In the Day 4 box, we saw an interesting implementation for the factorial function:

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

Okay, so *how* does that work? Opening up today’s Advent box provides some answers!

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 expression

[+] 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 ASCII `>>`

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 “in-place” 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;

$c min= $d; is one of the most awesome things i’ve seen since … i last learned something new about perl6!

thank you

Wow, this is very impressive! Can’t wait to use this in real world applications!

Very impressive, but I can’t help thinking about “APL”. Will we soon need special keyboards to code in Perl?

(And yes, APL did have bi- and tri-graphs for all its special characters, but that made for a lot of extra typing)

Wow, just like APL but 50 years later!

in APL direct definition:

fac: */ιω

where ω is a the argument of the “fac” function, and “/” is the reduction operator. As for the “hyper” operator, this was the default operator for scalar functions in APL – it was never explicit. You could write “A + B” and if A and B were conformal arrays, the result was a conformal array where each element was the result of adding each corresponding element of A and B.

The influence of LISP continues… “meta operators”

Да уж. По поводу коментариев – навеяла на меня где-то услышанная фраза:

Только наш клиент в графе “Телефон” мог написать Samsung.

Дискутировать можно бесконечно, поэтому просто поблагодарю автора. Спасибо!

Wonderful article! As far as I can tell, just one line of code needed an update (a “flat”) for it to work this Christmas:

Thanks so much for your years of work on Perl 6! Merry Christmas!