Hello,
On Wed, Apr 16, 2008 at 11:06 PM, Martin Sulzmann
3) Multi-range FDs
Consider
class C a b c | a -> b c
instance C a b b => C [a] [b] [b]
This time it's straightforward.
C [x] y z yields the improvement y = [b] and z = [b] which then allows us to apply the instance.
I don't think that this improvement rule is justified (unless there are some assumptions that are added to the system that go beyond FD?). By the way, note that the above example does not have any instances for C, so lets first add a base case like this: instance C Char Bool Bool Now the instances for C are: { C Char Bool Bool, C [Char] [Bool] [Bool], ... }. Certainly, if you just consider these instances, then the improvement rule that you suggest is valid. However, suppose that we also add the instance: instance C [Int] Char Bool Note that this instance does not violate the FD: if we know the first argument, then we know exactly what are the other two arguments. In this context, it is not OK to improve C [x] y z as you suggest because 'x' may be instantiate to 'Int'. -Iavor