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 ofabstract 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, powerfulreflection 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 toparse each string into an object called an expression, represented by the Julia typeExpr:

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

Expr objects contain two parts:

• aSymbol identifying the kind of expression. A symbol is aninterned string identifier (more discussion below).

julia> ex1.head:call

• the expression arguments, which may be symbols, other expressions, or literal values:

julia> ex1.args3-element Vector{Any}:  :+ 1 1

Expressions may also be constructed directly inprefix notation:

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

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

julia> ex1 == ex2true

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

Thedump function provides indented and annotated display ofExpr objects:

julia> dump(ex2)Expr  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 withMeta.show_sexpr, which displays theS-expression form of a givenExpr, which may look very familiar to users of Lisp. Here's an example illustrating the display on a nestedExpr:

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

Symbols

The: character has two syntactic purposes in Julia. The first form creates aSymbol, aninterned string used as one building-block of expressions, from valid identifiers:

julia> s = :foo:foojulia> typeof(s)Symbol

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

julia> :foo === Symbol("foo")truejulia> Symbol("1foo") # `:1foo` would not work, as `1foo` is not a valid identifierSymbol("1foo")julia> Symbol("func",10):func10julia> Symbol(:var,'_',"sym"):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 appropriatescope.

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 explicitExpr constructor. This is referred to asquoting. The: character, followed by paired parentheses around a single statement of Julia code, produces anExpr object based on the enclosed code. Here is an example of the short form used to quote an arithmetic expression:

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

(to view the structure of this expression, tryex.head andex.args, or usedump as above orMeta.@dump)

Note that equivalent expressions may be constructed usingMeta.parse or the directExpr form:

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

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,+ anda are symbols,*(b,c) is a subexpression, and1 is a literal 64-bit signed integer.

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

julia> ex = quote           x = 1           y = 2           x + y       endquote    #= none:2 =#    x = 1    #= none:3 =#    y = 2    #= none:4 =#    x + yendjulia> typeof(ex)Expr

Interpolation

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

In this example, the value of variablea 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> $a + bERROR: syntax: "$" 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 ofstring interpolation andcommand 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 endquote    #= none:1 =#    $(Expr(:quote, quote    #= none:1 =#    $(Expr(:$, :x))end))end

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

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

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

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

Notice that(1 + 2) now appears in the result instead of the symbolx. Evaluating this expression yields an interpolated3:

julia> eval(e)quote    #= none:1 =#    3end

The intuition behind this behavior is thatx is evaluated once for each$: one$ works similarly toeval(:x), givingx's value, while two$s do the equivalent ofeval(eval(:x)).

QuoteNode

The usual representation of aquote form in an AST is anExpr with head:quote:

julia> dump(Meta.parse(":(1+2)"))Expr  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 codewithout performing interpolation. This kind of quoting does not yet have syntax, but is represented internally as an object of typeQuoteNode:

julia> eval(Meta.quot(Expr(:$, :(1+2))))3julia> eval(QuoteNode(Expr(:$, :(1+2)))):($(Expr(:$, :(1 + 2))))

The parser yieldsQuoteNodes for simple quoted items like symbols:

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

QuoteNode can also be used for certain advanced metaprogramming tasks.

Evaluating expressions

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

julia> ex1 = :(1 + 2):(1 + 2)julia> eval(ex1)3julia> ex = :(a + b):(a + b)julia> eval(ex)ERROR: UndefVarError: `b` not defined in `Main`[...]julia> a = 1; b = 2;julia> eval(ex)3

Everymodule has its owneval function that evaluates expressions in its global scope. Expressions passed toeval 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> xERROR: UndefVarError: `x` not defined in `Main`julia> eval(ex)1julia> x1

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

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

julia> a = 1;julia> ex = Expr(:call, :+, a, :b):(1 + b)julia> a = 0; b = 2;julia> eval(ex)3

The value ofa is used to construct the expressionex which applies the+ function to the value 1 and the variableb. Note the important distinction between the waya andb are used:

• The value of thevariablea at expression construction time is used as an immediate value in the expression. Thus, the value ofa when the expression is evaluated no longer matters: the value in the expression is already1, independent of whatever the value ofa might be.
• On the other hand, thesymbol:b is used in the expression construction, so the value of the variableb at that time is irrelevant –:b is just a symbol and the variableb 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 variableb.

Functions onExpressions

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 returningExpr objects: theMeta.parse function, which takes a string of Julia code and returns the correspondingExpr. A function can also take one or moreExpr objects as arguments, and return anotherExpr. Here is a simple, motivating example:

julia> function math_expr(op, op1, op2)           expr = Expr(:call, op, op1, op2)           return expr       endmath_expr (generic function with 1 method)julia>  ex = math_expr(:+, 1, Expr(:call, :*, 4, 5)):(1 + 4 * 5)julia> eval(ex)21

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

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       endmake_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)42

Macros

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

Basics

Here is an extraordinarily simple macro:

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

Macros have a dedicated character in Julia's syntax: the@ (at-sign), followed by the unique name declared in amacro 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) )       end@sayhello (macro with 1 method)

This macro takes one argument:name. When@sayhello is encountered, the quoted expression isexpanded 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 functionmacroexpand (important note: this is an extremely useful tool for debugging macros):

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

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 themacroexpand function:

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

Hold up: why macros?

We have already seen a functionf(::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 codebefore 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))       end@twostep (macro with 1 method)julia> ex = macroexpand(Main, :(@twostep :(1, 2, 3)) );I execute at parse time. The argument is: :((1, 2, 3))

The first call toprintln is executed whenmacroexpand is called. The resulting expression containsonly the secondprintln:

julia> typeof(ex)Exprjulia> 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 theshow function within the macro body:

julia> macro showarg(x)           show(x)           # ... remainder of macro, returning an expression       end@showarg (macro with 1 method)julia> @showarg(a):ajulia> @showarg(1+1):(1 + 1)julia> @showarg(println("Yo!")):(println("Yo!"))julia> @showarg(1)        # Numeric literal1julia> @showarg("Yo!")    # String literal"Yo!"julia> @showarg("Yo! $("hello")")    # String with interpolation is an Expr rather than a String:("Yo! $("hello")")

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 aLineNumberNode 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(            @__LOCATION__(       ))LineNumberNode  line: Int64 2  file: Symbol none

The argument__module__ provides information (in the form of aModule 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)))) )       end@assert (macro with 1 method)

This macro can be used like this:

julia> @assert 1 == 1.0julia> @assert 1 == 0ERROR: 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 ofstring(:(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, thennothing 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 thevalue 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 (Varargs Functions), 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)))       end@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 bymsgs 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.nothing    else        Main.throw(Main.AssertionError("a == b"))    end)julia> @macroexpand @assert a==b "a should equal b!":(if Main.a == Main.b        Main.nothing    else        Main.throw(Main.AssertionError("a should equal b!"))    end)

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 fromstring interpolation that an interpolated string is rewritten to a call tostring. Compare:

julia> typeof(:("a should equal b"))Stringjulia> typeof(:("a ($a) should equal b ($b)!"))Exprjulia> dump(:("a ($a) should equal b ($b)!"))Expr  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 inmsg_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 thestring call; seeerror.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 ofhygiene. 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 oftenexpected 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 asmsg in@assert above) follow thenormal scoping block behavior.

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_ns()        local val = $ex        local t1 = time_ns()        println("elapsed time: ", (t1-t0)/1e9, " seconds")        val    endend

Here, we wantt0,t1, andval to be private temporary variables, and we wanttime_ns to refer to thetime_ns function in Julia Base, not to anytime_ns variable the user might have (the same applies toprintln). Imagine the problems that could occur if the user expressionex also contained assignments to a variable calledt0, or defined its owntime_ns 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 thegensym 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, andtime_ns andprintln will refer to the Julia Base definitions.

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

module MyModuleimport Base.@timetime_ns() = ... # compute something@time time_ns()end

Here the user expressionex is a call totime_ns, but not the sametime_ns function that the macro uses. It clearly refers toMyModule.time_ns. Therefore we must arrange for the code inex to be resolved in the macro call environment. This is done by "escaping" the expression withesc:

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

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 setsx to zero in the call environment:

julia> macro zerox()           return esc(:(x = 0))       end@zerox (macro with 1 method)julia> function foo()           x = 1           @zerox           return x # is zero       endfoo (generic function with 1 method)julia> foo()0

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 aQuoteNode or other similarExpr. Some examples of this include@task body which simply returnsschedule(Task(() -> $body)), and@eval expr, which simply returnseval(QuoteNode(expr)).

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

macro time(expr)    return :(timeit(() -> $(esc(expr))))endfunction timeit(f)    t0 = time_ns()    val = f()    t1 = time_ns()    println("elapsed time: ", (t1-t0)/1e9, " seconds")    return valend

However, we don't do this for a good reason: wrapping theexpr 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")       end@m (macro with 1 method)julia> macro m(x,y)           println("Two arguments")       end@m (macro with 2 methods)julia> @m "asd"1 argumentsjulia> @m 1 2Two 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")       end@m (macro with 3 methods)julia> @m 2An Integerjulia> x = 22julia> @m x1 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 andeval allow such code generation to take place in the normal course of program execution. For example, consider the following custom type

struct MyNumber    x::Float64end# 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)    eval(quote        Base.$op(a::MyNumber) = MyNumber($op(a.x))    end)end# output

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

julia> x = MyNumber(π)MyNumber(3.141592653589793)julia> sin(x)MyNumber(1.2246467991473532e-16)julia> cos(x)MyNumber(-1.0)

In this manner, Julia acts as its ownpreprocessor, 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))))end

This sort of in-language code generation, however, using theeval(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))end

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 block:

@eval begin    # multiple linesend

Non-Standard String Literals

Recall fromStrings 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 aregular expression object rather than a string
• b"DATA\xff\u2200" is abyte 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)    Regex(p)end

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

Regex("^\\s*(?:#|\$)")

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 theRegex object is actually createdwhen 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    else        # comment    endend

Since the regular expressionr"^\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    else        # comment    endend

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.

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

macro cmd(str)    :(cmd_gen($(shell_parse(str)[1])))end

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.

Like string literals, command literals can also be prefixed by an identifier to form what are called non-standard command literals. These command literals are parsed as calls to specially-named macros. For example, the syntaxcustom`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 bothFoo andBar provide non-standard string literal@x_str, then one can writeFoo.x"literal" orBar.x"literal" to disambiguate between the two.

Another way to define a macro would be like this:

macro foo_str(str, flag)    # do stuffend

This macro can then be called with the following syntax:

foo"str"flag

The type of flag in the above mentioned syntax would be aString with contents of whatever trails after the string literal.

Generated functions

A very special macro is@generated, which allows you to define so-calledgenerated 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 five 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 thetypes of the arguments – not their values.
3. Instead of calculating something or performing some action, you return aquoted expression which, when evaluated, does what you want.
4. Generated functions are only permitted to call functions that were definedbefore the definition of the generated function. (Failure to follow this may result in gettingMethodErrors referring to functions from a future world-age.)
5. Generated functions must notmutate orobserve any non-constant global state (including, for example, IO, locks, non-local dictionaries, or usinghasmethod). 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 functionfoo as

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

Note that the body returns a quoted expression, namely:(x * x), rather than just the value ofx * 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 howfoo behaves:

julia> x = foo(2); # note: output is from println() statement in the bodyInt64julia> x           # now we print x4julia> y = foo("bar");Stringjulia> y"barbar"

So, we see that in the body of the generated function,x is thetype 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 thevalue ofx.

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

julia> foo(4)16

Note that there is no printout ofInt64. 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 generatedmight be only once, but itmight also be more often, or appear to not happen at all. As a consequence, you shouldnever 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 ofeval 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 toeval, 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 functioncannot call any method that was not defined prior to thedefinition of the generated function itself.

Initiallyf(x) has one definition

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

Define other operations that usef(x):

julia> g(x) = f(x);julia> @generated gen1(x) = f(x);julia> @generated gen2(x) = :(f(x));

We now add some new definitions forf(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 functionfoo above did not do anything a normal functionfoo(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)           else               return :(x)           end       endbar (generic function with 1 method)julia> bar(4)16julia> bar("baz")"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)           else               return :("boo!")           end       endbaz (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:

• thefoo function has side-effects (the call toCore.println), and it is undefined exactly when, how often or how many times these side-effects will occur
• thebar function solves a problem that is better solved with multiple dispatch - definingbar(x) = x andbar(x::Integer) = x ^ 2 will do the same thing, but it is both simpler and faster.
• thebaz 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 ofCore.Compiler in any way.

3. Observing any mutable state.

   • Inference on the generated function may be run atany 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 callmalloc, 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 an internalsub2ind 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 indexi that can be used to index into an arrayA usingA[i], instead ofA[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           end           return ind + 1       end;julia> sub2ind_loop((3, 5), 1, 2)4

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)4

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. This allows the compiler to move the iteration to compile time and eliminate the runtime loops altogether. We can utilize generated functions to achieve a similar effect; 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 anexpression 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] * $ex)           end           return :($ex + 1)       end;julia> sub2ind_gen((3, 5), 1, 2)4

What code will this generate?

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

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] * $ex)           end           return :($ex + 1)       end;julia> @generated function sub2ind_gen(dims::NTuple{N}, I::Integer...) where N           return sub2ind_gen_impl(dims, I...)       end;julia> sub2ind_gen((3, 5), 1, 2)4

We can now executesub2ind_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 looponce per type, in this case once perN (except in edge cases where the function is generated more than once - see disclaimer above).

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 thesub2ind example above, it would look like this:

julia> function sub2ind_gen_impl(dims::Type{T}, I...) where T <: NTuple{N,Any} where N           ex = :(I[$N] - 1)           for i = (N - 1):-1:1               ex = :(I[$i] - 1 + dims[$i] * $ex)           end           return :($ex + 1)       end;julia> function sub2ind_gen_fallback(dims::NTuple{N}, I) where N           ind = I[N] - 1           for i = (N - 1):-1:1               ind = I[i] - 1 + dims[i]*ind           end           return ind + 1       end;julia> function sub2ind_gen(dims::NTuple{N}, I::Integer...) where N           length(I) == N || error("partial indexing is unsupported")           if @generated               return sub2ind_gen_impl(dims, I...)           else               return sub2ind_gen_fallback(dims, I)           end       end;julia> sub2ind_gen((3, 5), 1, 2)4

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