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Rockin' with Raku

Selected code examples showcasing the power of the Raku programming language. Watch it flex!

A Detailed Walk Through of Code for Finding Specific Prime Numbers

What's the 5th prime number? How about the 500th? 50,000th?! Easy (and super fast):

my $x = ^Inf;
sub get-prime(Int:D $nth where * > 0) {
    say ($x.grep: *.is-prime)[$nth - 1];
for (5, 50, 500, 5000, 50000) { get-prime $_ };

When we run this, we get the following output after just a second or two:

11      # 5th prime
229     # 50th prime
3571    # 500th prime
48611   # 5000th prime
611953  # 50000th prime

Can you match the speed and conciseness of this code in your favorite language? More than likely, you'll have a hard time writing and executing this problem in a reasonable time. But with Raku, it's a snap.

Let's walk through the code in detail.

How it works

First we assign variable $x to ^Inf which represents a Range of Integers from 0 to infinity. In Raku, a Range is a class which generates Range objects. Range objects are "lazy," which means the actual set of numbers in the Range aren't actually calculated or generated. This is unlike an Array where each element is calculated ahead of time by the compiler and inserted into the array and eats up memory. And so laziness makes your program much more efficient. You certainly don't want to wait around for your computer to count to infinity but you'd certainly run out of memory long before then anyway!

Next we create a simple subroutine called get-prime that accepts a single argument called $nth, which is placed inside a set of parentheses. The parentheses and the code inside of it is part the function's Signature, which is itself an object. The Signature tells code calling get-prime what kind of parameters are acceptable to send. In get-prime's signature, we ensure that $nth is a defined integer object by slapping Int:D in front of it. The Int requires the caller to pass an Integer object. The :D bit ensures that it's a "defined" object, meaning that has a value associate with it. We also add a nice touch by ensuring the number passed is greater than 0 with the where * > 0 because it doesn't make sense to ask for the 0th or -1st prime number. If you're you're wondering what the * symbol is, hang tight. We'll cover this symbol again shortly.

Restricting the kinds of argument that can be passed to a subroutine is known as "type checking." But thanks to Raku's flexibility, we could have chosen to not type check our arguments. If you want to bang out a simple script without a lot of hassle and headache trying to keep the compiler happy, Raku will accommodate your desires and not make onerous demands that make your work unnecessarily tedious.

Inside the subroutine is a single line of code consisting of a say routine that prints out the result of the expression to the right of it to standard output, followed by a newline character. Every time get-prime is called, a new number, the prime number calculated by the expression, is printed out on a separate line. Here it is:

say ($x.grep: *.is-prime)[$nth - 1];

So how is the number printed calculated? Well, the first thing you have to understand is that the code inside the parentheses results in a data structure called a Sequence which is basically a list of data in a specific order. This means Sequences are a type of Positional data structure. For the purposes of this discussion, that means we can find a specific value in the Sequence using the square bracket notation, the [$nth - 1] bit you see there on the end where $nth is the value passed into the subroutine. So this is how we tell the code in the parentheses which prime number to pull out. Those new to programming may be wondering why we subtract "1" from $nth. This small nice touch makes the subroutine more intuitive to use because a Sequence's index number starts at '0', not '1'. So to get the first element, we pass in a value of "1" which we gets reduced to "0" for us. If we didn't subtract one, passing in a "5" would actually return the 6th prime number, which is confusing.

You can imagine that in between the parentheses is every prime number that can exist from 0 to infinity (but that hasn't actually been calculated and so uses no memory). The number in the brackets chooses which number in that list to select, whether it be the 1st, 2nd, 3rd, 10th, or 10,232nd.

Now let's look inside the parentheses in our line of code in the subroutine, the code that generates the Sequence. We can see our value $x in there representing every positive integer possible, both primary and non-primary numbers. But, we don't want all numbers, we only want a list of all the primary numbers. So what we do is run the grep method on our infinite list of numbers by placing a . after $x, followed by a method called grep. grep is named after the command grep found on computers since the 70s to find text inside of lots of computer files on your storage device. You can think of grep as a filter that creates a list of stuff. It puts the stuff you want on a list and keeps the stuff you don't want off of it. As you might guess, it's the grep method that generates our Sequence of prime numbers for us.

Now all that's left to do is to tell grep what numbers we want on our list. We do that by passing an argument to grep, expressed as *.is-prime. Notice the colon immediately after grep. That indicates that what follows is the argument we will be passing to the grep method. Alternatively, we could do away with the colon and surround the *.is-primate argument with a set of parentheses. In line with one of Raku's mantras, "There is more than one way to do it" (TIMTOWTDI), it's up to you to decide what you think is most readable in a given situation.

So what exactly is the *.is-prime doing? It tells grep which stuff to place into the Sequence. You can think of it as a test that runs on every number in the range. First we look at the first number in the range, '0', and determine if it's prime with the is-prime method, one of the many math functions baked into Raku, making it a great language for people interested in solving math calculations. The is-prime method returns True if the number is prime and False if it isn't. If it's prime, grep will add the number to the Sequence. If it isn't prime, grep will filter it out and it won't get added to the Sequence. Then we go to the next number to determine if it's prime and so on until we reach infinity.

But again we have to stress--and what makes this code so fast--is that we only do these calculations for the prime numbers we are interested in. It would be very wasteful to calculate the 1,000th prime number when we are only interested in the 5th.

You can you think of the * symbol, what Raku calls the "Whatever" object, as a placeholder for each number in our infinite list (kind of like how the "glob" character is used in popular OS shells). The .is-prime method gets run on the "Whatever." Together, this expression can be read as "whatever is prime." The expression returns True if "Whatever" is prime or False if it isn't. If True, grep puts the tested number into the Sequence, the list of all the prime numbers, which again, isn't actually calculated (an impossible task). Only the minimum work necessary is done to determine the specific prime number we are looking for out of the theoretical series of all prime numbers that exist.

After the get-prime subroutine, we call it five different times, using a list of 5 numbers using a for loop:

for 5, 50, 500, 5000, 50000 { get-prime $_ };

For each number in the list of numbers we supply, we run the code in the curly braces which, in turn, calls the get-prime subroutine for us. The technical term for this kind of looping process is called "iteration".

Note the $_ variable in the curly braces. It has a special meaning in Raku. It is called the "topic variable." It's helpful to think of it to mean the "topic" of discussion. Each time we iterate over the list of our numbers, the topic variable gets assigned to the next number in the list and this becomes the $nth parameter the get-prime sub receives for its $nth argument.

Wow, so that's well over 1,000 words to explain just four lines of Raku code. It demonstrates the power of Raku and how how efficient it can be. Amazingly, we can make this bit of code even more concise:

for (5, 50, 500, 5000, 50000) { ((^Inf).grep: *.is-prime)[$_ - 1].say };

And don't worry if this seems a little overwhelming. Most of Raku is much more straightforward than this example so don't let yourself get scared off. The larger takeaway is Raku excels at taking hard problems and making them a whole lot easier, even problems that are nearly impossible or impractical in many other programming languages.

The brevity of Raku's code also makes it much easier to understand what a large code base is doing because the code won't be cluttered with dozens of lines of code. And, of course, fewer lines of code means fewer bugs. And for the bugs that do crop up, they'll be easier for you to isolate and squash.