Good observation! I forgot about this.... so one gets the difference and the intersection with one operation, thats brilliant.

So a simple upgrade of delete with an extra switch to ignore undefs would give Perl a native primitive to handle set operations...

And I enjoyed your post too, I'm still meditating about how to make use of your approach...

> (Even though I am a failed mathematician, it does sting a little that you felt the need to give me a link to De Morgan's laws.)

The link wasn't meant for you, believe me. :)

I'm mathematician by training but not a native English speaker, so I need to elaborate my posts longer and stuff them with extra informations to avoid misunderstandings. (And the monastery is full of obsessed nitpickers...)

Such a kind response deserves a little extra effort. Below is my "cleanest" attempt at solving your puzzle. It was motivated by two facts 1) I was wrong about the behavior of delete in that it returns the deleted values, not the deleted keys, so the "value equal key" array is necessary and 2) I've read a few responses on perlmonks that say hash elements that have undef as a value actually point to the same undef and thus potentially save some space. (I cannot find this stated in the documentation, but it probably is that I just don't know where to look; plus all the keywords that spring to mind are ubiquitous ;-)

• Union is dead easy.
• Intersection uses a temporary hash as well as a grep. I chose this way as being more succinct than efficient, but admit it violates your rules.
• Symmetric Difference is about the same effort as two intersections; however, there is no grep!

All three constructs were written to be independent of the others, but obviously that need not be a constraint; thus symmetric difference could be as easy as taking a copy of the union and deleting the intersection (as in your approach). I decided to make intersection "easier" than symmetric difference because I think intersections are more common, at least in the type of code I write. Lastly, I have decided to have all the result hashes "look the same" in that every element value is undef--which may or may not be more efficient!

That's all I can do. Thanks, this has been fun.

#!/usr/bin/env perl

use strict;
use warnings;
use Data::Dump qw(pp);

my @A = qw( 1 2 3 4 5 );
my @B = qw(     3 4 5 6 7 );

my %unionAB;
@unionAB{@A,@B} = undef;

my %interAB;
{
    my (%tmpA);
    @tmpA{@A} = @A;
    @interAB{(grep {defined} delete @tmpA{@B})} = undef;
}

my %sdiffAB;
{
    my (%tmpA, %tmpB);
    @tmpA{@A} = @A;
    @tmpB{@B} = @B;
    delete @tmpA{@B};
    delete @tmpB{@A};
    @sdiffAB{keys %tmpA, keys %tmpB} = undef;
}

# View results
print 'unionAB: ', pp(\%unionAB), "\n";
print 'interAB: ', pp(\%interAB), "\n";
print 'sdiffAB: ', pp(\%sdiffAB), "\n";
[download]

(Sadly, I feel your point about adding detail. Most of my time not coding was spent trying to guard against the charge that I'm an idiot who doesn't know set theory. Of course if my beloved Dr. Kaiser were on perlmonks and posted such, I would have to agree, but since he loves PROLOG, I think I'm safe.)

Thanks! :)

> Lastly, I have decided to have all the result hashes "look the same" in that every element value is undef--which may or may not be more efficient!

unfortunately this collides with my requirement to support all kind of sets:

From the OP

This is fundamentally wrong because keys are stringifications and any reference type will not be reproduced (just think about arrays of objects or a AoH or ...)

Cheers Rolf