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
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