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Today’s post is a follow-up. Exactly two years ago, Matthew Walton wrote on this blog about overloading operators:

You can exercise further control over the operator’s parsing by adding traits to the definition, such as `tighter``equiv` and `looser`, which let you specify the operator’s precedence in relationship to operators which have already been defined. Unfortunately, at the time of writing this is not supported in Rakudo so we will not consider it further today.

Rakudo is still lagging in precedence support (though at this point there are no blockers that I know about to simply going ahead and implementing it). But there’s a new implementation on the block, one that didn’t exist two years ago: Niecza.

Let’s try out operator precedence in Niecza.

```\$ niecza -e 'sub infix:<mean>(\$a, \$b) { (\$a + \$b) / 2 }; say 10 mean 4 * 5'
15```

Per default, an operator gets the same precedence as `infix<+>`. This is per spec. (How do we know it got the same precedence as `infix<+>` above? Well, we know it’s not tighter than multiplication, otherwise we’d have gotten the result 35.)

That’s all well and good, but what if we want to make our mean little operator evaluate tighter than multiplication? Nothing could be simpler:

```\$ niecza -e 'sub infix:<mean>(\$a, \$b) is tighter(&infix:<*>) { (\$a + \$b) / 2 }; say 10 mean 4 * 5'
35```

See what we did there? `is tighter` is a trait that we apply to the operator definition. The trait accepts an argument, in this case the language-provided multiplication operator. It all reads quite well, too: “infix mean is tighter [than] infix multiplication”.

Note the explicit use of intuitive naming for the precedence levels. Rather than the inherently confusing terms “higher/lower”, Perl 6 talks about “tighter/looser”, as in “multiplication binds tighter than addition”. Easier to think about precedence that way.

Internally, the precedence levels are stored not as numbers but as strings. Each original precedence level gets a letter of the alphabet and an equals sign (`=`). Subsequent added precendence levels append either a less-than sign (`<`) or a greater-than sign (`>`) to an existing precedence level representation. Using this system, we never “run out” of levels between existing ones (as we could if we were using integers, for example), and tighter levels always come lexigographically before looser ones. Language designers, take heed.

A few last passing notes about operators in Perl 6, while we’re on the subject:

• In Perl 6, operators are subroutines. They just happen to have funny names, like prefix:<-> or postfix:<++> or infix:<?? !!>. This actually takes a lot of the hand-wavey magic out of defining them. The traits that we’ve seen applied to operators are really subroutine traits… these just happen to be relevant to operator definitions.
• As a consequence, just like subroutines, operators are lexically scoped by default. Lexical scoping is something we like in Perl 6; it keeps popping up in unexpected places as a solid, sound design principle in the language. In practice, this means that if you declare an operator within a given scope, the operator will be visible and usable within that scope. You’re modifying the parser, but you’re doing it locally, within some block or other. (Or within the whole file, of course.)
• Likewise, if you want to export your operators, you just use the same exporting mechanism used with subroutines. See how this unification between operators and subroutines keeps making sense? (In Perl 6-land, we say “operators are just funny-looking subroutines”.)
• Multiple dispatch in operators works just as with ordinary subroutines. Great if you want to dispatch your operators on different types. As with all other routines in the core library in Perl 6, all operators are declared multi to be able to co-exist peacefully with module extensions to the language.
• Operators can be macros, too. This is not an exceptions to the rule that operators are subroutines, because in Perl 6, macros are subroutines. In other words, if you want some syntactic sugar to execute at parse time (which is what a macro does), you can dress it up either as a normal-looking sub, or as an operator.

That’s it for today. Now, go forth and multiply, or even define your own operator that’s either tighter or looser than multiplication.