Arbitrary mathematical relations, not just hashes

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Many programming languages (including Perl, Ruby, and PHP) support hashes:

$color['apple'] = 'red';
$color['ruby'] = 'red';

$type['apple'] = 'fruit';
$type['ruby'] = 'gem';

This quickly lets me find the color or type of a given item.

In this sense, color() and type() are like mathematical functions.

However, I can't easily find all items whose $color is 'red', nor all
items whose $type is 'fruit'. In other words, color() and type()
aren't full mathematical relations.

Of course, I could create the inverse function as I go along:

$inverse_color['red'] = ['apple', 'ruby']; # uglyish, assigning list to value

and there are many other ways to do this, but they all seem kludgey.

Is there a clean way to add 'relation' support to Perl, Ruby, or PHP?

Is there a language that handles mathematical relations naturally/natively?

I realize SQL does all this and more, but that seems like overkill for
something this simple?

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