Martin Sulzmann wrote:
We're also looking for (practical) examples of "multi-range" functional dependencies
class C a b c | c -> a b
Notice that there are multiple (two) parameters in the range of the FD.
It's tempting to convert the above to
class C a b c | c -> a, c -> b
but this yields a weaker (in terms of type improvement) system.
I agree with Iavor. In fact, the two sets of dependencies that you have given here are provably equivalent, so it would be decidedly odd to have a "type improvement" system that distinguishes between them. While you're looking for unusual examples of fundeps, you might also want to consider things like: class C a b c | a -> b, b -> c Note that this is subtly different from a -> b c because {a -> b, b -> c} |= {a -> b c} while the reverse does not hold. Instead of type classes, I'll give you some more down-to-earth examples of relations that satisfy these dependencies: {Paper, Conference, Year} {Professor, University, Country} {Person, FavoriteFood, FoodGroup} ... For further insight, you might want to take a look at the theory of relational databases to see how functional dependencies are used there. In that context, some sets of dependencies (such as {a -> b, b -> c}) can be interpreted as indicators of bad design. This, in turn, might give you some ideas about the kinds of dependencies you can expect to encounter in well-designed Haskell code. (Of course, you might still find examples in other Haskell code of dependencies that would make a database person wince :-) All the best, Mark