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In the previous post, we saw an interesting implementation for the factorial function:

    sub fac(Int $n) {
        [*] 1..$n
    }

Okay, so how does that work? Perl 6 has a number of different "meta operators" that modify the existing operators to perform more powerful functions.

The square brackets about are an example of the "reduce metaoperator"; they cause an infix operator to become a list operator that acts as though the infix was placed between each pair of elements. For example, the statement

    [+]  1, $a, 5, $b

is essentially the same as writing

    1 + $a + 5 + $b

This gives us a handy mechanism to "sum all elements in a list":

    $sum = [+] @a;            # sum all elements of @a

Most of the infix operators (including user-defined operators) can be placed inside of square brackets to turn them into reductions:

    $prod = [*] @a;           # multiply all elements of @a

    $mean = ([+] @a) / @a;    # calculate mean of @a

    $sorted = [<=] @a;        # true if elements of @a are numerically sorted

    $min = [min] @a, @b;      # find the smallest element of @a and @b combined

So, in the factorial subroutine above, the expression [*] 1..$n returns the product of multiplying all of 1 through $n together.

Another useful metaoperator is the "hyper" operator. Placing » and/or « (or the ASCI >> and << equivalents) next to an operator makes it "hyper", which causes it operate on elements of lists. For example, the following calculates @c as the pairwise addition of the elements in @a and @b:

    @c = @a »+« @b;

In Perl 5, we'd generally write something like

    for ($i = 0; $i < @a; $i++) {
        $c[$i] = $a[$i] + $b[$i];
    }

which is quite a bit longer.

As with the square brackets above, we can use hyper on a variety of operators, including user-defined operators:

    # increment all elements of @xyz
    @xyz»++

    # each element of @x is the smaller of @a and @b
    @x = @a »min« @b;

We can also flip the angles to enable a scalar to act like an array:

    # multiply each element of @a by 3.5
    @b = @a »*» 3.5;

    # multiply each element of @x by $m and add $b
    @y = @x »*» $m »+» $b;

    # invert all elements of @x
    @inv = 1 «/« @x;

    # concatenate @last, @first to produce @full
    @full = (@last »~» ', ') »~« @first;

Of course, reductions and hyper operators can be combined in expressions:

    # calculate the sum of squares of @x
    $sumsq = [+] ( @x »**» 2);

There are many other metaoperators available, including X (cross), R (reverse), S (sequential). In fact, the "inplace" operators such as +=, *=, ~=, are just meta forms created by suffixing an operator with an equals sign:

    $a += 5;      # same as $a = $a + 5;
    $b //= 7;     # same as $b = $b // 7;
    $c min= $d;   # same as $c = $c min $d;