Julia 中文文档

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Julia 元编程

# Metaprogramming

The strongest legacy of Lisp in the Julia language is its metaprogramming support. Like Lisp, Julia represents its own code as a data structure of the language itself. Since code is represented by objects that can be created and manipulated from within the language, it is possible for a program to transform and generate its own code. This allows sophisticated code generation without extra build steps, and also allows true Lisp-style macros operating at the level of abstract syntax trees. In contrast, preprocessor "macro" systems, like that of C and C++, perform textual manipulation and substitution before any actual parsing or interpretation occurs. Because all data types and code in Julia are represented by Julia data structures, powerful reflection capabilities are available to explore the internals of a program and its types just like any other data.

# Program representation

Every Julia program starts life as a string:

julia> prog = "1 + 1"
"1 + 1"

What happens next?

The next step is to parse each string
into an object called an expression, represented by the Julia type Expr:

julia> ex1 = Meta.parse(prog)
:(1 + 1)

julia> typeof(ex1)

Expr objects contain two parts:

  • a Symbol identifying the kind of expression. A symbol is an interned string
    identifier (more discussion below).
julia> ex1.head
  • the expression arguments, which may be symbols, other expressions, or literal values:
julia> ex1.args
3-element Array{Any,1}:

Expressions may also be constructed directly in prefix notation:

julia> ex2 = Expr(:call, :+, 1, 1)
:(1 + 1)

The two expressions constructed above – by parsing and by direct construction – are equivalent:

julia> ex1 == ex2

The key point here is that Julia code is internally represented as a data structure that is accessible
from the language itself.

The dump function provides indented and annotated display of Expr objects:

julia> dump(ex2)
  head: Symbol call
  args: Array{Any}((3,))
    1: Symbol +
    2: Int64 1
    3: Int64 1

Expr objects may also be nested:

julia> ex3 = Meta.parse("(4 + 4) / 2")
:((4 + 4) / 2)

Another way to view expressions is with Meta.show_sexpr, which displays the S-expression
form of a given Expr, which may look very familiar to users of Lisp. Here's an example illustrating
the display on a nested Expr:

julia> Meta.show_sexpr(ex3)
(:call, :/, (:call, :+, 4, 4), 2)

# Symbols

The : character has two syntactic purposes in Julia. The first form creates a Symbol,
an interned string used as one building-block
of expressions:

julia> :foo

julia> typeof(ans)

The Symbol constructor takes any number of arguments and creates a new symbol by concatenating
their string representations together:

julia> :foo == Symbol("foo")

julia> Symbol("func",10)

julia> Symbol(:var,'_',"sym")

In the context of an expression, symbols are used to indicate access to variables; when an expression
is evaluated, a symbol is replaced with the value bound to that symbol in the appropriate [scope](@ref scope-of-variables).

Sometimes extra parentheses around the argument to : are needed to avoid ambiguity in parsing.:

julia> :(:)

julia> :(::)

# Expressions and evaluation

# Quoting

The second syntactic purpose of the : character is to create expression objects without using
the explicit Expr constructor. This is referred to as quoting. The : character, followed
by paired parentheses around a single statement of Julia code, produces an Expr object based
on the enclosed code. Here is example of the short form used to quote an arithmetic expression:

julia> ex = :(a+b*c+1)
:(a + b * c + 1)

julia> typeof(ex)

(to view the structure of this expression, try ex.head and ex.args, or use dump
as above or Meta.@dump)

Note that equivalent expressions may be constructed using Meta.parse or the direct Expr

julia>      :(a + b*c + 1)       ==
       Meta.parse("a + b*c + 1") ==
       Expr(:call, :+, :a, Expr(:call, :*, :b, :c), 1)

Expressions provided by the parser generally only have symbols, other expressions, and literal
values as their args, whereas expressions constructed by Julia code can have arbitrary run-time
values without literal forms as args. In this specific example, + and a are symbols, *(b,c)
is a subexpression, and 1 is a literal 64-bit signed integer.

There is a second syntactic form of quoting for multiple expressions: blocks of code enclosed
in quote ... end.

julia> ex = quote
           x = 1
           y = 2
           x + y
    #= none:2 =#
    x = 1
    #= none:3 =#
    y = 2
    #= none:4 =#
    x + y

julia> typeof(ex)

# Interpolation

Direct construction of Expr objects with value arguments is powerful, but Expr constructors
can be tedious compared to "normal" Julia syntax. As an alternative, Julia allows interpolation of
literals or expressions into quoted expressions. Interpolation is indicated by a prefix $.

In this example, the value of variable a is interpolated:

julia> a = 1;

julia> ex = :($a + b)
:(1 + b)

Interpolating into an unquoted expression is not supported and will cause a compile-time error:

julia> $a + b
ERROR: syntax: "$" expression outside quote

In this example, the tuple (1,2,3) is interpolated as an expression into a conditional test:

julia> ex = :(a in $:((1,2,3)) )
:(a in (1, 2, 3))

The use of $ for expression interpolation is intentionally reminiscent of [string interpolation](@ref string-interpolation)
and [command interpolation](@ref command-interpolation). Expression interpolation allows convenient, readable programmatic
construction of complex Julia expressions.

# Splatting interpolation

Notice that the $ interpolation syntax allows inserting only a single expression into an
enclosing expression.
Occasionally, you have an array of expressions and need them all to become arguments of
the surrounding expression.
This can be done with the syntax $(xs...).
For example, the following code generates a function call where the number of arguments is
determined programmatically:

julia> args = [:x, :y, :z];

julia> :(f(1, $(args...)))
:(f(1, x, y, z))

# Nested quote

Naturally, it is possible for quote expressions to contain other quote expressions.
Understanding how interpolation works in these cases can be a bit tricky.
Consider this example:

julia> x = :(1 + 2);

julia> e = quote quote $x end end
    #= none:1 =#
    $(Expr(:quote, quote
    #= none:1 =#
    $(Expr(:$, :x))

Notice that the result contains Expr(:$, :x), which means that x has not been
evaluated yet.
In other words, the $ expression "belongs to" the inner quote expression, and
so its argument is only evaluated when the inner quote expression is:

julia> eval(e)
    #= none:1 =#
    1 + 2

However, the outer quote expression is able to interpolate values inside the $
in the inner quote.
This is done with multiple $s:

julia> e = quote quote $$x end end
    #= none:1 =#
    $(Expr(:quote, quote
    #= none:1 =#
    $(Expr(:$, :(1 + 2)))

Notice that :(1 + 2) now appears in the result instead of the symbol :x.
Evaluating this expression yields an interpolated 3:

julia> eval(e)
    #= none:1 =#

The intuition behind this behavior is that x is evaluated once for each $:
one $ works similarly to eval(:x), giving x's value, while two $s do the
equivalent of eval(eval(:x)).

# QuoteNode

The usual representation of a quote form in an AST is an Expr with head :quote:

julia> dump(Meta.parse(":(1+2)"))
  head: Symbol quote
  args: Array{Any}((1,))
    1: Expr
      head: Symbol call
      args: Array{Any}((3,))
        1: Symbol +
        2: Int64 1
        3: Int64 2

As we have seen, such expressions support interpolation with $.
However, in some situations it is necessary to quote code without performing interpolation.
This kind of quoting does not yet have syntax, but is represented internally
as an object of type QuoteNode.
The parser yields QuoteNodes for simple quoted items like symbols:

julia> dump(Meta.parse(":x"))
  value: Symbol x

QuoteNode can also be used for certain advanced metaprogramming tasks.

# eval and effects

Given an expression object, one can cause Julia to evaluate (execute) it at global scope using

julia> :(1 + 2)
:(1 + 2)

julia> eval(ans)

julia> ex = :(a + b)
:(a + b)

julia> eval(ex)
ERROR: UndefVarError: b not defined

julia> a = 1; b = 2;

julia> eval(ex)

Every [module](@ref modules) has its own eval function that evaluates expressions in its global
scope. Expressions passed to eval are not limited to returning values -- they can
also have side-effects that alter the state of the enclosing module's environment:

julia> ex = :(x = 1)
:(x = 1)

julia> x
ERROR: UndefVarError: x not defined

julia> eval(ex)

julia> x

Here, the evaluation of an expression object causes a value to be assigned to the global variable

Since expressions are just Expr objects which can be constructed programmatically and then evaluated,
it is possible to dynamically generate arbitrary code which can then be run using eval.
Here is a simple example:

julia> a = 1;

julia> ex = Expr(:call, :+, a, :b)
:(1 + b)

julia> a = 0; b = 2;

julia> eval(ex)

The value of a is used to construct the expression ex which applies the + function to the
value 1 and the variable b. Note the important distinction between the way a and b are used:

  • The value of the variable a at expression construction time is used as an immediate value in
    the expression. Thus, the value of a when the expression is evaluated no longer matters: the
    value in the expression is already 1, independent of whatever the value of a might be.
  • On the other hand, the symbol :b is used in the expression construction, so the value of the
    variable b at that time is irrelevant -- :b is just a symbol and the variable b need not
    even be defined. At expression evaluation time, however, the value of the symbol :b is resolved
    by looking up the value of the variable b.

# Functions on Expressions

As hinted above, one extremely useful feature of Julia is the capability to generate and manipulate
Julia code within Julia itself. We have already seen one example of a function returning Expr
objects: the parse function, which takes a string of Julia code and returns the corresponding
Expr. A function can also take one or more Expr objects as arguments, and return another
Expr. Here is a simple, motivating example:

julia> function math_expr(op, op1, op2)
           expr = Expr(:call, op, op1, op2)
           return expr
math_expr (generic function with 1 method)

julia>  ex = math_expr(:+, 1, Expr(:call, :*, 4, 5))
:(1 + 4 * 5)

julia> eval(ex)

As another example, here is a function that doubles any numeric argument, but leaves expressions

julia> function make_expr2(op, opr1, opr2)
           opr1f, opr2f = map(x -> isa(x, Number) ? 2*x : x, (opr1, opr2))
           retexpr = Expr(:call, op, opr1f, opr2f)
           return retexpr
make_expr2 (generic function with 1 method)

julia> make_expr2(:+, 1, 2)
:(2 + 4)

julia> ex = make_expr2(:+, 1, Expr(:call, :*, 5, 8))
:(2 + 5 * 8)

julia> eval(ex)

# [Macros](@id man-macros)

Macros provide a method to include generated code in the final body of a program. A macro maps
a tuple of arguments to a returned expression, and the resulting expression is compiled directly
rather than requiring a runtime eval call. Macro arguments may include expressions,
literal values, and symbols.

# Basics

Here is an extraordinarily simple macro:

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

Macros have a dedicated character in Julia's syntax: the @ (at-sign), followed by the unique
name declared in a macro NAME ... end block. In this example, the compiler will replace all
instances of @sayhello with:

:( println("Hello, world!") )

When @sayhello is entered in the REPL, the expression executes immediately, thus we only see the
evaluation result:

julia> @sayhello()
Hello, world!

Now, consider a slightly more complex macro:

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

This macro takes one argument: name. When @sayhello is encountered, the quoted expression
is expanded to interpolate the value of the argument into the final expression:

julia> @sayhello("human")
Hello, human

We can view the quoted return expression using the function macroexpand (important note:
this is an extremely useful tool for debugging macros):

julia> ex = macroexpand(Main, :(@sayhello("human")) )
:((Main.println)("Hello, ", "human"))

julia> typeof(ex)

We can see that the "human" literal has been interpolated into the expression.

There also exists a macro @macroexpand that is perhaps a bit more convenient than the macroexpand function:

julia> @macroexpand @sayhello "human"
:((println)("Hello, ", "human"))

# Hold up: why macros?

We have already seen a function f(::Expr...) -> Expr in a previous section. In fact, macroexpand
is also such a function. So, why do macros exist?

Macros are necessary because they execute when code is parsed, therefore, macros allow the programmer
to generate and include fragments of customized code before the full program is run. To illustrate
the difference, consider the following example:

julia> macro twostep(arg)
           println("I execute at parse time. The argument is: ", arg)
           return :(println("I execute at runtime. The argument is: ", $arg))
@twostep (macro with 1 method)

julia> ex = macroexpand(Main, :(@twostep :(1, 2, 3)) );
I execute at parse time. The argument is: $(Expr(:quote, :((1, 2, 3))))

The first call to println is executed when macroexpand is called. The
resulting expression contains only the second println:

julia> typeof(ex)

julia> ex
:((println)("I execute at runtime. The argument is: ", $(Expr(:copyast, :($(QuoteNode(:((1, 2, 3)))))))))

julia> eval(ex)
I execute at runtime. The argument is: (1, 2, 3)

# Macro invocation

Macros are invoked with the following general syntax:

@name expr1 expr2 ...
@name(expr1, expr2, ...)

Note the distinguishing @ before the macro name and the lack of commas between the argument
expressions in the first form, and the lack of whitespace after @name in the second form. The
two styles should not be mixed. For example, the following syntax is different from the examples
above; it passes the tuple (expr1, expr2, ...) as one argument to the macro:

@name (expr1, expr2, ...)

An alternative way to invoke a macro over an array literal (or comprehension) is to juxtapose both without using parentheses. In this case, the array will be the only expression fed to the macro. The following syntax is equivalent (and different from @name [a b] * v):

@name[a b] * v
@name([a b]) * v

It is important to emphasize that macros receive their arguments as expressions, literals, or
symbols. One way to explore macro arguments is to call the show function within the
macro body:

julia> macro showarg(x)
           # ... remainder of macro, returning an expression
@showarg (macro with 1 method)

julia> @showarg(a)

julia> @showarg(1+1)
:(1 + 1)

julia> @showarg(println("Yo!"))

In addition to the given argument list, every macro is passed extra arguments named __source__ and __module__.

The argument __source__ provides information (in the form of a LineNumberNode object) about the parser location
of the @ sign from the macro invocation.
This allows macros to include better error diagnostic information,
and is commonly used by logging, string-parser macros, and docs, for example,
as well as to implement the @__LINE__, @__FILE__, and @__DIR__ macros.

The location information can be accessed by referencing __source__.line and __source__.file:

julia> macro __LOCATION__(); return QuoteNode(__source__); end
@__LOCATION__ (macro with 1 method)

julia> dump(
  line: Int64 2
  file: Symbol none

The argument __module__ provides information (in the form of a Module object)
about the expansion context of the macro invocation.
This allows macros to look up contextual information, such as existing bindings,
or to insert the value as an extra argument to a runtime function call doing self-reflection
in the current module.

# Building an advanced macro

Here is a simplified definition of Julia's @assert macro:

julia> macro assert(ex)
           return :( $ex ? nothing : throw(AssertionError($(string(ex)))) )
@assert (macro with 1 method)

This macro can be used like this:

julia> @assert 1 == 1.0

julia> @assert 1 == 0
ERROR: AssertionError: 1 == 0

In place of the written syntax, the macro call is expanded at parse time to its returned result.
This is equivalent to writing:

1 == 1.0 ? nothing : throw(AssertionError("1 == 1.0"))
1 == 0 ? nothing : throw(AssertionError("1 == 0"))

That is, in the first call, the expression :(1 == 1.0) is spliced into the test condition slot,
while the value of string(:(1 == 1.0)) is spliced into the assertion message slot. The entire
expression, thus constructed, is placed into the syntax tree where the @assert macro call occurs.
Then at execution time, if the test expression evaluates to true, then nothing is returned,
whereas if the test is false, an error is raised indicating the asserted expression that was false.
Notice that it would not be possible to write this as a function, since only the value of the
condition is available and it would be impossible to display the expression that computed it in
the error message.

The actual definition of @assert in Julia Base is more complicated. It allows the
user to optionally specify their own error message, instead of just printing the failed expression.
Just like in functions with a variable number of arguments, this is specified with an ellipses
following the last argument:

julia> macro assert(ex, msgs...)
           msg_body = isempty(msgs) ? ex : msgs[1]
           msg = string(msg_body)
           return :($ex ? nothing : throw(AssertionError($msg)))
@assert (macro with 1 method)

Now @assert has two modes of operation, depending upon the number of arguments it receives!
If there's only one argument, the tuple of expressions captured by msgs will be empty and it
will behave the same as the simpler definition above. But now if the user specifies a second argument,
it is printed in the message body instead of the failing expression. You can inspect the result
of a macro expansion with the aptly named @macroexpand macro:

julia> @macroexpand @assert a == b
:(if Main.a == Main.b
        (Main.throw)((Main.AssertionError)("a == b"))

julia> @macroexpand @assert a==b "a should equal b!"
:(if Main.a == Main.b
        (Main.throw)((Main.AssertionError)("a should equal b!"))

There is yet another case that the actual @assert macro handles: what if, in addition to printing
"a should equal b," we wanted to print their values? One might naively try to use string interpolation
in the custom message, e.g., @assert a==b "a ($a) should equal b ($b)!", but this won't work
as expected with the above macro. Can you see why? Recall from [string interpolation](@ref string-interpolation) that
an interpolated string is rewritten to a call to string. Compare:

julia> typeof(:("a should equal b"))

julia> typeof(:("a ($a) should equal b ($b)!"))

julia> dump(:("a ($a) should equal b ($b)!"))
  head: Symbol string
  args: Array{Any}((5,))
    1: String "a ("
    2: Symbol a
    3: String ") should equal b ("
    4: Symbol b
    5: String ")!"

So now instead of getting a plain string in msg_body, the macro is receiving a full expression
that will need to be evaluated in order to display as expected. This can be spliced directly into
the returned expression as an argument to the string call; see error.jl
for the complete implementation.

The @assert macro makes great use of splicing into quoted expressions to simplify the manipulation
of expressions inside the macro body.

# Hygiene

An issue that arises in more complex macros is that of hygiene.
In short, macros must ensure that the variables they introduce in their returned expressions do
not accidentally clash with existing variables in the surrounding code they expand into. Conversely,
the expressions that are passed into a macro as arguments are often expected to evaluate in
the context of the surrounding code, interacting with and modifying the existing variables. Another
concern arises from the fact that a macro may be called in a different module from where it was
defined. In this case we need to ensure that all global variables are resolved to the correct
module. Julia already has a major advantage over languages with textual macro expansion (like
C) in that it only needs to consider the returned expression. All the other variables (such as
msg in @assert above) follow the [normal scoping block behavior](@ref scope-of-variables).

To demonstrate these issues, let us consider writing a @time macro that takes an expression
as its argument, records the time, evaluates the expression, records the time again, prints the
difference between the before and after times, and then has the value of the expression as its
final value. The macro might look like this:

macro time(ex)
    return quote
        local t0 = time()
        local val = $ex
        local t1 = time()
        println("elapsed time: ", t1-t0, " seconds")

Here, we want t0, t1, and val to be private temporary variables, and we want time to refer
to the time function in Julia Base, not to any time variable the user
might have (the same applies to println). Imagine the problems that could occur if the user
expression ex also contained assignments to a variable called t0, or defined its own time
variable. We might get errors, or mysteriously incorrect behavior.

Julia's macro expander solves these problems in the following way. First, variables within a macro
result are classified as either local or global. A variable is considered local if it is assigned
to (and not declared global), declared local, or used as a function argument name. Otherwise,
it is considered global. Local variables are then renamed to be unique (using the gensym
function, which generates new symbols), and global variables are resolved within the macro definition
environment. Therefore both of the above concerns are handled; the macro's locals will not conflict
with any user variables, and time and println will refer to the Julia Base definitions.

One problem remains however. Consider the following use of this macro:

module MyModule
import Base.@time

time() = ... # compute something

@time time()

Here the user expression ex is a call to time, but not the same time function that the macro
uses. It clearly refers to MyModule.time. Therefore we must arrange for the code in ex to
be resolved in the macro call environment. This is done by "escaping" the expression with esc:

macro time(ex)
    local val = $(esc(ex))

An expression wrapped in this manner is left alone by the macro expander and simply pasted into
the output verbatim. Therefore it will be resolved in the macro call environment.

This escaping mechanism can be used to "violate" hygiene when necessary, in order to introduce
or manipulate user variables. For example, the following macro sets x to zero in the call environment:

julia> macro zerox()
           return esc(:(x = 0))
@zerox (macro with 1 method)

julia> function foo()
           x = 1
           return x # is zero
foo (generic function with 1 method)

julia> foo()

This kind of manipulation of variables should be used judiciously, but is occasionally quite handy.

Getting the hygiene rules correct can be a formidable challenge.
Before using a macro, you might want to consider whether a function closure
would be sufficient. Another useful strategy is to defer as much work as possible to runtime.
For example, many macros simply wrap their arguments in a QuoteNode or other similar Expr.
Some examples of this include @task body which simply returns schedule(Task(() -> $body)),
and @eval expr, which simply returns eval(QuoteNode(expr)).

To demonstrate, we might rewrite the @time example above as:

macro time(expr)
    return :(timeit(() -> $(esc(expr))))
function timeit(f)
    t0 = time()
    val = f()
    t1 = time()
    println("elapsed time: ", t1-t0, " seconds")
    return val

However, we don't do this for a good reason: wrapping the expr in a new scope block (the anonymous function)
also slightly changes the meaning of the expression (the scope of any variables in it),
while we want @time to be usable with minimum impact on the wrapped code.

# Macros and dispatch

Macros, just like Julia functions, are generic. This means they can also have multiple method definitions, thanks to multiple dispatch:

julia> macro m end
@m (macro with 0 methods)

julia> macro m(args...)
           println("$(length(args)) arguments")
@m (macro with 1 method)

julia> macro m(x,y)
           println("Two arguments")
@m (macro with 2 methods)

julia> @m "asd"
1 arguments

julia> @m 1 2
Two arguments

However one should keep in mind, that macro dispatch is based on the types of AST
that are handed to the macro, not the types that the AST evaluates to at runtime:

julia> macro m(::Int)
           println("An Integer")
@m (macro with 3 methods)

julia> @m 2
An Integer

julia> x = 2

julia> @m x
1 arguments

# Code Generation

When a significant amount of repetitive boilerplate code is required, it is common to generate
it programmatically to avoid redundancy. In most languages, this requires an extra build step,
and a separate program to generate the repetitive code. In Julia, expression interpolation and
eval allow such code generation to take place in the normal course of program execution.
For example, consider the following custom type

struct MyNumber
# output

for which we want to add a number of methods to. We can do this programmatically in the
following loop:

for op = (:sin, :cos, :tan, :log, :exp)
        Base.$op(a::MyNumber) = MyNumber($op(a.x))
# output

and we can now use those functions with our custom type:

julia> x = MyNumber(π)

julia> sin(x)

julia> cos(x)

In this manner, Julia acts as its own preprocessor,
and allows code generation from inside the language. The above code could be written slightly
more tersely using the : prefix quoting form:

for op = (:sin, :cos, :tan, :log, :exp)
    eval(:(Base.$op(a::MyNumber) = MyNumber($op(a.x))))

This sort of in-language code generation, however, using the eval(quote(...)) pattern, is common
enough that Julia comes with a macro to abbreviate this pattern:

for op = (:sin, :cos, :tan, :log, :exp)
    @eval Base.$op(a::MyNumber) = MyNumber($op(a.x))

The @eval macro rewrites this call to be precisely equivalent to the above longer versions.
For longer blocks of generated code, the expression argument given to @eval can be a

@eval begin
    # multiple lines

# Non-Standard String Literals

Recall from [Strings](@ref non-standard-string-literals) that string literals prefixed by an identifier are called non-standard
string literals, and can have different semantics than un-prefixed string literals. For example:

  • r"^\s*(?:#|$)" produces a regular expression object rather than a string
  • b"DATA\xff\u2200" is a byte array literal for [68,65,84,65,255,226,136,128].

Perhaps surprisingly, these behaviors are not hard-coded into the Julia parser or compiler. Instead,
they are custom behaviors provided by a general mechanism that anyone can use: prefixed string
literals are parsed as calls to specially-named macros. For example, the regular expression macro
is just the following:

macro r_str(p)

That's all. This macro says that the literal contents of the string literal r"^\s*(?:#|$)" should
be passed to the @r_str macro and the result of that expansion should be placed in the syntax
tree where the string literal occurs. In other words, the expression r"^\s*(?:#|$)" is equivalent
to placing the following object directly into the syntax tree:


Not only is the string literal form shorter and far more convenient, but it is also more efficient:
since the regular expression is compiled and the Regex object is actually created when the code is compiled,
the compilation occurs only once, rather than every time the code is executed. Consider if the
regular expression occurs in a loop:

for line = lines
    m = match(r"^\s*(?:#|$)", line)
    if m === nothing
        # non-comment
        # comment

Since the regular expression r"^\s*(?:#|$)" is compiled and inserted into the syntax tree when
this code is parsed, the expression is only compiled once instead of each time the loop is executed.
In order to accomplish this without macros, one would have to write this loop like this:

re = Regex("^\\s*(?:#|\$)")
for line = lines
    m = match(re, line)
    if m === nothing
        # non-comment
        # comment

Moreover, if the compiler could not determine that the regex object was constant over all loops,
certain optimizations might not be possible, making this version still less efficient than the
more convenient literal form above. Of course, there are still situations where the non-literal
form is more convenient: if one needs to interpolate a variable into the regular expression, one
must take this more verbose approach; in cases where the regular expression pattern itself is
dynamic, potentially changing upon each loop iteration, a new regular expression object must be
constructed on each iteration. In the vast majority of use cases, however, regular expressions
are not constructed based on run-time data. In this majority of cases, the ability to write regular
expressions as compile-time values is invaluable.

Like non-standard string literals, non-standard command literals exist using a prefixed variant
of the command literal syntax. The command literal custom`literal` is parsed as @custom_cmd "literal".
Julia itself does not contain any non-standard command literals, but packages can make use of
this syntax. Aside from the different syntax and the _cmd suffix instead of the _str suffix,
non-standard command literals behave exactly like non-standard string literals.

In the event that two modules provide non-standard string or command literals with the same name,
it is possible to qualify the string or command literal with a module name. For instance, if both
Foo and Bar provide non-standard string literal @x_str, then one can write Foo.x"literal"
or Bar.x"literal" to disambiguate between the two.

The mechanism for user-defined string literals is deeply, profoundly powerful. Not only are Julia's
non-standard literals implemented using it, but also the command literal syntax (`echo "Hello, $person"`)
is implemented with the following innocuous-looking macro:

macro cmd(str)

Of course, a large amount of complexity is hidden in the functions used in this macro definition,
but they are just functions, written entirely in Julia. You can read their source and see precisely
what they do -- and all they do is construct expression objects to be inserted into your program's
syntax tree.

# Generated functions

A very special macro is @generated, which allows you to define so-called generated functions.
These have the capability to generate specialized code depending on the types of their arguments
with more flexibility and/or less code than what can be achieved with multiple dispatch. While
macros work with expressions at parse time and cannot access the types of their inputs, a generated
function gets expanded at a time when the types of the arguments are known, but the function is
not yet compiled.

Instead of performing some calculation or action, a generated function declaration returns a quoted
expression which then forms the body for the method corresponding to the types of the arguments.
When a generated function is called, the expression it returns is compiled and then run.
To make this efficient, the result is usually cached. And to make this inferable, only a limited
subset of the language is usable. Thus, generated functions provide a flexible way to move work from
run time to compile time, at the expense of greater restrictions on allowed constructs.

When defining generated functions, there are four main differences to ordinary functions:

  1. You annotate the function declaration with the @generated macro. This adds some information
    to the AST that lets the compiler know that this is a generated function.
  2. In the body of the generated function you only have access to the types of the arguments –
    not their values – and any function that was defined before the definition of the generated
  3. Instead of calculating something or performing some action, you return a quoted expression which,
    when evaluated, does what you want.
  4. Generated functions must not mutate or observe any non-constant global state (including,
    for example, IO, locks, non-local dictionaries, or using hasmethod).
    This means they can only read global constants, and cannot have any side effects.
    In other words, they must be completely pure.
    Due to an implementation limitation, this also means that they currently cannot define a closure
    or generator.

It's easiest to illustrate this with an example. We can declare a generated function foo as

julia> @generated function foo(x)
           return :(x * x)
foo (generic function with 1 method)

Note that the body returns a quoted expression, namely :(x * x), rather than just the value
of x * x.

From the caller's perspective, this is identical to a regular function; in fact, you don't
have to know whether you're calling a regular or generated function. Let's see how foo behaves:

julia> x = foo(2); # note: output is from println() statement in the body

julia> x           # now we print x

julia> y = foo("bar");

julia> y

So, we see that in the body of the generated function, x is the type of the passed argument,
and the value returned by the generated function, is the result of evaluating the quoted expression
we returned from the definition, now with the value of x.

What happens if we evaluate foo again with a type that we have already used?

julia> foo(4)

Note that there is no printout of Int64. We can see that the body of the generated function
was only executed once here, for the specific set of argument types, and the result was cached.
After that, for this example, the expression returned from the generated function on the first
invocation was re-used as the method body. However, the actual caching behavior is an implementation-defined
performance optimization, so it is invalid to depend too closely on this behavior.

The number of times a generated function is generated might be only once, but it might also
be more often, or appear to not happen at all. As a consequence, you should never write a generated
function with side effects - when, and how often, the side effects occur is undefined. (This is
true for macros too - and just like for macros, the use of eval in a generated function
is a sign that you're doing something the wrong way.) However, unlike macros, the runtime system
cannot correctly handle a call to eval, so it is disallowed.

It is also important to see how @generated functions interact with method redefinition.
Following the principle that a correct @generated function must not observe any
mutable state or cause any mutation of global state, we see the following behavior.
Observe that the generated function cannot call any method that was not defined
prior to the definition of the generated function itself.

Initially f(x) has one definition

julia> f(x) = "original definition";

Define other operations that use f(x):

julia> g(x) = f(x);

julia> @generated gen1(x) = f(x);

julia> @generated gen2(x) = :(f(x));

We now add some new definitions for f(x):

julia> f(x::Int) = "definition for Int";

julia> f(x::Type{Int}) = "definition for Type{Int}";

and compare how these results differ:

julia> f(1)
"definition for Int"

julia> g(1)
"definition for Int"

julia> gen1(1)
"original definition"

julia> gen2(1)
"definition for Int"

Each method of a generated function has its own view of defined functions:

julia> @generated gen1(x::Real) = f(x);

julia> gen1(1)
"definition for Type{Int}"

The example generated function foo above did not do anything a normal function foo(x) = x * x
could not do (except printing the type on the first invocation, and incurring higher overhead).
However, the power of a generated function lies in its ability to compute different quoted expressions
depending on the types passed to it:

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

julia> bar(4)

julia> bar("baz")

(although of course this contrived example would be more easily implemented using multiple dispatch...)

Abusing this will corrupt the runtime system and cause undefined behavior:

julia> @generated function baz(x)
           if rand() < .9
               return :(x^2)
               return :("boo!")
baz (generic function with 1 method)

Since the body of the generated function is non-deterministic, its behavior, and the behavior of all subsequent code
is undefined.

Don't copy these examples!

These examples are hopefully helpful to illustrate how generated functions work, both in the definition
end and at the call site; however, don't copy them, for the following reasons:

  • the foo function has side-effects (the call to Core.println), and it is undefined exactly
    when, how often or how many times these side-effects will occur
  • the bar function solves a problem that is better solved with multiple dispatch - defining bar(x) = x
    and bar(x::Integer) = x ^ 2 will do the same thing, but it is both simpler and faster.
  • the baz function is pathological

Note that the set of operations that should not be attempted in a generated function is unbounded,
and the runtime system can currently only detect a subset of the invalid operations. There are
many other operations that will simply corrupt the runtime system without notification, usually
in subtle ways not obviously connected to the bad definition. Because the function generator is
run during inference, it must respect all of the limitations of that code.

Some operations that should not be attempted include:

  1. Caching of native pointers.
  2. Interacting with the contents or methods of Core.Compiler in any way.
  3. Observing any mutable state.

    • Inference on the generated function may be run at any time, including while your code is attempting
      to observe or mutate this state.
  4. Taking any locks: C code you call out to may use locks internally, (for example, it is not problematic
    to call malloc, even though most implementations require locks internally) but don't attempt
    to hold or acquire any while executing Julia code.
  5. Calling any function that is defined after the body of the generated function. This condition
    is relaxed for incrementally-loaded precompiled modules to allow calling any function in the module.

Alright, now that we have a better understanding of how generated functions work, let's use them
to build some more advanced (and valid) functionality...

# An advanced example

Julia's base library has a an internal sub2ind function to calculate a linear index into an n-dimensional
array, based on a set of n multilinear indices - in other words, to calculate the index i that
can be used to index into an array A using A[i], instead of A[x,y,z,...]. One possible implementation
is the following:

julia> function sub2ind_loop(dims::NTuple{N}, I::Integer...) where N
           ind = I[N] - 1
           for i = N-1:-1:1
               ind = I[i]-1 + dims[i]*ind
           return ind + 1
sub2ind_loop (generic function with 1 method)

julia> sub2ind_loop((3, 5), 1, 2)

The same thing can be done using recursion:

julia> sub2ind_rec(dims::Tuple{}) = 1;

julia> sub2ind_rec(dims::Tuple{}, i1::Integer, I::Integer...) =
           i1 == 1 ? sub2ind_rec(dims, I...) : throw(BoundsError());

julia> sub2ind_rec(dims::Tuple{Integer, Vararg{Integer}}, i1::Integer) = i1;

julia> sub2ind_rec(dims::Tuple{Integer, Vararg{Integer}}, i1::Integer, I::Integer...) =
           i1 + dims[1] * (sub2ind_rec(Base.tail(dims), I...) - 1);

julia> sub2ind_rec((3, 5), 1, 2)

Both these implementations, although different, do essentially the same thing: a runtime loop
over the dimensions of the array, collecting the offset in each dimension into the final index.

However, all the information we need for the loop is embedded in the type information of the arguments.
Thus, we can utilize generated functions to move the iteration to compile-time; in compiler parlance,
we use generated functions to manually unroll the loop. The body becomes almost identical, but
instead of calculating the linear index, we build up an expression that calculates the index:

julia> @generated function sub2ind_gen(dims::NTuple{N}, I::Integer...) where N
           ex = :(I[$N] - 1)
           for i = (N - 1):-1:1
               ex = :(I[$i] - 1 + dims[$i] * $ex)
           return :($ex + 1)
sub2ind_gen (generic function with 1 method)

julia> sub2ind_gen((3, 5), 1, 2)

What code will this generate?

An easy way to find out is to extract the body into another (regular) function:

julia> @generated function sub2ind_gen(dims::NTuple{N}, I::Integer...) where N
           return sub2ind_gen_impl(dims, I...)
sub2ind_gen (generic function with 1 method)

julia> function sub2ind_gen_impl(dims::Type{T}, I...) where T <: NTuple{N,Any} where N
           length(I) == N || return :(error("partial indexing is unsupported"))
           ex = :(I[$N] - 1)
           for i = (N - 1):-1:1
               ex = :(I[$i] - 1 + dims[$i] * $ex)
           return :($ex + 1)
sub2ind_gen_impl (generic function with 1 method)

We can now execute sub2ind_gen_impl and examine the expression it returns:

julia> sub2ind_gen_impl(Tuple{Int,Int}, Int, Int)
:(((I[1] - 1) + dims[1] * (I[2] - 1)) + 1)

So, the method body that will be used here doesn't include a loop at all - just indexing into
the two tuples, multiplication and addition/subtraction. All the looping is performed compile-time,
and we avoid looping during execution entirely. Thus, we only loop once per type, in this case
once per N (except in edge cases where the function is generated more than once - see disclaimer

# Optionally-generated functions

Generated functions can achieve high efficiency at run time, but come with a compile time cost:
a new function body must be generated for every combination of concrete argument types.
Typically, Julia is able to compile "generic" versions of functions that will work for any
arguments, but with generated functions this is impossible.
This means that programs making heavy use of generated functions might be impossible to
statically compile.

To solve this problem, the language provides syntax for writing normal, non-generated
alternative implementations of generated functions.
Applied to the sub2ind example above, it would look like this:

function sub2ind_gen(dims::NTuple{N}, I::Integer...) where N
    if N != length(I)
        throw(ArgumentError("Number of dimensions must match number of indices."))
    if @generated
        ex = :(I[$N] - 1)
        for i = (N - 1):-1:1
            ex = :(I[$i] - 1 + dims[$i] * $ex)
        return :($ex + 1)
        ind = I[N] - 1
        for i = (N - 1):-1:1
            ind = I[i] - 1 + dims[i]*ind
        return ind + 1

Internally, this code creates two implementations of the function: a generated one where
the first block in if @generated is used, and a normal one where the else block is used.
Inside the then part of the if @generated block, code has the same semantics as other
generated functions: argument names refer to types, and the code should return an expression.
Multiple if @generated blocks may occur, in which case the generated implementation uses
all of the then blocks and the alternate implementation uses all of the else blocks.

Notice that we added an error check to the top of the function.
This code will be common to both versions, and is run-time code in both versions
(it will be quoted and returned as an expression from the generated version).
That means that the values and types of local variables are not available at code generation
time --- the code-generation code can only see the types of arguments.

In this style of definition, the code generation feature is essentially an optional
The compiler will use it if convenient, but otherwise may choose to use the normal
implementation instead.
This style is preferred, since it allows the compiler to make more decisions and compile
programs in more ways, and since normal code is more readable than code-generating code.
However, which implementation is used depends on compiler implementation details, so it
is essential for the two implementations to behave identically.