Is there an elegant way in Raku to see if two ranges overlap?

Is there an elegant way to see if two ranges have any overlap?

For instance, if

my $r = 1..10;
my $r1 = 2..5;
my $r2 = 7..15;

then $r1 ~~ $r is True. But $r ~~ $r1, $r2 ~~ $r, $r ~~ $r2 are all False.

Is there an elegant way to do this, and optionally even determine the overlap?

I can do (e.g.) $r ∩ $r1, but that creates a Set instead of a Range, and isn't feasible for huge ranges.

The following does the trick, but if there is a more elegant, built-in way, I'd prefer that.

sub infix:<∩>(Range $r1, Range $r2)
{
    my ($min1, $max1) = $r1.int-bounds;
    my ($min2, $max2) = $r2.int-bounds;
    return Nil if $max1 < $min2 || $max2 < $min1;
    return max($min1,$min2) .. min($max1,$max2);
}

my $r = 1..10;
my $r1 = 2..5;
my $r2 = 7..15;

say $r ∩ $r1;   # 2..5
say $r ∩ $r2;   # 7..10
say $r1 ∩ $r2;  # Nil

Solution

Here's how this works with my Math::Interval module:

use Math::Interval;

my $i0 = (1..10).Interval;
my $i1 = (2..5).Interval;
my $i2 = (7..15).Interval;

## smartmatch ~~ does the same as for Range ("x is contained by y")
say $i1 ~~ $i0;  # True
say $i0 ~~ $i1;  # False
say $i2 ~~ $i0;  # False 
say $i0 ~~ $i2;  # False

# cmp returns Nil on overlap (ie overlaps are not ordered)
say $i1 cmp $i0;  # Nil 
say $i0 cmp $i1;  # Nil 
say $i2 cmp $i0;  # Nil 
say $i1 cmp $i2;  # Less    NB. this is $i1 vs $i2!

#  ∩ [also (&)] gives the intersect as an Interval (ie a subset of Range)
say $i1  ∩  $i0;  # 2..5 
say $i0  ∩  $i1;  # 2..5 
say $i2  ∩  $i0;  # 7..10 
say $i1  ∩  $i2;  # Set()   NB. this is $i1 vs $i2!

say ($i1  ∩  $i0) ~~ Range;  # True

There are a couple of wrinkles here, but I believe that substantially this provides what you need.

its provided via a raku module you have to install with zef install Math::Interval
you need to use the .Interval coercion methid to convert a standard raku Range to an Interval (which is a subset of Range so can then be used interchangeably)
the intersect operation returns an Interval (which is a subset of Range) so will do what you need, except when there is no overlap ... in that case it gives back ∅ (aka the null Set())

I am open to changing this in the module, perhaps we need to specify what is meant by the null Range, eg. Nil..Nil ? I have made an issue for this here, all f/back welcome!