 2, c = 3)

As in keyword arguments, identifiers and dot expressions imply names:

    julia> x = 0
    0

    julia> t = (; x)
    (x = 0,)

    julia> (; t.x)
    (x = 0,)

Julia 1.5

Implicit names from identifiers and dot expressions are available as of Julia 1.5.

source
`Base.@NamedTuple` — Macro

    @NamedTuple{key1::Type1, key2::Type2, ...}
    @NamedTuple begin key1::Type1; key2::Type2; ...; end

This macro gives a more convenient syntax for declaring `NamedTuple` types. It returns a `NamedTuple` type with the given keys and types, equivalent to `NamedTuple{(:key1, :key2, ...), Tuple{Type1,Type2,...}}`. If the `::Type` declaration is omitted, it is taken to be `Any`. The `begin ... end` form allows the declarations to be split across multiple lines (similar to a `struct` declaration), but is otherwise equivalent.

For example, the tuple `(a=3.1, b="hello")` has a type `NamedTuple{(:a, :b),Tuple{Float64,String}}`, which can also be declared via `@NamedTuple` as:

    julia> @NamedTuple{a::Float64, b::String}
    NamedTuple{(:a, :b), Tuple{Float64, String}}

    julia> @NamedTuple begin
               a::Float64
               b::String
           end
    NamedTuple{(:a, :b), Tuple{Float64, String}}

Julia 1.5

This macro is available as of Julia 1.5.

source
`Base.Val` — Type

    Val(c)

Return `Val{c}()`, which contains no run-time data. Types like this can be used to pass the information between functions through the value `c`, which must be an `isbits` value or a `Symbol`. The intent of this construct is to be able to dispatch on constants directly (at compile time) without having to test the value of the constant at run time.

Examples

    julia> f(::Val{true}) = "Good"
    f (generic function with 1 method)

    julia> f(::Val{false}) = "Bad"
    f (generic function with 2 methods)

    julia> f(Val(true))
    "Good"

source
`Core.Vararg` — Type

    Vararg{T,N}

The last parameter of a tuple type `Tuple` can be the special type `Vararg`, which denotes any number of trailing elements. The type `Vararg{T,N}` corresponds to exactly `N` elements of type `T`. `Vararg{T}` corresponds to zero or more elements of type `T`. `Vararg` tuple types are used to represent the arguments accepted by varargs methods (see the section on Varargs Functions in the manual.)

Examples

    julia> mytupletype = Tuple{AbstractString, Vararg{Int}}
    Tuple{AbstractString, Vararg{Int64, N} where N}

    julia> isa(("1",), mytupletype)
    true

    julia> isa(("1",1), mytupletype)
    true

    julia> isa(("1",1,2), mytupletype)
    true

    julia> isa(("1",1,2,3.0), mytupletype)
    false

source
`Core.Nothing` — Type

    Nothing

A type with no fields that is the type of `nothing`.

source
`Base.isnothing` — Function

    isnothing(x)

Return `true` if `x === nothing`, and return `false` if not.

Julia 1.1

This function requires at least Julia 1.1.

source
`Base.Some` — Type

    Some{T}

A wrapper type used in `Union{Some{T}, Nothing}` to distinguish between the absence of a value (`nothing`) and the presence of a `nothing` value (i.e. `Some(nothing)`).

Use `something` to access the value wrapped by a `Some` object.

source
`Base.something` — Function

    something(x, y...)

Return the first value in the arguments which is not equal to `nothing`, if any. Otherwise throw an error. Arguments of type `Some` are unwrapped.

See also `coalesce`.

Examples

    julia> something(nothing, 1)
    1

    julia> something(Some(1), nothing)
    1

    julia> something(missing, nothing)
    missing

    julia> something(nothing, nothing)
    ERROR: ArgumentError: No value arguments present

source
`Base.Enums.Enum` — Type

    Enum{T<:Integer}

The abstract supertype of all enumerated types defined with `@enum`.

source
`Base.Enums.@enum` — Macro

    @enum EnumName[::BaseType] value1[=x] value2[=y]

Create an `Enum{BaseType}` subtype with name `EnumName` and enum member values of `value1` and `value2` with optional assigned values of `x` and `y`, respectively. `EnumName` can be used just like other types and enum member values as regular values, such as

Examples

    julia> @enum Fruit apple=1 orange=2 kiwi=3

    julia> f(x::Fruit) = "I'm a Fruit with value: $(Int(x))"
    f (generic function with 1 method)

    julia> f(apple)
    "I'm a Fruit with value: 1"

    julia> Fruit(1)
    apple::Fruit = 1

Values can also be specified inside a `begin` block, e.g.

    @enum EnumName begin
        value1
        value2
    end

`BaseType`, which defaults to `Int32`, must be a primitive subtype of `Integer`. Member values can be converted between the enum type and `BaseType`. `read` and `write` perform these conversions automatically. In case the enum is created with a non-default `BaseType`, `Integer(value1)` will return the integer `value1` with the type `BaseType`.

To list all the instances of an enum use `instances`, e.g.

    julia> instances(Fruit)
    (apple, orange, kiwi)

source
`Core.Expr` — Type

    Expr(head::Symbol, args...)

A type representing compound expressions in parsed julia code (ASTs). Each expression consists of a `head` `Symbol` identifying which kind of expression it is (e.g. a call, for loop, conditional statement, etc.), and subexpressions (e.g. the arguments of a call). The subexpressions are stored in a `Vector{Any}` field called `args`.

See the manual chapter on Metaprogramming and the developer documentation Julia ASTs.

Examples

    julia> Expr(:call, :+, 1, 2)
    :(1 + 2)

    julia> dump(:(a ? b : c))
    Expr
      head: Symbol if
      args: Array{Any}((3,))
        1: Symbol a
        2: Symbol b
        3: Symbol c

source
`Core.Symbol` — Type

    Symbol

The type of object used to represent identifiers in parsed julia code (ASTs). Also often used as a name or label to identify an entity (e.g. as a dictionary key). `Symbol`s can be entered using the `:` quote operator:

    julia> :name
    :name

    julia> typeof(:name)
    Symbol

    julia> x = 42
    42

    julia> eval(:x)
    42

`Symbol`s can also be constructed from strings or other values by calling the constructor `Symbol(x...)`.

`Symbol`s are immutable and should be compared using `===`. The implementation re-uses the same object for all `Symbol`s with the same name, so comparison tends to be efficient (it can just compare pointers).

Unlike strings, `Symbol`s are "atomic" or "scalar" entities that do not support iteration over characters.

source
`Core.Symbol` — Method

    Symbol(x...) -> Symbol

Create a `Symbol` by concatenating the string representations of the arguments together.

Examples

    julia> Symbol("my", "name")
    :myname

    julia> Symbol("day", 4)
    :day4

source
`Core.Module` — Type

    Module

A `Module` is a separate global variable workspace. See `module` and the manual section about modules for details.

source

## Generic Functions

`Core.Function` — Type

    Function

Abstract type of all functions.

Examples

    julia> isa(+, Function)
    true

    julia> typeof(sin)
    typeof(sin)

    julia> ans <: Function
    true

source
`Base.hasmethod` — Function

    hasmethod(f, t::Type{<:Tuple}[, kwnames]; world=typemax(UInt)) -> Bool

Determine whether the given generic function has a method matching the given `Tuple` of argument types with the upper bound of world age given by `world`.

If a tuple of keyword argument names `kwnames` is provided, this also checks whether the method of `f` matching `t` has the given keyword argument names. If the matching method accepts a variable number of keyword arguments, e.g. with `kwargs...`, any names given in `kwnames` are considered valid. Otherwise the provided names must be a subset of the method's keyword arguments.

See also `applicable`.

Julia 1.2

Providing keyword argument names requires Julia 1.2 or later.

Examples

    julia> hasmethod(length, Tuple{Array})
    true

    julia> f(; oranges=0) = oranges;

    julia> hasmethod(f, Tuple{}, (:oranges,))
    true

    julia> hasmethod(f, Tuple{}, (:apples, :bananas))
    false

    julia> g(; xs...) = 4;

    julia> hasmethod(g, Tuple{}, (:a, :b, :c, :d))  # g accepts arbitrary kwargs
    true

source
`Core.applicable` — Function

    applicable(f, args...) -> Bool

Determine whether the given generic function has a method applicable to the given arguments.

See also `hasmethod`.

Examples

    julia> function f(x, y)
               x + y
           end;

    julia> applicable(f, 1)
    false

    julia> applicable(f, 1, 2)
    true

source
`Core.invoke` — Function

    invoke(f, argtypes::Type, args...; kwargs...)

Invoke a method for the given generic function `f` matching the specified types `argtypes` on the specified arguments `args` and passing the keyword arguments `kwargs`. The arguments `args` must conform with the specified types in `argtypes`, i.e. conversion is not automatically performed. This method allows invoking a method other than the most specific matching method, which is useful when the behavior of a more general definition is explicitly needed (often as part of the implementation of a more specific method of the same function).

Be careful when using `invoke` for functions that you don't write. What definition is used for given `argtypes` is an implementation detail unless the function is explicitly states that calling with certain `argtypes` is a part of public API. For example, the change between `f1` and `f2` in the example below is usually considered compatible because the change is invisible by the caller with a normal (non-`invoke`) call. However, the change is visible if you use `invoke`.

Examples

    julia> f(x::Real) = x^2;

    julia> f(x::Integer) = 1 + invoke(f, Tuple{Real}, x);

    julia> f(2)
    5

    julia> f1(::Integer) = Integer
           f1(::Real) = Real;

    julia> f2(x::Real) = _f2(x)
           _f2(::Integer) = Integer
           _f2(_) = Real;

    julia> f1(1)
    Integer

    julia> f2(1)
    Integer

    julia> invoke(f1, Tuple{Real}, 1)
    Real

    julia> invoke(f2, Tuple{Real}, 1)
    Integer

source
`Base.invokelatest` — Function

    invokelatest(f, args...; kwargs...)

Calls `f(args...; kwargs...)`, but guarantees that the most recent method of `f` will be executed. This is useful in specialized circumstances, e.g. long-running event loops or callback functions that may call obsolete versions of a function `f`. (The drawback is that `invokelatest` is somewhat slower than calling `f` directly, and the type of the result cannot be inferred by the compiler.)

source
`Base.@invokelatest` — Macro

    @invokelatest f(args...; kwargs...)

Provides a convenient way to call `Base.invokelatest`. `@invokelatest f(args...; kwargs...)` will simply be expanded into `Base.invokelatest(f, args...; kwargs...)`.

source
`new` — Keyword

    new

Special function available to inner constructors which created a new object of the type. See the manual section on Inner Constructor Methods for more information.

source
`Base.:|>` — Function

    |>(x, f)

Applies a function to the preceding argument. This allows for easy function chaining.

Examples

    julia> [1:5;] |> x->x.^2 |> sum |> inv
    0.01818181818181818

source
`Base.:∘` — Function

    f ∘ g

Compose functions: i.e. `(f ∘ g)(args...)` means `f(g(args...))`. The `∘` symbol can be entered in the Julia REPL (and most editors, appropriately configured) by typing `\circ<tab>`.

Function composition also works in prefix form: `∘(f, g)` is the same as `f ∘ g`. The prefix form supports composition of multiple functions: `∘(f, g, h) = f ∘ g ∘ h` and splatting `∘(fs...)` for composing an iterable collection of functions.

Julia 1.4

Multiple function composition requires at least Julia 1.4.

Julia 1.5

Composition of one function ∘(f) requires at least Julia 1.5.

Examples

    julia> map(uppercase∘first, ["apple", "banana", "carrot"])
    3-element Vector{Char}:
     'A': ASCII/Unicode U+0041 (category Lu: Letter, uppercase)
     'B': ASCII/Unicode U+0042 (category Lu: Letter, uppercase)
     'C': ASCII/Unicode U+0043 (category Lu: Letter, uppercase)

    julia> fs = [
               x -> 2x
               x -> x/2
               x -> x-1
               x -> x+1
           ];

    julia> ∘(fs...)(3)
    3.0

See also `ComposedFunction`.

source
`Base.ComposedFunction` — Type

    ComposedFunction{Outer,Inner} <: Function

Represents the composition of two callable objects `outer::Outer` and `inner::Inner`. That is

    ComposedFunction(outer, inner)(args...; kw...) === outer(inner(args...; kw...))

The preferred way to construct instance of `ComposedFunction` is to use the composition operator `∘`:

    julia> sin ∘ cos === ComposedFunction(sin, cos)
    true

    julia> typeof(sin∘cos)
    ComposedFunction{typeof(sin), typeof(cos)}

The composed pieces are stored in the fields of `ComposedFunction` and can be retrieved as follows:

    julia> composition = sin ∘ cos
    sin ∘ cos

    julia> composition.outer === sin
    true

    julia> composition.inner === cos
    true

Julia 1.6

ComposedFunction requires at least Julia 1.6. In earlier versions `∘` returns an anonymous function instead.

See also `∘`.

source

## Syntax

`Core.eval` — Function

    Core.eval(m::Module, expr)

Evaluate an expression in the given module and return the result.

source
`Base.MainInclude.eval` — Function

    eval(expr)

Evaluate an expression in the global scope of the containing module. Every `Module` (except those defined with `baremodule`) has its own 1-argument definition of `eval`, which evaluates expressions in that module.

source
`Base.@eval` — Macro

    @eval [mod,] ex

Evaluate an expression with values interpolated into it using `eval`. If two arguments are provided, the first is the module to evaluate in.

source
`Base.evalfile` — Function

    evalfile(path::AbstractString, args::Vector{String}=String[])

Load the file using `include`, evaluate all expressions, and return the value of the last one.

source
`Base.esc` — Function

    esc(e)

Only valid in the context of an `Expr` returned from a macro. Prevents the macro hygiene pass from turning embedded variables into gensym variables. See the Macros section of the Metaprogramming chapter of the manual for more details and examples.

source
`Base.@inbounds` — Macro

    @inbounds(blk)

Eliminates array bounds checking within expressions.

In the example below the in-range check for referencing element `i` of array `A` is skipped to improve performance.

    function sum(A::AbstractArray)
        r = zero(eltype(A))
        for i = 1:length(A)
            @inbounds r += A[i]
        end
        return r
    end

Warning

Using `@inbounds` may return incorrect results/crashes/corruption for out-of-bounds indices. The user is responsible for checking it manually. Only use `@inbounds` when it is certain from the information locally available that all accesses are in bounds.

source
`Base.@boundscheck` — Macro

    @boundscheck(blk)

Annotates the expression `blk` as a bounds checking block, allowing it to be elided by `@inbounds`.

Note

The function in which `@boundscheck` is written must be inlined into its caller in order for `@inbounds` to have effect.

Examples

    julia> @inline function g(A, i)
               @boundscheck checkbounds(A, i)
               return "accessing ($A)[$i]"
           end;

    julia> f1() = return g(1:2, -1);

    julia> f2() = @inbounds return g(1:2, -1);

    julia> f1()
    ERROR: BoundsError: attempt to access 2-element UnitRange{Int64} at index [-1]
    Stacktrace:
     [1] throw_boundserror(::UnitRange{Int64}, ::Tuple{Int64}) at ./abstractarray.jl:455
     [2] checkbounds at ./abstractarray.jl:420 [inlined]
     [3] g at ./none:2 [inlined]
     [4] f1() at ./none:1
     [5] top-level scope

    julia> f2()
    "accessing (1:2)[-1]"

Warning

The `@boundscheck` annotation allows you, as a library writer, to opt-in to allowing other code to remove your bounds checks with `@inbounds`. As noted there, the caller must verify—using information they can access—that their accesses are valid before using `@inbounds`. For indexing into your `AbstractArray` subclasses, for example, this involves checking the indices against its `size`. Therefore, `@boundscheck` annotations should only be added to a `getindex` or `setindex!` implementation after you are certain its behavior is correct.

source
`Base.@propagate_inbounds` — Macro

    @propagate_inbounds

Tells the compiler to inline a function while retaining the caller's inbounds context.

source
`Base.@inline` — Macro

    @inline

Give a hint to the compiler that this function is worth inlining.

Small functions typically do not need the `@inline` annotation, as the compiler does it automatically. By using `@inline` on bigger functions, an extra nudge can be given to the compiler to inline it. This is shown in the following example:

    @inline function bigfunction(x)
        #=
            Function Definition
        =#
    end

source
`Base.@noinline` — Macro

    @noinline

Give a hint to the compiler that it should not inline a function.

Small functions are typically inlined automatically. By using `@noinline` on small functions, auto-inlining can be prevented. This is shown in the following example:

    @noinline function smallfunction(x)
        #=
            Function Definition
        =#
    end

Note

If the function is trivial (for example returning a constant) it might get inlined anyway.

source
`Base.@nospecialize` — Macro

    @nospecialize

Applied to a function argument name, hints to the compiler that the method should not be specialized for different types of that argument, but instead to use precisely the declared type for each argument. This is only a hint for avoiding excess code generation. Can be applied to an argument within a formal argument list, or in the function body. When applied to an argument, the macro must wrap the entire argument expression. When used in a function body, the macro must occur in statement position and before any code.

When used without arguments, it applies to all arguments of the parent scope. In local scope, this means all arguments of the containing function. In global (top-level) scope, this means all methods subsequently defined in the current module.

Specialization can reset back to the default by using `@specialize`.

    function example_function(@nospecialize x)
        ...
    end

    function example_function(x, @nospecialize(y = 1))
        ...
    end

    function example_function(x, y, z)
        @nospecialize x y
        ...
    end

    @nospecialize
    f(y) = [x for x in y]
    @specialize

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`Base.@specialize` — Macro

    @specialize

Reset the specialization hint for an argument back to the default. For details, see `@nospecialize`.

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`Base.gensym` — Function

    gensym([tag])

Generates a symbol which will not conflict with other variable names.

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`Base.@gensym` — Macro

    @gensym

Generates a gensym symbol for a variable. For example, `@gensym x y` is transformed into `x = gensym("x"); y = gensym("y")`.

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`var"name"` — Keyword

    var

The syntax `var"#example#"` refers to a variable named `Symbol("#example#")`, even though `#example#` is not a valid Julia identifier name.

This can be useful for interoperability with programming languages which have different rules for the construction of valid identifiers. For example, to refer to the `R` variable `draw.segments`, you can use `var"draw.segments"` in your Julia code.

It is also used to `show` julia source code which has gone through macro hygiene or otherwise contains variable names which can't be parsed normally.

Note that this syntax requires parser support so it is expanded directly by the parser rather than being implemented as a normal string macro `@var_str`.

Julia 1.3

This syntax requires at least Julia 1.3.

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`Base.@goto` — Macro

    @goto name

`@goto name` unconditionally jumps to the statement at the location `@label name`.

`@label` and `@goto` cannot create jumps to different top-level statements. Attempts cause an error. To still use `@goto`, enclose the `@label` and `@goto` in a block.

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`Base.@label` — Macro

    @label name

Labels a statement with the symbolic label `name`. The label marks the end-point of an unconditional jump with `@goto name`.

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`Base.SimdLoop.@simd` — Macro

    @simd

Annotate a `for` loop to allow the compiler to take extra liberties to allow loop re-ordering

Warning

This feature is experimental and could change or disappear in future versions of Julia. Incorrect use of the `@simd` macro may cause unexpected results.

The object iterated over in a `@simd for` loop should be a one-dimensional range. By using `@simd`, you are asserting several properties of the loop:

- It is safe to execute iterations in arbitrary or overlapping order, with special consideration for reduction variables.
- Floating-point operations on reduction variables can be reordered, possibly causing different results than without `@simd`.

In many cases, Julia is able to automatically vectorize inner for loops without the use of `@simd`. Using `@simd` gives the compiler a little extra leeway to make it possible in more situations. In either case, your inner loop should have the following properties to allow vectorization:

- The loop must be an innermost loop
- The loop body must be straight-line code. Therefore, `@inbounds` is currently needed for all array accesses. The compiler can sometimes turn short `&&`, `||`, and `?:` expressions into straight-line code if it is safe to evaluate all operands unconditionally. Consider using the `ifelse` function instead of `?:` in the loop if it is safe to do so.
- Accesses must have a stride pattern and cannot be "gathers" (random-index reads) or "scatters" (random-index writes).
- The stride should be unit stride.

Note

The `@simd` does not assert by default that the loop is completely free of loop-carried memory dependencies, which is an assumption that can easily be violated in generic code. If you are writing non-generic code, you can use `@simd ivdep for ... end` to also assert that:

- There exists no loop-carried memory dependencies
- No iteration ever waits on a previous iteration to make forward progress.

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`Base.@polly` — Macro

    @polly

Tells the compiler to apply the polyhedral optimizer Polly to a function.

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`Base.@generated` — Macro

    @generated f
    @generated(f)

`@generated` is used to annotate a function which will be generated. In the body of the generated function, only types of arguments can be read (not the values). The function returns a quoted expression evaluated when the function is called. The `@generated` macro should not be used on functions mutating the global scope or depending on mutable elements.

See Metaprogramming for further details.

Example:

    julia> @generated function bar(x)
               if x <: Integer
                   return :(x ^ 2)
               else
                   return :(x)
               end
           end
    bar (generic function with 1 method)

    julia> bar(4)
    16

    julia> bar("baz")
    "baz"

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`Base.@pure` — Macro

    @pure ex
    @pure(ex)

`@pure` gives the compiler a hint for the definition of a pure function, helping for type inference.

A pure function can only depend on immutable information. This also means a `@pure` function cannot use any global mutable state, including generic functions. Calls to generic functions depend on method tables which are mutable global state. Use with caution, incorrect `@pure` annotation of a function may introduce hard to identify bugs. Double check for calls to generic functions. This macro is intended for internal compiler use and may be subject to changes.

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`Base.@deprecate` — Macro

    @deprecate old new [ex=true]

Deprecate method `old` and specify the replacement call `new`. Prevent `@deprecate` from exporting `old` by setting `ex` to `false`. `@deprecate` defines a new method with the same signature as `old`.

Julia 1.5

As of Julia 1.5, functions defined by `@deprecate` do not print warning when `julia` is run without the `--depwarn=yes` flag set, as the default value of `--depwarn` option is `no`. The warnings are printed from tests run by `Pkg.test()`.

Examples

    julia> @deprecate old(x) new(x)
    old (generic function with 1 method)

    julia> @deprecate old(x) new(x) false
    old (generic function with 1 method)

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## Missing Values

`Base.Missing` — Type

    Missing

A type with no fields whose singleton instance `missing` is used to represent missing values.

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`Base.missing` — Constant

    missing

The singleton instance of type `Missing` representing a missing value.

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`Base.coalesce` — Function

    coalesce(x, y...)

Return the first value in the arguments which is not equal to `missing`, if any. Otherwise return `missing`.

See also `something`.

Examples

    julia> coalesce(missing, 1)
    1

    julia> coalesce(1, missing)
    1

    julia> coalesce(nothing, 1)  # returns `nothing`

    julia> coalesce(missing, missing)
    missing

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`Base.ismissing` — Function

    ismissing(x)

Indicate whether `x` is `missing`.

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`Base.skipmissing` — Function

    skipmissing(itr)

Return an iterator over the elements in `itr` skipping `missing` values. The returned object can be indexed using indices of `itr` if the latter is indexable. Indices corresponding to missing values are not valid: they are skipped by `keys` and `eachindex`, and a `MissingException` is thrown when trying to use them.

Use `collect` to obtain an `Array` containing the non-`missing` values in `itr`. Note that even if `itr` is a multidimensional array, the result will always be a `Vector` since it is not possible to remove missings while preserving dimensions of the input.

Examples

    julia> x = skipmissing([1, missing, 2])
    skipmissing(Union{Missing, Int64}[1, missing, 2])

    julia> sum(x)
    3

    julia> x[1]
    1

    julia> x[2]
    ERROR: MissingException: the value at index (2,) is missing
    [...]

    julia> argmax(x)
    3

    julia> collect(keys(x))
    2-element Vector{Int64}:
     1
     3

    julia> collect(skipmissing([1, missing, 2]))
    2-element Vector{Int64}:
     1
     2

    julia> collect(skipmissing([1 missing; 2 missing]))
    2-element Vector{Int64}:
     1
     2

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`Base.nonmissingtype` — Function

    nonmissingtype(T::Type)

If `T` is a union of types containing `Missing`, return a new type with `Missing` removed.

Examples

    julia> nonmissingtype(Union{Int64,Missing})
    Int64

    julia> nonmissingtype(Any)
    Any

Julia 1.3

This function is exported as of Julia 1.3.

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## System

`Base.run` — Function

    run(command, args...; wait::Bool = true)

Run a command object, constructed with backticks (see the Running External Programs section in the manual). Throws an error if anything goes wrong, including the process exiting with a non-zero status (when `wait` is true).

If `wait` is false, the process runs asynchronously. You can later wait for it and check its exit status by calling `success` on the returned process object.

When `wait` is false, the process' I/O streams are directed to `devnull`. When `wait` is true, I/O streams are shared with the parent process. Use `pipeline` to control I/O redirection.

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`Base.devnull` — Constant

    devnull

Used in a stream redirect to discard all data written to it. Essentially equivalent to `/dev/null` on Unix or `NUL` on Windows. Usage:

    run(pipeline(`cat test.txt`, devnull))

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`Base.success` — Function

    success(command)

Run a command object, constructed with backticks (see the Running External Programs section in the manual), and tell whether it was successful (exited with a code of 0). An exception is raised if the process cannot be started.

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`Base.process_running` — Function

    process_running(p::Process)

Determine whether a process is currently running.

source
`Base.process_exited` — Function

    process_exited(p::Process)

Determine whether a process has exited.

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`Base.kill` — Method

    kill(p::Process, signum=Base.SIGTERM)

Send a signal to a process. The default is to terminate the process. Returns successfully if the process has already exited, but throws an error if killing the process failed for other reasons (e.g. insufficient permissions).

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`Base.Sys.set_process_title` — Function

    Sys.set_process_title(title::AbstractString)

Set the process title. No-op on some operating systems.

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`Base.Sys.get_process_title` — Function

    Sys.get_process_title()

Get the process title. On some systems, will always return an empty string.

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`Base.ignorestatus` — Function

    ignorestatus(command)

Mark a command object so that running it will not throw an error if the result code is non-zero.

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`Base.detach` — Function

    detach(command)

Mark a command object so that it will be run in a new process group, allowing it to outlive the julia process, and not have Ctrl-C interrupts passed to it.

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`Base.Cmd` — Type

    Cmd(cmd::Cmd; ignorestatus, detach, windows_verbatim, windows_hide, env, dir)

Construct a new `Cmd` object, representing an external program and arguments, from `cmd`, while changing the settings of the optional keyword arguments:

- `ignorestatus::Bool`: If `true` (defaults to `false`), then the `Cmd` will not throw an error if the return code is nonzero.
- `detach::Bool`: If `true` (defaults to `false`), then the `Cmd` will be run in a new process group, allowing it to outlive the `julia` process and not have Ctrl-C passed to it.
- `windows_verbatim::Bool`: If `true` (defaults to `false`), then on Windows the `Cmd` will send a command-line string to the process with no quoting or escaping of arguments, even arguments containing spaces. (On Windows, arguments are sent to a program as a single "command-line" string, and programs are responsible for parsing it into arguments. By default, empty arguments and arguments with spaces or tabs are quoted with double quotes `"` in the command line, and `\` or `"` are preceded by backslashes. `windows_verbatim=true` is useful for launching programs that parse their command line in nonstandard ways.) Has no effect on non-Windows systems.
- `windows_hide::Bool`: If `true` (defaults to `false`), then on Windows no new console window is displayed when the `Cmd` is executed. This has no effect if a console is already open or on non-Windows systems.
- `env`: Set environment variables to use when running the `Cmd`. `env` is either a dictionary mapping strings to strings, an array of strings of the form `"var=val"`, an array or tuple of `"var"=>val` pairs. In order to modify (rather than replace) the existing environment, initialize `env` with `copy(ENV)` and then set `env["var"]=val` as desired. To add to an environment block within a `Cmd` object without replacing all elements, use `addenv()` which will return a `Cmd` object with the updated environment.
- `dir::AbstractString`: Specify a working directory for the command (instead of the current directory).

For any keywords that are not specified, the current settings from `cmd` are used. Normally, to create a `Cmd` object in the first place, one uses backticks, e.g.

    Cmd(`echo "Hello world"`, ignorestatus=true, detach=false)

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`Base.setenv` — Function

    setenv(command::Cmd, env; dir)

Set environment variables to use when running the given `command`. `env` is either a dictionary mapping strings to strings, an array of strings of the form `"var=val"`, or zero or more `"var"=>val` pair arguments. In order to modify (rather than replace) the existing environment, create `env` through `copy(ENV)` and then setting `env["var"]=val` as desired, or use `addenv`.

The `dir` keyword argument can be used to specify a working directory for the command. `dir` defaults to the currently set `dir` for `command` (which is the current working directory if not specified already).

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`Base.withenv` — Function

    withenv(f::Function, kv::Pair...)

Execute `f` in an environment that is temporarily modified (not replaced as in `setenv`) by zero or more `"var"=>val` arguments `kv`. `withenv` is generally used via the `withenv(kv...) do ... end` syntax. A value of `nothing` can be used to temporarily unset an environment variable (if it is set). When `withenv` returns, the original environment has been restored.

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`Base.pipeline` — Method

    pipeline(from, to, ...)

Create a pipeline from a data source to a destination. The source and destination can be commands, I/O streams, strings, or results of other `pipeline` calls. At least one argument must be a command. Strings refer to filenames. When called with more than two arguments, they are chained together from left to right. For example, `pipeline(a,b,c)` is equivalent to `pipeline(pipeline(a,b),c)`. This provides a more concise way to specify multi-stage pipelines.

Examples:

    run(pipeline(`ls`, `grep xyz`))
    run(pipeline(`ls`, "out.txt"))
    run(pipeline("out.txt", `grep xyz`))

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`Base.pipeline` — Method

    pipeline(command; stdin, stdout, stderr, append=false)

Redirect I/O to or from the given `command`. Keyword arguments specify which of the command's streams should be redirected. `append` controls whether file output appends to the file. This is a more general version of the 2-argument `pipeline` function. `pipeline(from, to)` is equivalent to `pipeline(from, stdout=to)` when `from` is a command, and to `pipeline(to, stdin=from)` when `from` is another kind of data source.

Examples:

    run(pipeline(`dothings`, stdout="out.txt", stderr="errs.txt"))
    run(pipeline(`update`, stdout="log.txt", append=true))

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`Base.Libc.gethostname` — Function

    gethostname() -> AbstractString

Get the local machine's host name.

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`Base.Libc.getpid` — Function

    getpid() -> Int32

Get Julia's process ID.

source

    getpid(process) -> Int32

Get the child process ID, if it still exists.

Julia 1.1

This function requires at least Julia 1.1.

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`Base.Libc.time` — Method

    time()

Get the system time in seconds since the epoch, with fairly high (typically, microsecond) resolution.

source
`Base.time_ns` — Function

    time_ns()

Get the time in nanoseconds. The time corresponding to 0 is undefined, and wraps every 5.8 years.

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`Base.@time` — Macro

    @time

A macro to execute an expression, printing the time it took to execute, the number of allocations, and the total number of bytes its execution caused to be allocated, before returning the value of the expression. Any time spent garbage collecting (gc) or compiling is shown as a percentage.

In some cases the system will look inside the `@time` expression and compile some of the called code before execution of the top-level expression begins. When that happens, some compilation time will not be counted. To include this time you can run `@time @eval ...`.

See also `@timev`, `@timed`, `@elapsed`, and `@allocated`.

Note

For more serious benchmarking, consider the `@btime` macro from the BenchmarkTools.jl package which among other things evaluates the function multiple times in order to reduce noise.

    julia> x = rand(10,10);

    julia> @time x * x;
      0.606588 seconds (2.19 M allocations: 116.555 MiB, 3.75% gc time, 99.94% compilation time)

    julia> @time x * x;
      0.000009 seconds (1 allocation: 896 bytes)

    julia> @time begin
               sleep(0.3)
               1+1
           end
      0.301395 seconds (8 allocations: 336 bytes)
    2

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`Base.@timev` — Macro

    @timev

This is a verbose version of the `@time` macro. It first prints the same information as `@time`, then any non-zero memory allocation counters, and then returns the value of the expression.

See also `@time`, `@timed`, `@elapsed`, and `@allocated`.

    julia> x = rand(10,10);

    julia> @timev x * x;
      0.546770 seconds (2.20 M allocations: 116.632 MiB, 4.23% gc time, 99.94% compilation time)
    elapsed time (ns): 546769547
    gc time (ns):      23115606
    bytes allocated:   122297811
    pool allocs:       2197930
    non-pool GC allocs:1327
    malloc() calls:    36
    realloc() calls:   5
    GC pauses:         3

    julia> @timev x * x;
      0.000010 seconds (1 allocation: 896 bytes)
    elapsed time (ns): 9848
    bytes allocated:   896
    pool allocs:       1

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`Base.@timed` — Macro

    @timed

A macro to execute an expression, and return the value of the expression, elapsed time, total bytes allocated, garbage collection time, and an object with various memory allocation counters.

In some cases the system will look inside the `@timed` expression and compile some of the called code before execution of the top-level expression begins. When that happens, some compilation time will not be counted. To include this time you can run `@timed @eval ...`.

See also `@time`, `@timev`, `@elapsed`, and `@allocated`.

    julia> stats = @timed rand(10^6);

    julia> stats.time
    0.006634834

    julia> stats.bytes
    8000256

    julia> stats.gctime
    0.0055765

    julia> propertynames(stats.gcstats)
    (:allocd, :malloc, :realloc, :poolalloc, :bigalloc, :freecall, :total_time, :pause, :full_sweep)

    julia> stats.gcstats.total_time
    5576500

Julia 1.5

The return type of this macro was changed from `Tuple` to `NamedTuple` in Julia 1.5.

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`Base.@elapsed` — Macro

    @elapsed

A macro to evaluate an expression, discarding the resulting value, instead returning the number of seconds it took to execute as a floating-point number.

In some cases the system will look inside the `@elapsed` expression and compile some of the called code before execution of the top-level expression begins. When that happens, some compilation time will not be counted. To include this time you can run `@elapsed @eval ...`.

See also `@time`, `@timev`, `@timed`, and `@allocated`.

    julia> @elapsed sleep(0.3)
    0.301391426

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`Base.@allocated` — Macro

    @allocated

A macro to evaluate an expression, discarding the resulting value, instead returning the total number of bytes allocated during evaluation of the expression.

See also `@time`, `@timev`, `@timed`, and `@elapsed`.

    julia> @allocated rand(10^6)
    8000080

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`Base.EnvDict` — Type

    EnvDict() -> EnvDict

A singleton of this type provides a hash table interface to environment variables.

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`Base.ENV` — Constant

    ENV

Reference to the singleton `EnvDict`, providing a dictionary interface to system environment variables.

(On Windows, system environment variables are case-insensitive, and `ENV` correspondingly converts all keys to uppercase for display, iteration, and copying. Portable code should not rely on the ability to distinguish variables by case, and should beware that setting an ostensibly lowercase variable may result in an uppercase `ENV` key.)

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`Base.Sys.isunix` — Function

    Sys.isunix([os])

Predicate for testing if the OS provides a Unix-like interface. See documentation in Handling Operating System Variation.

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`Base.Sys.isapple` — Function

    Sys.isapple([os])

Predicate for testing if the OS is a derivative of Apple Macintosh OS X or Darwin. See documentation in Handling Operating System Variation.

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`Base.Sys.islinux` — Function

    Sys.islinux([os])

Predicate for testing if the OS is a derivative of Linux. See documentation in Handling Operating System Variation.

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`Base.Sys.isbsd` — Function

    Sys.isbsd([os])

Predicate for testing if the OS is a derivative of BSD. See documentation in Handling Operating System Variation.

Note

The Darwin kernel descends from BSD, which means that `Sys.isbsd()` is `true` on macOS systems. To exclude macOS from a predicate, use `Sys.isbsd() && !Sys.isapple()`.

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`Base.Sys.isfreebsd` — Function

    Sys.isfreebsd([os])

Predicate for testing if the OS is a derivative of FreeBSD. See documentation in Handling Operating System Variation.

Note

Not to be confused with `Sys.isbsd()`, which is `true` on FreeBSD but also on other BSD-based systems. `Sys.isfreebsd()` refers only to FreeBSD.

Julia 1.1

This function requires at least Julia 1.1.

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`Base.Sys.isopenbsd` — Function

    Sys.isopenbsd([os])

Predicate for testing if the OS is a derivative of OpenBSD. See documentation in Handling Operating System Variation.

Note

Not to be confused with `Sys.isbsd()`, which is `true` on OpenBSD but also on other BSD-based systems. `Sys.isopenbsd()` refers only to OpenBSD.

Julia 1.1

This function requires at least Julia 1.1.

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`Base.Sys.isnetbsd` — Function

    Sys.isnetbsd([os])

Predicate for testing if the OS is a derivative of NetBSD. See documentation in Handling Operating System Variation.

Note

Not to be confused with `Sys.isbsd()`, which is `true` on NetBSD but also on other BSD-based systems. `Sys.isnetbsd()` refers only to NetBSD.

Julia 1.1

This function requires at least Julia 1.1.

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`Base.Sys.isdragonfly` — Function

    Sys.isdragonfly([os])

Predicate for testing if the OS is a derivative of DragonFly BSD. See documentation in Handling Operating System Variation.

Note

Not to be confused with `Sys.isbsd()`, which is `true` on DragonFly but also on other BSD-based systems. `Sys.isdragonfly()` refers only to DragonFly.

Julia 1.1

This function requires at least Julia 1.1.

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`Base.Sys.iswindows` — Function

    Sys.iswindows([os])

Predicate for testing if the OS is a derivative of Microsoft Windows NT. See documentation in Handling Operating System Variation.

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`Base.Sys.windows_version` — Function

    Sys.windows_version()

Return the version number for the Windows NT Kernel as a `VersionNumber`, i.e. `v"major.minor.build"`, or `v"0.0.0"` if this is not running on Windows.

source
`Base.Sys.free_memory` — Function

    Sys.free_memory()

Get the total free memory in RAM in bytes.

source
`Base.Sys.total_memory` — Function

    Sys.total_memory()

Get the total memory in RAM (including that which is currently used) in bytes.

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`Base.@static` — Macro

    @static

Partially evaluate an expression at parse time.

For example, `@static Sys.iswindows() ? foo : bar` will evaluate `Sys.iswindows()` and insert either `foo` or `bar` into the expression. This is useful in cases where a construct would be invalid on other platforms, such as a `ccall` to a non-existent function. `@static if Sys.isapple() foo end` and `@static foo <&&,||> bar` are also valid syntax.

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## Versioning

`Base.VersionNumber` — Type

    VersionNumber

Version number type which follow the specifications of semantic versioning, composed of major, minor and patch numeric values, followed by pre-release and build alpha-numeric annotations. See also `@v_str`.

Examples

    julia> VersionNumber("1.2.3")
    v"1.2.3"

    julia> VersionNumber("2.0.1-rc1")
    v"2.0.1-rc1"

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`Base.@v_str` — Macro

    @v_str

String macro used to parse a string to a `VersionNumber`.

Examples

    julia> v"1.2.3"
    v"1.2.3"

    julia> v"2.0.1-rc1"
    v"2.0.1-rc1"

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## Errors

`Base.error` — Function

    error(message::AbstractString)

Raise an `ErrorException` with the given message.

source

    error(msg...)

Raise an `ErrorException` with the given message.

source
`Core.throw` — Function

    throw(e)

Throw an object as an exception.

source
`Base.rethrow` — Function

    rethrow()

Rethrow the current exception from within a `catch` block. The rethrown exception will continue propagation as if it had not been caught.

Note

The alternative form `rethrow(e)` allows you to associate an alternative exception object `e` with the current backtrace. However this misrepresents the program state at the time of the error so you're encouraged to instead throw a new exception using `throw(e)`. In Julia 1.1 and above, using `throw(e)` will preserve the root cause exception on the stack, as described in `catch_stack`.

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`Base.backtrace` — Function

    backtrace()

Get a backtrace object for the current program point.

source
`Base.catch_backtrace` — Function

    catch_backtrace()

Get the backtrace of the current exception, for use within `catch` blocks.

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`Base.catch_stack` — Function

    catch_stack(task=current_task(); [inclue_bt=true])

Get the stack of exceptions currently being handled. For nested catch blocks there may be more than one current exception in which case the most recently thrown exception is last in the stack. The stack is returned as a Vector of `(exception,backtrace)` pairs, or a Vector of exceptions if `include_bt` is false.

Explicitly passing `task` will return the current exception stack on an arbitrary task. This is useful for inspecting tasks which have failed due to uncaught exceptions.

Julia 1.1

This function is experimental in Julia 1.1 and will likely be renamed in a future release (see https://github.com/JuliaLang/julia/pull/29901).

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`Base.@assert` — Macro

    @assert cond [text]

Throw an `AssertionError` if `cond` is `false`. Preferred syntax for writing assertions. Message `text` is optionally displayed upon assertion failure.

Warning

An assert might be disabled at various optimization levels. Assert should therefore only be used as a debugging tool and not used for authentication verification (e.g., verifying passwords), nor should side effects needed for the function to work correctly be used inside of asserts.

Examples

    julia> @assert iseven(3) "3 is an odd number!"
    ERROR: AssertionError: 3 is an odd number!

    julia> @assert isodd(3) "What even are numbers?"

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`Base.Experimental.register_error_hint` — Function

    Experimental.register_error_hint(handler, exceptiontype)

Register a "hinting" function `handler(io, exception)` that can suggest potential ways for users to circumvent errors. `handler` should examine `exception` to see whether the conditions appropriate for a hint are met, and if so generate output to `io`. Packages should call `register_error_hint` from within their `__init__` function.

For specific exception types, `handler` is required to accept additional arguments:

- `MethodError`: provide `handler(io, exc::MethodError, argtypes, kwargs)`, which splits the combined arguments into positional and keyword arguments.

When issuing a hint, the output should typically start with `\n`.

If you define custom exception types, your `showerror` method can support hints by calling `Experimental.show_error_hints`.

Example

    julia> module Hinter

           only_int(x::Int)      = 1
           any_number(x::Number) = 2

           function __init__()
               Base.Experimental.register_error_hint(MethodError) do io, exc, argtypes, kwargs
                   if exc.f == only_int
                        # Color is not necessary, this is just to show it's possible.
                        print(io, "\nDid you mean to call ")
                        printstyled(io, "`any_number`?", color=:cyan)
                   end
               end
           end

           end

Then if you call `Hinter.only_int` on something that isn't an `Int` (thereby triggering a `MethodError`), it issues the hint:

    julia> Hinter.only_int(1.0)
    ERROR: MethodError: no method matching only_int(::Float64)
    Did you mean to call `any_number`?
    Closest candidates are:
        ...

Julia 1.5

Custom error hints are available as of Julia 1.5.

Warning

This interface is experimental and subject to change or removal without notice. To insulate yourself against changes, consider putting any registrations inside an `if isdefined(Base.Experimental, :register_error_hint) ... end` block.

source
`Base.Experimental.show_error_hints` — Function

    Experimental.show_error_hints(io, ex, args...)

Invoke all handlers from `Experimental.register_error_hint` for the particular exception type `typeof(ex)`. `args` must contain any other arguments expected by the handler for that type.

Julia 1.5

Custom error hints are available as of Julia 1.5.

Warning

This interface is experimental and subject to change or removal without notice.

source
`Core.ArgumentError` — Type

    ArgumentError(msg)

The parameters to a function call do not match a valid signature. Argument `msg` is a descriptive error string.

source
`Core.AssertionError` — Type

    AssertionError([msg])

The asserted condition did not evaluate to `true`. Optional argument `msg` is a descriptive error string.

Examples

    julia> @assert false "this is not true"
    ERROR: AssertionError: this is not true

`AssertionError` is usually thrown from `@assert`.

source
`Core.BoundsError` — Type

    BoundsError([a],[i])

An indexing operation into an array, `a`, tried to access an out-of-bounds element at index `i`.

Examples

    julia> A = fill(1.0, 7);

    julia> A[8]
    ERROR: BoundsError: attempt to access 7-element Vector{Float64} at index [8]

    julia> B = fill(1.0, (2,3));

    julia> B[2, 4]
    ERROR: BoundsError: attempt to access 2×3 Matrix{Float64} at index [2, 4]

    julia> B[9]
    ERROR: BoundsError: attempt to access 2×3 Matrix{Float64} at index [9]

source
`Base.CompositeException` — Type

    CompositeException

Wrap a `Vector` of exceptions thrown by a `Task` (e.g. generated from a remote worker over a channel or an asynchronously executing local I/O write or a remote worker under `pmap`) with information about the series of exceptions. For example, if a group of workers are executing several tasks, and multiple workers fail, the resulting `CompositeException` will contain a "bundle" of information from each worker indicating where and why the exception(s) occurred.

source
`Base.DimensionMismatch` — Type

    DimensionMismatch([msg])

The objects called do not have matching dimensionality. Optional argument `msg` is a descriptive error string.

source
`Core.DivideError` — Type

    DivideError()

Integer division was attempted with a denominator value of 0.

Examples

    julia> 2/0
    Inf

    julia> div(2, 0)
    ERROR: DivideError: integer division error
    Stacktrace:
    [...]

source
`Core.DomainError` — Type

    DomainError(val)
    DomainError(val, msg)

The argument `val` to a function or constructor is outside the valid domain.

Examples

    julia> sqrt(-1)
    ERROR: DomainError with -1.0:
    sqrt will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).
    Stacktrace:
    [...]

source
`Base.EOFError` — Type

    EOFError()

No more data was available to read from a file or stream.

source
`Core.ErrorException` — Type

    ErrorException(msg)

Generic error type. The error message, in the `.msg` field, may provide more specific details.

Examples

    julia> ex = ErrorException("I've done a bad thing");

    julia> ex.msg
    "I've done a bad thing"

source
`Core.InexactError` — Type

    InexactError(name::Symbol, T, val)

Cannot exactly convert `val` to type `T` in a method of function `name`.

Examples

    julia> convert(Float64, 1+2im)
    ERROR: InexactError: Float64(1 + 2im)
    Stacktrace:
    [...]

source
`Core.InterruptException` — Type

    InterruptException()

The process was stopped by a terminal interrupt (CTRL+C).

Note that, in Julia script started without `-i` (interactive) option, `InterruptException` is not thrown by default. Calling `Base.exit_on_sigint(false)` in the script can recover the behavior of the REPL. Alternatively, a Julia script can be started with

    julia -e "include(popfirst!(ARGS))" script.jl

to let `InterruptException` be thrown by CTRL+C during the execution.

source
`Base.KeyError` — Type

    KeyError(key)

An indexing operation into an `AbstractDict` (`Dict`) or `Set` like object tried to access or delete a non-existent element.

source
`Core.LoadError` — Type

    LoadError(file::AbstractString, line::Int, error)

An error occurred while `include`ing, `require`ing, or `using` a file. The error specifics should be available in the `.error` field.

source
`Core.MethodError` — Type

    MethodError(f, args)

A method with the required type signature does not exist in the given generic function. Alternatively, there is no unique most-specific method.

source
`Base.MissingException` — Type

    MissingException(msg)

Exception thrown when a `missing` value is encountered in a situation where it is not supported. The error message, in the `msg` field may provide more specific details.

source
`Core.OutOfMemoryError` — Type

    OutOfMemoryError()

An operation allocated too much memory for either the system or the garbage collector to handle properly.

source
`Core.ReadOnlyMemoryError` — Type

    ReadOnlyMemoryError()

An operation tried to write to memory that is read-only.

source
`Core.OverflowError` — Type

    OverflowError(msg)

The result of an expression is too large for the specified type and will cause a wraparound.

source
`Base.ProcessFailedException` — Type

    ProcessFailedException

Indicates problematic exit status of a process. When running commands or pipelines, this is thrown to indicate a nonzero exit code was returned (i.e. that the invoked process failed).

source
`Core.StackOverflowError` — Type

    StackOverflowError()

The function call grew beyond the size of the call stack. This usually happens when a call recurses infinitely.

source
`Base.SystemError` — Type

    SystemError(prefix::AbstractString, [errno::Int32])

A system call failed with an error code (in the `errno` global variable).

source
`Core.TypeError` — Type

    TypeError(func::Symbol, context::AbstractString, expected::Type, got)

A type assertion failure, or calling an intrinsic function with an incorrect argument type.

source
`Core.UndefKeywordError` — Type

    UndefKeywordError(var::Symbol)

The required keyword argument `var` was not assigned in a function call.

Examples

    julia> function my_func(;my_arg)
               return my_arg + 1
           end
    my_func (generic function with 1 method)

    julia> my_func()
    ERROR: UndefKeywordError: keyword argument my_arg not assigned
    Stacktrace:
     [1] my_func() at ./REPL[1]:2
     [2] top-level scope at REPL[2]:1

source
`Core.UndefRefError` — Type

    UndefRefError()

The item or field is not defined for the given object.

Examples

    julia> struct MyType
               a::Vector{Int}
               MyType() = new()
           end

    julia> A = MyType()
    MyType(#undef)

    julia> A.a
    ERROR: UndefRefError: access to undefined reference
    Stacktrace:
    [...]

source
`Core.UndefVarError` — Type

    UndefVarError(var::Symbol)

A symbol in the current scope is not defined.

Examples

    julia> a
    ERROR: UndefVarError: a not defined

    julia> a = 1;

    julia> a
    1

source
`Base.StringIndexError` — Type

    StringIndexError(str, i)

An error occurred when trying to access `str` at index `i` that is not valid.

source
`Core.InitError` — Type

    InitError(mod::Symbol, error)

An error occurred when running a module's `__init__` function. The actual error thrown is available in the `.error` field.

source
`Base.retry` — Function

    retry(f;  delays=ExponentialBackOff(), check=nothing) -> Function

Return an anonymous function that calls function `f`. If an exception arises, `f` is repeatedly called again, each time `check` returns `true`, after waiting the number of seconds specified in `delays`. `check` should input `delays`'s current state and the `Exception`.

Julia 1.2

Before Julia 1.2 this signature was restricted to `f::Function`.

Examples

    retry(f, delays=fill(5.0, 3))
    retry(f, delays=rand(5:10, 2))
    retry(f, delays=Base.ExponentialBackOff(n=3, first_delay=5, max_delay=1000))
    retry(http_get, check=(s,e)->e.status == "503")(url)
    retry(read, check=(s,e)->isa(e, IOError))(io, 128; all=false)

source
`Base.ExponentialBackOff` — Type

    ExponentialBackOff(; n=1, first_delay=0.05, max_delay=10.0, factor=5.0, jitter=0.1)

A `Float64` iterator of length `n` whose elements exponentially increase at a rate in the interval `factor` * (1 ± `jitter`). The first element is `first_delay` and all elements are clamped to `max_delay`.

source

## Events

`Base.Timer` — Method

    Timer(callback::Function, delay; interval = 0)

Create a timer that runs the function `callback` at each timer expiration.

Waiting tasks are woken and the function `callback` is called after an initial delay of `delay` seconds, and then repeating with the given `interval` in seconds. If `interval` is equal to `0`, the callback is only run once. The function `callback` is called with a single argument, the timer itself. Stop a timer by calling `close`. The `cb` may still be run one final time, if the timer has already expired.

Examples

Here the first number is printed after a delay of two seconds, then the following numbers are printed quickly.

    julia> begin
               i = 0
               cb(timer) = (global i += 1; println(i))
               t = Timer(cb, 2, interval=0.2)
               wait(t)
               sleep(0.5)
               close(t)
           end
    1
    2
    3

source
`Base.Timer` — Type

    Timer(delay; interval = 0)

Create a timer that wakes up tasks waiting for it (by calling `wait` on the timer object).

Waiting tasks are woken after an initial delay of at least `delay` seconds, and then repeating after at least `interval` seconds again elapse. If `interval` is equal to `0`, the timer is only triggered once. When the timer is closed (by `close`) waiting tasks are woken with an error. Use `isopen` to check whether a timer is still active.

Note: `interval` is subject to accumulating time skew. If you need precise events at a particular absolute time, create a new timer at each expiration with the difference to the next time computed.

source
`Base.AsyncCondition` — Type

    AsyncCondition()

Create a async condition that wakes up tasks waiting for it (by calling `wait` on the object) when notified from C by a call to `uv_async_send`. Waiting tasks are woken with an error when the object is closed (by `close`). Use `isopen` to check whether it is still active.

source
`Base.AsyncCondition` — Method

    AsyncCondition(callback::Function)

Create a async condition that calls the given `callback` function. The `callback` is passed one argument, the async condition object itself.

source

## Reflection

`Base.nameof` — Method

    nameof(m::Module) -> Symbol

Get the name of a `Module` as a `Symbol`.

Examples

    julia> nameof(Base.Broadcast)
    :Broadcast

source
`Base.parentmodule` — Function

    parentmodule(m::Module) -> Module

Get a module's enclosing `Module`. `Main` is its own parent.

Examples

    julia> parentmodule(Main)
    Main

    julia> parentmodule(Base.Broadcast)
    Base

source

    parentmodule(t::DataType) -> Module

Determine the module containing the definition of a (potentially `UnionAll`-wrapped) `DataType`.

Examples

    julia> module Foo
               struct Int end
           end
    Foo

    julia> parentmodule(Int)
    Core

    julia> parentmodule(Foo.Int)
    Foo

source

    parentmodule(f::Function) -> Module

Determine the module containing the (first) definition of a generic function.

source

    parentmodule(f::Function, types) -> Module

Determine the module containing a given definition of a generic function.

source
`Base.pathof` — Method

    pathof(m::Module)

Return the path of the `m.jl` file that was used to `import` module `m`, or `nothing` if `m` was not imported from a package.

Use `dirname` to get the directory part and `basename` to get the file name part of the path.

source
`Base.moduleroot` — Function

    moduleroot(m::Module) -> Module

Find the root module of a given module. This is the first module in the chain of parent modules of `m` which is either a registered root module or which is its own parent module.

source
`Base.@__MODULE__` — Macro

    @__MODULE__ -> Module

Get the `Module` of the toplevel eval, which is the `Module` code is currently being read from.

source
`Base.@__FILE__` — Macro

    @__FILE__ -> AbstractString

Expand to a string with the path to the file containing the macrocall, or an empty string if evaluated by `julia -e <expr>`. Return `nothing` if the macro was missing parser source information. Alternatively see `PROGRAM_FILE`.

source
`Base.@__DIR__` — Macro

    @__DIR__ -> AbstractString

Expand to a string with the absolute path to the directory of the file containing the macrocall. Return the current working directory if run from a REPL or if evaluated by `julia -e <expr>`.

source
`Base.@__LINE__` — Macro

    @__LINE__ -> Int

Expand to the line number of the location of the macrocall. Return `0` if the line number could not be determined.

source
`Base.fullname` — Function

    fullname(m::Module)

Get the fully-qualified name of a module as a tuple of symbols. For example,

Examples

    julia> fullname(Base.Iterators)
    (:Base, :Iterators)

    julia> fullname(Main)
    (:Main,)

source
`Base.names` — Function

    names(x::Module; all::Bool = false, imported::Bool = false)

Get an array of the names exported by a `Module`, excluding deprecated names. If `all` is true, then the list also includes non-exported names defined in the module, deprecated names, and compiler-generated names. If `imported` is true, then names explicitly imported from other modules are also included.

As a special case, all names defined in `Main` are considered "exported", since it is not idiomatic to explicitly export names from `Main`.

source
`Core.nfields` — Function

    nfields(x) -> Int

Get the number of fields in the given object.

Examples

    julia> a = 1//2;

    julia> nfields(a)
    2

    julia> b = 1
    1

    julia> nfields(b)
    0

    julia> ex = ErrorException("I've done a bad thing");

    julia> nfields(ex)
    1

In these examples, `a` is a `Rational`, which has two fields. `b` is an `Int`, which is a primitive bitstype with no fields at all. `ex` is an `ErrorException`, which has one field.

source
`Base.isconst` — Function

    isconst(m::Module, s::Symbol) -> Bool

Determine whether a global is declared `const` in a given `Module`.

source
`Base.nameof` — Method

    nameof(f::Function) -> Symbol

Get the name of a generic `Function` as a symbol. For anonymous functions, this is a compiler-generated name. For explicitly-declared subtypes of `Function`, it is the name of the function's type.

source
`Base.functionloc` — Method

    functionloc(f::Function, types)

Returns a tuple `(filename,line)` giving the location of a generic `Function` definition.

source
`Base.functionloc` — Method

    functionloc(m::Method)

Returns a tuple `(filename,line)` giving the location of a `Method` definition.

source

## Internals

`Base.GC.gc` — Function

    GC.gc([full=true])

Perform garbage collection. The argument `full` determines the kind of collection: A full collection (default) sweeps all objects, which makes the next GC scan much slower, while an incremental collection may only sweep so-called young objects.

Warning

Excessive use will likely lead to poor performance.

source
`Base.GC.enable` — Function

    GC.enable(on::Bool)

Control whether garbage collection is enabled using a boolean argument (`true` for enabled, `false` for disabled). Return previous GC state.

Warning

Disabling garbage collection should be used only with caution, as it can cause memory use to grow without bound.

source
`Base.GC.@preserve` — Macro

    GC.@preserve x1 x2 ... xn expr

Mark the objects `x1, x2, ...` as being in use during the evaluation of the expression `expr`. This is only required in unsafe code where `expr` implicitly uses memory or other resources owned by one of the `x`s.

Implicit use of `x` covers any indirect use of resources logically owned by `x` which the compiler cannot see. Some examples:

- Accessing memory of an object directly via a `Ptr`
- Passing a pointer to `x` to `ccall`
- Using resources of `x` which would be cleaned up in the finalizer.

`@preserve` should generally not have any performance impact in typical use cases where it briefly extends object lifetime. In implementation, `@preserve` has effects such as protecting dynamically allocated objects from garbage collection.

Examples

When loading from a pointer with `unsafe_load`, the underlying object is implicitly used, for example `x` is implicitly used by `unsafe_load(p)` in the following:

    julia> let
               x = Ref{Int}(101)
               p = Base.unsafe_convert(Ptr{Int}, x)
               GC.@preserve x unsafe_load(p)
           end
    101

When passing pointers to `ccall`, the pointed-to object is implicitly used and should be preserved. (Note however that you should normally just pass `x` directly to `ccall` which counts as an explicit use.)

    julia> let
               x = "Hello"
               p = pointer(x)
               Int(GC.@preserve x @ccall strlen(p::Cstring)::Csize_t)
               # Preferred alternative
               Int(@ccall strlen(x::Cstring)::Csize_t)
           end
    5

source
`Base.GC.safepoint` — Function

    GC.safepoint()

Inserts a point in the program where garbage collection may run. This can be useful in rare cases in multi-threaded programs where some threads are allocating memory (and hence may need to run GC) but other threads are doing only simple operations (no allocation, task switches, or I/O). Calling this function periodically in non-allocating threads allows garbage collection to run.

Julia 1.4

This function is available as of Julia 1.4.

source
`Base.Meta.lower` — Function

    lower(m, x)

Takes the expression `x` and returns an equivalent expression in lowered form for executing in module `m`. See also `code_lowered`.

source
`Base.Meta.@lower` — Macro

    @lower [m] x

Return lowered form of the expression `x` in module `m`. By default `m` is the module in which the macro is called. See also `lower`.

source
`Base.Meta.parse` — Method

    parse(str, start; greedy=true, raise=true, depwarn=true)

Parse the expression string and return an expression (which could later be passed to eval for execution). `start` is the index of the first character to start parsing. If `greedy` is `true` (default), `parse` will try to consume as much input as it can; otherwise, it will stop as soon as it has parsed a valid expression. Incomplete but otherwise syntactically valid expressions will return `Expr(:incomplete, "(error message)")`. If `raise` is `true` (default), syntax errors other than incomplete expressions will raise an error. If `raise` is `false`, `parse` will return an expression that will raise an error upon evaluation. If `depwarn` is `false`, deprecation warnings will be suppressed.

    julia> Meta.parse("x = 3, y = 5", 7)
    (:(y = 5), 13)

    julia> Meta.parse("x = 3, y = 5", 5)
    (:((3, y) = 5), 13)

source
`Base.Meta.parse` — Method

    parse(str; raise=true, depwarn=true)

Parse the expression string greedily, returning a single expression. An error is thrown if there are additional characters after the first expression. If `raise` is `true` (default), syntax errors will raise an error; otherwise, `parse` will return an expression that will raise an error upon evaluation. If `depwarn` is `false`, deprecation warnings will be suppressed.

    julia> Meta.parse("x = 3")
    :(x = 3)

    julia> Meta.parse("x = ")
    :($(Expr(:incomplete, "incomplete: premature end of input")))

    julia> Meta.parse("1.0.2")
    ERROR: Base.Meta.ParseError("invalid numeric constant \"1.0.\"")
    Stacktrace:
    [...]

    julia> Meta.parse("1.0.2"; raise = false)
    :($(Expr(:error, "invalid numeric constant \"1.0.\"")))

source
`Base.Meta.ParseError` — Type

    ParseError(msg)

The expression passed to the `parse` function could not be interpreted as a valid Julia expression.

source
`Core.QuoteNode` — Type

    QuoteNode

A quoted piece of code, that does not support interpolation. See the manual section about QuoteNodes for details.

source
`Base.macroexpand` — Function

    macroexpand(m::Module, x; recursive=true)

Take the expression `x` and return an equivalent expression with all macros removed (expanded) for executing in module `m`. The `recursive` keyword controls whether deeper levels of nested macros are also expanded. This is demonstrated in the example below:

    julia> module M
               macro m1()
                   42
               end
               macro m2()
                   :(@m1())
               end
           end
    M

    julia> macroexpand(M, :(@m2()), recursive=true)
    42

    julia> macroexpand(M, :(@m2()), recursive=false)
    :(#= REPL[16]:6 =# M.@m1)

source
`Base.@macroexpand` — Macro

    @macroexpand

Return equivalent expression with all macros removed (expanded).

There are differences between `@macroexpand` and `macroexpand`.

- While `macroexpand` takes a keyword argument `recursive`, `@macroexpand` is always recursive. For a non recursive macro version, see `@macroexpand1`.

- While `macroexpand` has an explicit `module` argument, `@macroexpand` always expands with respect to the module in which it is called.

This is best seen in the following example:

    julia> module M
               macro m()
                   1
               end
               function f()
                   (@macroexpand(@m),
                    macroexpand(M, :(@m)),
                    macroexpand(Main, :(@m))
                   )
               end
           end
    M

    julia> macro m()
               2
           end
    @m (macro with 1 method)

    julia> M.f()
    (1, 1, 2)

With `@macroexpand` the expression expands where `@macroexpand` appears in the code (module `M` in the example). With `macroexpand` the expression expands in the module given as the first argument.

source
`Base.@macroexpand1` — Macro

    @macroexpand1

Non recursive version of `@macroexpand`.

source
`Base.code_lowered` — Function

    code_lowered(f, types; generated=true, debuginfo=:default)

Return an array of the lowered forms (IR) for the methods matching the given generic function and type signature.

If `generated` is `false`, the returned `CodeInfo` instances will correspond to fallback implementations. An error is thrown if no fallback implementation exists. If `generated` is `true`, these `CodeInfo` instances will correspond to the method bodies yielded by expanding the generators.

The keyword `debuginfo` controls the amount of code metadata present in the output.

Note that an error will be thrown if `types` are not leaf types when `generated` is `true` and any of the corresponding methods are an `@generated` method.

source
`Base.code_typed` — Function

    code_typed(f, types; optimize=true, debuginfo=:default)

Returns an array of type-inferred lowered form (IR) for the methods matching the given generic function and type signature. The keyword argument `optimize` controls whether additional optimizations, such as inlining, are also applied. The keyword `debuginfo` controls the amount of code metadata present in the output, possible options are `:source` or `:none`.

source
`Base.precompile` — Function

    precompile(f, args::Tuple{Vararg{Any}})

Compile the given function `f` for the argument tuple (of types) `args`, but do not execute it.

source

## Meta

`Base.Meta.quot` — Function

    Meta.quot(ex)::Expr

Quote expression `ex` to produce an expression with head `quote`. This can for instance be used to represent objects of type `Expr` in the AST. See also the manual section about QuoteNode.

Examples

    julia> eval(Meta.quot(:x))
    :x

    julia> dump(Meta.quot(:x))
    Expr
      head: Symbol quote
      args: Array{Any}((1,))
        1: Symbol x

    julia> eval(Meta.quot(:(1+2)))
    :(1 + 2)

source
`Base.Meta.isexpr` — Function

    Meta.isexpr(ex, head[, n])::Bool

Return true if `ex` is an `Expr` with the given type `head` and optionally that the argument list is of length `n`. `head` may be a `Symbol` or collection of `Symbol`s. For example, to check that a macro was passed a function call expression, you might use `isexpr(ex, :call)`.

Examples

    julia> ex = :(f(x))
    :(f(x))

    julia> Meta.isexpr(ex, :block)
    false

    julia> Meta.isexpr(ex, :call)
    true

    julia> Meta.isexpr(ex, [:block, :call]) # multiple possible heads
    true

    julia> Meta.isexpr(ex, :call, 1)
    false

    julia> Meta.isexpr(ex, :call, 2)
    true

source
`Base.isidentifier` — Function

     isidentifier(s) -> Bool

Return whether the symbol or string `s` contains characters that are parsed as a valid identifier in Julia code.

Internally Julia allows any sequence of characters in a `Symbol` (except `\0`s), and macros automatically use variable names containing `#` in order to avoid naming collision with the surrounding code. In order for the parser to recognize a variable, it uses a limited set of characters (greatly extended by Unicode). `isidentifier()` makes it possible to query the parser directly whether a symbol contains valid characters.

Examples

    julia> Meta.isidentifier(:x), Meta.isidentifier("1x")
    (true, false)

source
`Base.isoperator` — Function

    isoperator(s::Symbol)

Return `true` if the symbol can be used as an operator, `false` otherwise.

Examples

    julia> Meta.isoperator(:+), Meta.isoperator(:f)
    (true, false)

source
`Base.isunaryoperator` — Function

    isunaryoperator(s::Symbol)

Return `true` if the symbol can be used as a unary (prefix) operator, `false` otherwise.

Examples

    julia> Meta.isunaryoperator(:-), Meta.isunaryoperator(:√), Meta.isunaryoperator(:f)
    (true, true, false)

source
`Base.isbinaryoperator` — Function

    isbinaryoperator(s::Symbol)

Return `true` if the symbol can be used as a binary (infix) operator, `false` otherwise.

Examples

    julia> Meta.isbinaryoperator(:-), Meta.isbinaryoperator(:√), Meta.isbinaryoperator(:f)
    (true, false, false)

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`Base.Meta.show_sexpr` — Function

    Meta.show_sexpr([io::IO,], ex)

Show expression `ex` as a lisp style S-expression.

Examples

    julia> Meta.show_sexpr(:(f(x, g(y,z))))
    (:call, :f, :x, (:call, :g, :y, :z))

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Theme

This document was generated with Documenter.jl version 0.27.10 on Tuesday 29 March 2022. Using Julia version 1.6.6.