Control Flow¶

Compound Expressions¶

Sometimes it is convenient to have a single expression which evaluates several subexpressions in order, returning the value of the last subexpression as its value. There are two Julia constructs that accomplish this: begin blocks and (;) chains. The value of both compound expression constructs is that of the last subexpression. Here’s an example of a begin block:

julia>z=beginx=1y=2x+yend3

Since these are fairly small, simple expressions, they could easily be placed onto a single line, which is where the (;) chain syntax comes in handy:

julia>z=(x=1;y=2;x+y)3

This syntax is particularly useful with the terse single-line function definition form introduced in Functions. Although it is typical, there is no requirement that begin blocks be multiline or that (;) chains be single-line:

julia>beginx=1;y=2;x+yend3julia>(x=1;y=2;x+y)3

Conditional Evaluation¶

Conditional evaluation 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:

ifx<yprintln("x is less than y")elseifx>yprintln("x is greater than y")elseprintln("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. Here it is in action:

julia>function test(x,y)ifx<yprintln("x is less than y")elseifx>yprintln("x is greater than y")elseprintln("x is equal to y")endendtest(genericfunction with1method)julia>test(1,2)xislessthanyjulia>test(2,1)xisgreaterthanyjulia>test(1,1)xisequaltoy

The elseif and else blocks are optional, and as many elseif blocks as desired can be used. The condition expressions in the if-elseif-else construct are evaluated until the first one evaluates to true, after which the associated block is evaluated, and no further condition expressions or blocks are evaluated.

if blocks are “leaky”, i.e. they do not introduce a local scope. This means that new variables defined inside the ìf clauses can be used after the if block, even if they weren’t defined before. So, we could have defined the test function above as

julia>function test(x,y)ifx<yrelation="less than"elseifx==yrelation="equal to"elserelation="greater than"endprintln("x is ",relation," than y.")end;

if blocks also return a value, which may seem unintuitive to users coming from many other languages. This value is simply the return value of the last executed statement in the branch that was chosen, so

julia>x=33julia>ifx>0"positive!"else"negative..."end"positive!"

Note that very short conditional statements (one-liners) are frequently expressed using Short-Circuit Evaluation in Julia, as outlined in the next section.

Unlike C, MATLAB, Perl, Python, and Ruby — but like Java, and a few other stricter, typed languages — it is an error if the value of a conditional expression is anything but true or false:

julia>if1println("true")endERROR:type:non-boolean(Int64)usedinbooleancontext

This error indicates that the conditional was of the wrong type: Int64 rather than the required Bool.

The so-called “ternary operator”, ?:, is closely related to the if-elseif-else syntax, but is used where a conditional choice between single expression values is required, as opposed to conditional execution of longer blocks of code. It gets its name from being the only operator in most languages taking three operands:

a?b:c

The expression a, before the ?, is a condition expression, and the ternary operation evaluates the expression b, before the :, if the condition a is true or the expression c, after the :, if it is false.

The easiest way to understand this behavior is to see an example. In the previous example, the println call is shared by all three branches: the only real choice is which literal string to print. This could be written more concisely using the ternary operator. For the sake of clarity, let’s try a two-way version first:

julia>x=1;y=2;julia>println(x<y?"less than":"not less than")lessthanjulia>x=1;y=0;julia>println(x<y?"less than":"not less than")notlessthan

If the expression x<y is true, the entire ternary operator expression evaluates to the string "lessthan" and otherwise it evaluates to the string "notlessthan". The original three-way example requires chaining multiple uses of the ternary operator together:

julia>test(x,y)=println(x<y?"x is less than y":x>y?"x is greater than y":"x is equal to y")test(genericfunction with1method)julia>test(1,2)xislessthanyjulia>test(2,1)xisgreaterthanyjulia>test(1,1)xisequaltoy

To facilitate chaining, the operator associates from right to left.

It is significant that like if-elseif-else, the expressions before and after the : are only evaluated if the condition expression evaluates to true or false, respectively:

julia>v(x)=(println(x);x)v(genericfunction with1method)julia>1<2?v("yes"):v("no")yes"yes"julia>1>2?v("yes"):v("no")no"no"

Short-Circuit Evaluation¶

Short-circuit evaluation is quite similar to conditional evaluation. The behavior is found in most imperative programming languages having the && and || boolean operators: in a series of boolean expressions connected by these operators, only the minimum number of expressions are evaluated as are necessary to determine the final boolean value of the entire chain. Explicitly, this means that:

• In the expression a&&b, the subexpression b is only evaluated if a evaluates to true.
• In the expression a||b, the subexpression b is only evaluated if a evaluates to false.

The reasoning is that a&&b must be false if a is false, regardless of the value of b, and likewise, the value of a||b must be true if a is true, regardless of the value of b. Both && and || associate to the right, but && has higher precedence than || does. It’s easy to experiment with this behavior:

julia>t(x)=(println(x);true)t(genericfunction with1method)julia>f(x)=(println(x);false)f(genericfunction with1method)julia>t(1)&&t(2)12truejulia>t(1)&&f(2)12falsejulia>f(1)&&t(2)1falsejulia>f(1)&&f(2)1falsejulia>t(1)||t(2)1truejulia>t(1)||f(2)1truejulia>f(1)||t(2)12truejulia>f(1)||f(2)12false

You can easily experiment in the same way with the associativity and precedence of various combinations of && and || operators.

This behavior is frequently used in Julia to form an alternative to very short if statements. Instead of if<cond><statement>end, one can write <cond>&&<statement> (which could be read as: <cond> and then <statement>). Similarly, instead of if!<cond><statement>end, one can write <cond>||<statement> (which could be read as: <cond> or else <statement>).

For example, a recursive factorial routine could be defined like this:

julia>function factorial(n::Int)n>=0||error("n must be non-negative")n==0&&return1n*factorial(n-1)endfactorial(genericfunction with1method)julia>factorial(5)120julia>factorial(0)1julia>factorial(-1)ERROR:nmustbenon-negativeinfactorialatnone:2

Boolean operations without short-circuit evaluation can be done with the bitwise boolean operators introduced in Mathematical Operations and Elementary Functions: & and |. These are normal functions, which happen to support infix operator syntax, but always evaluate their arguments:

julia>f(1)&t(2)12falsejulia>t(1)|t(2)12true

Just like condition expressions used in if, elseif or the ternary operator, the operands of && or || must be boolean values (true or false). Using a non-boolean value anywhere except for the last entry in a conditional chain is an error:

julia>1&&trueERROR:type:non-boolean(Int64)usedinbooleancontext

On the other hand, any type of expression can be used at the end of a conditional chain. It will be evaluated and returned depending on the preceding conditionals:

julia>true&&(x=rand(2,2))2x2Array{Float64,2}:0.7684480.6739590.9405150.395453julia>false&&(x=rand(2,2))false

Repeated Evaluation: Loops¶

There are two constructs for repeated evaluation of expressions: the while loop and the for loop. Here is an example of a while loop:

julia>i=1;julia>whilei<=5println(i)i+=1end12345

The while loop evaluates the condition expression (i<=5 in this case), and as long it remains true, keeps also evaluating the body of the while loop. If the condition expression is false when the while loop is first reached, the body is never evaluated.

The for loop makes common repeated evaluation idioms easier to write. Since counting up and down like the above while loop does is so common, it can be expressed more concisely with a for loop:

julia>fori=1:5println(i)end12345

Here the 1:5 is a Range object, representing the sequence of numbers 1, 2, 3, 4, 5. The for loop iterates through these values, assigning each one in turn to the variable i. One rather important distinction between the previous while loop form and the for loop form is the scope during which the variable is visible. If the variable i has not been introduced in an other scope, in the for loop form, it is visible only inside of the for loop, and not afterwards. You’ll either need a new interactive session instance or a different variable name to test this:

julia>forj=1:5println(j)end12345julia>jERROR:jnotdefined

See Scope of Variables for a detailed explanation of variable scope and how it works in Julia.

In general, the for loop construct can iterate over any container. In these cases, the alternative (but fully equivalent) keyword in is typically used instead of =, since it makes the code read more clearly:

julia>foriin[1,4,0]println(i)end140julia>forsin["foo","bar","baz"]println(s)endfoobarbaz

Various types of iterable containers will be introduced and discussed in later sections of the manual (see, e.g., Multi-dimensional Arrays).

It is sometimes convenient to terminate the repetition of a while before the test condition is falsified or stop iterating in a for loop before the end of the iterable object is reached. This can be accomplished with the break keyword:

julia>i=1;julia>whiletrueprintln(i)ifi>=5breakendi+=1end12345julia>fori=1:1000println(i)ifi>=5breakendend12345

The above while loop would never terminate on its own, and the for loop would iterate up to 1000. These loops are both exited early by using the break keyword.

In other circumstances, it is handy to be able to stop an iteration and move on to the next one immediately. The continue keyword accomplishes this:

julia>fori=1:10ifi%3!=0continueendprintln(i)end369

This is a somewhat contrived example since we could produce the same behavior more clearly by negating the condition and placing the println call inside the if block. In realistic usage there is more code to be evaluated after the continue, and often there are multiple points from which one calls continue.

Multiple nested for loops can be combined into a single outer loop, forming the cartesian product of its iterables:

julia>fori=1:2,j=3:4println((i,j))end(1,3)(1,4)(2,3)(2,4)

A break statement inside such a loop exits the entire nest of loops, not just the inner one.

Exception Handling¶

When an unexpected condition occurs, a function may be unable to return a reasonable value to its caller. In such cases, it may be best for the exceptional condition to either terminate the program, printing a diagnostic error message, or if the programmer has provided code to handle such exceptional circumstances, allow that code to take the appropriate action.

julia>sqrt(-1)ERROR:DomainErrorsqrtwillonlyreturnacomplexresultifcalledwithacomplexargument.trysqrt(complex(x))insqrtatmath.jl:133

julia>type MyCustomException<:Exceptionend

julia>f(x)=x>=0?exp(-x):throw(DomainError())f(genericfunction with1method)julia>f(1)0.36787944117144233julia>f(-1)ERROR:DomainErrorinfatnone:1

julia>typeof(DomainError())<:Exceptiontruejulia>typeof(DomainError)<:Exceptionfalse

julia>throw(UndefVarError(:x))ERROR:xnotdefined

julia>type MyUndefVarError<:Exceptionvar::Symbolendjulia>Base.showerror(io::IO,e::MyUndefVarError)=print(io,e.var," not defined");

julia>fussy_sqrt(x)=x>=0?sqrt(x):error("negative x not allowed")fussy_sqrt(genericfunction with1method)julia>fussy_sqrt(2)1.4142135623730951julia>fussy_sqrt(-1)ERROR:negativexnotallowedinfussy_sqrtatnone:1

julia>function verbose_fussy_sqrt(x)println("before fussy_sqrt")r=fussy_sqrt(x)println("after fussy_sqrt")returnrendverbose_fussy_sqrt(genericfunction with1method)julia>verbose_fussy_sqrt(2)beforefussy_sqrtafterfussy_sqrt1.4142135623730951julia>verbose_fussy_sqrt(-1)beforefussy_sqrtERROR:negativexnotallowedinverbose_fussy_sqrtatnone:3

julia>info("Hi");1+1INFO:Hi2julia>warn("Hi");1+1WARNING:Hi2julia>error("Hi");1+1ERROR:Hiinerroraterror.jl:21

julia>f(x)=trysqrt(x)catchsqrt(complex(x,0))endf(genericfunction with1method)julia>f(1)1.0julia>f(-1)0.0+1.0im

julia>sqrt_second(x)=trysqrt(x[2])catchyifisa(y,DomainError)sqrt(complex(x[2],0))elseifisa(y,BoundsError)sqrt(x)endendsqrt_second(genericfunction with1method)julia>sqrt_second([14])2.0julia>sqrt_second([1-4])0.0+2.0imjulia>sqrt_second(9)3.0julia>sqrt_second(-9)ERROR:DomainErrorinsqrt_secondatnone:7

trybad()catchxend

trybad()catch;xendtrybad()catchxend

julia>tryerror()endfalse

f=open("file")try# operate on file ffinallyclose(f)end

Tasks (aka Coroutines)¶

Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. This feature is sometimes called by other names, such as symmetric coroutines, lightweight threads, cooperative multitasking, or one-shot continuations.

When a piece of computing work (in practice, executing a particular function) is designated as a Task, it becomes possible to interrupt it by switching to another Task. The original Task can later be resumed, at which point it will pick up right where it left off. At first, this may seem similar to a function call. However there are two key differences. First, switching tasks does not use any space, so any number of task switches can occur without consuming the call stack. Second, switching among tasks can occur in any order, unlike function calls, where the called function must finish executing before control returns to the calling function.

This kind of control flow can make it much easier to solve certain problems. In some problems, the various pieces of required work are not naturally related by function calls; there is no obvious “caller” or “callee” among the jobs that need to be done. An example is the producer-consumer problem, where one complex procedure is generating values and another complex procedure is consuming them. The consumer cannot simply call a producer function to get a value, because the producer may have more values to generate and so might not yet be ready to return. With tasks, the producer and consumer can both run as long as they need to, passing values back and forth as necessary.

Julia provides the functions produce() and consume() for solving this problem. A producer is a function that calls produce() on each value it needs to produce:

julia>function producer()produce("start")forn=1:4produce(2n)endproduce("stop")end;

To consume values, first the producer is wrapped in a Task, then consume() is called repeatedly on that object:

julia>p=Task(producer);julia>consume(p)"start"julia>consume(p)2julia>consume(p)4julia>consume(p)6julia>consume(p)8julia>consume(p)"stop"

One way to think of this behavior is that producer was able to return multiple times. Between calls to produce(), the producer’s execution is suspended and the consumer has control.

A Task can be used as an iterable object in a for loop, in which case the loop variable takes on all the produced values:

julia>forxinTask(producer)println(x)endstart2468stop

Note that the Task() constructor expects a 0-argument function. A common pattern is for the producer to be parameterized, in which case a partial function application is needed to create a 0-argument anonymous function. This can be done either directly or by use of a convenience macro:

function mytask(myarg)...endtaskHdl=Task(()->mytask(7))# or, equivalentlytaskHdl=@taskmytask(7)

produce() and consume() do not launch threads that can run on separate CPUs. True kernel threads are discussed under the topic of Parallel Computing.