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Control Flow

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Benoît Knecht edited this page Dec 3, 2011 · 2 revisions

Julia provides a variety of control flow constructs:

The first five control flow mechanisms are standard to high-level programming languages. Tasks are not so standard: they provide non-local control flow, making it possible to switch between temporarily-suspended computations. This is a powerful construct: both exception handling and cooperative multitasking are implemented in Julia using tasks. Everyday programming requires no direct usage of tasks, but certain problems can be solved much more easily by using tasks.

## 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 = begin
         x = 1
         y = 2
         x + y
       end
3

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> begin x = 1; y = 2; x + y end
3

julia> (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 another expression. Here is the anatomy of the if-elseif-else conditional syntax:

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

The semantics are just what you'd expect: 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)
         if x < y
           println("x is less than y")
         elseif x > y
           println("x is greater than y")
         else
           println("x is equal to y")
         end
       end

julia> test(1, 2)
x is less than y

julia> test(2, 1)
x is greater than y

julia> test(1, 1)
x is equal to y

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.

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> if 1
         println("true")
       end
type error: lambda: in if, expected Bool, got Int64

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")
less than

julia> x = 1; y = 0;

julia> println(x < y ? "less than" : "not less than")
not less than

If the expression x < y is true, the entire ternary operator expression evaluates to the string "less than" and otherwise it evaluates to the string "not less than". 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")

julia> test(1, 2)
x is less than y

julia> test(2, 1)
x is greater than y

julia> test(1, 1)
x is equal to y

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:

v(x) = (println(x); x)

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 than || does. It's easy to experiment with this behavior:

t(x) = (println(x); true)
f(x) = (println(x); false)

julia> t(1) && t(2)
1
2
true

julia> t(1) && f(2)
1
2
false

julia> f(1) && t(2)
1
false

julia> f(1) && f(2)
1
false

julia> t(1) || t(2)
1
true

julia> t(1) || f(2)
1
true

julia> f(1) || t(2)
1
2
true

julia> f(1) || f(2)
1
2
false

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

If you want to perform boolean operations without short-circuit evaluation behavior, you can use the bitwise boolean operators introduced in Mathematical Operations: & and |. These are normal functions, which happen to support infix operator syntax, but always evaluate their arguments:

julia> f(1) & t(2)
1
2
false

julia> t(1) | t(2)
1
2
true

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 is an error:

julia> 1 && 2
type error: lambda: in if, expected Bool, got Int64

Chained numeric comparisons also exhibit short-circuit evaluation behavior. Recall from Numeric Comparisons that numeric comparisons in Julia can be arbitrarily chained:

julia> a = 1; b = 2; c = 3;

julia> a < b <= c
true

This last expression is equivalent to the less concise:

julia> a < b && b <= c
true

In particular, this implies that chained comparisons exhibit short-circuit behavior. Let's see this in action:

v(x) = (println(x); x)

julia> v(1) > v(2) <= v(3)
2
1
false

The first two expressions in a comparison chain are always evaluated, since their values are required to check the first comparison, which must be checked. Subsequent expressions, however, need not be evaluated if a comparison earlier in the chain is false. Note that the middle expression is only evaluated once, rather than twice as it would be if the expression were written as v(1) < v(2) && v(2) <= v(3). However, the order of evaluations in a chained comparison is undefined. It is strongly recommended not to use expressions with side effects (such as printing) in chained comparisons. If side effects are required, the short-circuit && operator should be used explicitly.

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

The while loop evaluates the condition expression (i < n 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> for i = 1:5
         println(i)
       end
1
2
3
4
5

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> for j = 1:5
         println(j)
       end
1
2
3
4
5
()

julia> j
j not defined

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

In general, the for loop construct can iterate over all sorts of containers:

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

julia> for s = ["foo","bar","baz"]
         println(s)
       end
foo
bar
baz

Various types of iterable containers will be introduced and discussed in later section.

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

julia> for i = 1:1000
         println(i)               
         if i >= 5
           break
         end
       end
1
2
3
4
5

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> for i = 1:10
         if i % 3 != 0
           continue
         end
         println(i)
       end
3
6
9

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.

## 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.

The error function is used to indicate that an unexpected condition has occurred which should interrupt the normal flow of control. The built in sqrt function returns NaN if applied to a negative real value:

julia> sqrt(-1)
NaN

Suppose we want to stop execution immediately if the square root of a negative number is taken. To do this, we can define a fussy version of the sqrt function that raises an error if its argument is negative:

fussy_sqrt(x) = x >= 0 ? sqrt(x) : error("negative x not allowed")

julia> fussy_sqrt(2)
1.4142135623730951

julia> fussy_sqrt(-1)
negative x not allowed

If fussy_sqrt is called with a negative value from another function, instead of trying to continue execution of the calling function, it returns immediately, displaying the error message in the interactive session:

function verbose_fussy_sqrt(x)
  println("before fussy_sqrt")
  r = fussy_sqrt(x)
  println("after fussy_sqrt")
  return r
end

julia> verbose_fussy_sqrt(2)
before fussy_sqrt
after fussy_sqrt
1.4142135623730951

julia> verbose_fussy_sqrt(-1)
before fussy_sqrt
negative x not allowed

Now suppose we want to handle this circumstance rather than just giving with an error. To catch an error, you use the try and catch keywords. Here is a rather contrived example that computes the square root of the absolute value of x by handling the error raised by fussy_sqrt:

function sqrt_abs(x)
  try
    fussy_sqrt(x)
  catch
    fussy_sqrt(-x)
  end
end

julia> sqrt_abs(2)
1.4142135623730951

julia> sqrt_abs(-2)
1.4142135623730951

Of course, it would be far simpler and more efficient to just return sqrt(abs(x)). However, this demonstrates how try and catch operate: the try block is executed initially, and the value the entire construct is the value of the last expression if no exceptions are thrown during execution; if an exception is thrown during the evaluation of the try block, however, execution of the try code ceases immediately and the catch block is evaluated instead. If the catch block succeeds without incident (it can in turn raise an exception, which would unwind the call stack further), the value of the entire try-catch construct is that of the last expression in the catch block.

### Throw versus Error

The error function is convenient for indicating that an error has occurred, but it is built on a more fundamental function: throw. Perhaps throw should be introduced first, but typical usage calls for error, so we have deferred the introduction of throw. Above, we use a form of the try-catch expression in which no value is captured by the catch block, but there is another form:

try
  # execute some code
catch x
  # so something with x
end

In this form, if the built-in throw function is called by the "execute some code" expression, or any callee thereof, the catch block is executed with the argument of the throw function is bound to the variable x. The error function is simply a convenience which always throws an instance of the abstract type Exception. Here we can see that the object thrown when a divide-by-zero error occurs is of type DivideByZeroError:

julia> div(1,0)
error: integer divide by zero

julia> try 
         div(1,0)
       catch x
         println(typeof(x))
       end
DivideByZeroError

DivideByZeroError is a concrete subtype of Exception, thrown to indicate that some illegal division by zero has occurred in an function whose return type is integeral, thereby making it impossible to return a reasonable value. Floating-point functions, on the other hand, can simply return NaN rather than throwing an exception.

Unlike error, which should only be used to indicate an unexpected condition, throw is merely a control construct, and can be used to pass any value back to an enclosing try-catch:

julia> try
         throw("Hello, world.")
       catch x
         println(x)
       end
Hello, world.

This example is very contrived, of course — the power of the try-catch construct lies in the ability to unwind a deeply nested computation immediately to a much higher level in the stack of calling functions. There are situations where no error has occurred, but the ability to unwind the stack and pass a value to a higher level is desirable. These are the circumstances in which throw should be used rather than error. On the other hand, when something unexpected has occurred in a program's execution, error is the more appropriate way let a caller handle the problem or terminate the program with an error message.

## 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, you may switch among tasks 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:

function producer()
  produce("start")
  for n=1:4
    produce(2n)
  end
  produce("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)
Task

julia> consume(p)
"start"

julia> consume(p)
2

julia> consume(p)
4

julia> consume(p)
6

julia> consume(p)
8

julia> consume(p)
10

julia> 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> for x = Task(producer)
         println(x)
       end
start
2
4
6
8
10
stop

Previous: Functions — Next: Variables and Scoping

© 2010-2011 Stefan Karpinski, Jeff Bezanson, Viral Shah, Alan Edelman.

The Julia Manual — All Rights Reserved.

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