NOTE: 30 minutes from now is the start of the Raku Study Group of the San Francisco Perl Mongers. We can offer a "deep dive" into how the Leyland code works, if that would be helpful. Zoom details here: https://mail.pm.org/pipermail/sanfrancisco-pm/2020-October/004726.html
> On Oct 11, 2020, at 10:39 AM, Cezmi Pastirma <cezmisi...@yandex.com> wrote: > > I've got a question about a Leyland-numbers-listing Raku code which I saw at > codegolf.stackexchange.com at https://codegolf.stackexchange.com/a/83013/98132 > > I've slightly rearranged the code to make it print Leyland numbers up to 1 > Billion: > .say for grep {$_ < 1E11}, squish(sort [X[&({$^a**$^b+$b**$a})]] 2..32,2..32) > > The question in short is: > > How does the cross reduce work there? The reduction is a red herring to our understanding here. Note that, when you are only [reducing] on two lists, `[any_op_here] @a, @b` is the same as `@a any_op_here @b`. These are equivalent: say [X+] 2..4, 1..5; say 2..4 X+ 1..5; The operator need not be a meta-operator: say [*] 3, 5; say 3 * 5; > Extra info: > > That cross reduce section surely does what this half-pseudo code tries to do: > map { $^a ** $^b + $b ** $a }, 2..32,32…2 If @c has 20 elements, and @d has 30 elements, then `@c X+ @d` has 600 elements. You cannot produce the equivalent with a simple `map`. (You could with a flattened map-within-a-map) Simplifying your "slightly rearranged” code: .say for grep {$_ < 1E11}, squish(sort [X[&({$^a**$^b+$b**$a})]] 2..32,2..32) ...to just the part you are curious about, we get: say [X[&({$^a**$^b+$b**$a})]] 2..4,2..4; (8 17 32 17 54 145 32 145 512) We are only [reducing] on two lists, so we can remove the reduction, and just use the Xop: say 2..4 X[&({$^a**$^b+$b**$a})] 2..4; (8 17 32 17 54 145 32 145 512) > The tricky part here is the use of reduce operators two times in a row, once > before the cross operator, once before the & operator, which I guess donates > a closure. How to interpret this usage of operators? > The square brackets after the X, I think you mis-took as a second reduction. Those brackets are just there to disambiguate the `op` that the `X` is crossing on. See: https://docs.raku.org/language/operators#Nesting_of_metaoperators These are equivalent: .say for ^2 X+ ^2; .say for ^2 X[+] ^2; We can create our own operator, to further separate the Cross from the Op: multi infix:<⨁> ($a, $b) { $a ** $b + $b ** $a }; say 2 ⨁ 3; say 2..4 X⨁ 2..4; 17 (8 17 32 17 54 145 32 145 512) The `X` itself is the operator-form of the `cross` routine, well-documented here: https://docs.raku.org/routine/cross https://docs.raku.org/language/operators#index-entry-X_(cross_metaoperator) https://docs.raku.org/language/operators#index-entry-cross_product_operator If any part of this was lacking in clarity, please let me know where to focus, and I will be glad to expound. -- Hope this helps, Bruce Gray (Util of Perlmonks)
