Recursive functions

Functions can be nested, as demonstrated in the following example:

function a(x)
    z = x * 2
    function b(z)
        z += 1
    end
    b(z)
end

d = 5
a(d) #=> 11

A function can also be recursive, that is, it can call itself. To show some examples, we need to be able to test a condition in code. The simplest way to do this in Julia is to use the ternary operator ? of the form expr ? b : c (ternary because it takes three arguments). Julia also has a normal if construct (refer to the Conditional evaluation section of Chapter 4, Control Flow). expr is a condition and if it is true, then b is evaluated and the value is returned, else c is evaluated. This is used in the following recursive definition to calculate the sum of all the integers up to and including a certain number:

sum(n) =  n > 1 ? sum(n-1) + n : n

The recursion ends because there is a base case: when n is 1, this value is returned. Or here is the famous function to calculate the nth Fibonacci number...