Recently I was golfing the "hyperfactorial," defined for a number 𝑛 as
𝑛**𝑛 × (𝑛-1)**(𝑛-1) × (𝑛-2)**(𝑛-2) × ... × 1. I created a quite
concise Raku function:
{ [*] [\*] $_...1 }
The only problem was that this function returns zero for a zero input,
whereas the hyperfactorial of 0 is supposed to be 1. Of course I could
have just handled zero as a special case, but I hoped to find something
comparably short. After a bit of thought I tried reversing both the range
and the operator:
{ [*] [\R*] 1..$_ }
It worked! But I couldn't quite see how. * is commutative, so isn't it
exactly the same as R*?
It turns out, in Raku it isn't quite the same. On the operators page, I
found that the R metaoperator produces an operator that reverses the order
of the arguments, but *also* has the opposite associativity. So, for
example, [\R*] 1..4 reduces from the right, producing the list (4, 12, 24,
24). Somehow I had formed the idea that Raku operators are left-, right-,
or list-associative, but I was wrong.
Anyway, pretty cool!
