Arbitrary mathematical relations, not just hashes

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? -- We're just a Bunch Of Regular Guys, a collective group that's trying to understand and assimilate technology. We feel that resistance to new ideas and technology is unwise and ultimately futile.