Hi, I spent about a half hour toying around with this and came up with the following, which seems to work (in ghci, but not hugs -- question for smart people: which is correct, if either?)...
class Mul a b c | a b -> c where mul :: a -> b -> c -- our standard multiplication, with fundeps data Commute a b = Commute a b -- just pair them -- now, our helper class class Mul2 x a b c | a b -> c where mul2 :: x a b -> c -- given a helper instance with Commute, we have an instance of the -- original Mul class instance Mul2 Commute a b c => Mul a b c where mul a b = mul2 (Commute a b) -- now, we make Mul2 commutative over Commute: instance Mul2 Commute a b c => Mul2 Commute b a c where mul2 (Commute i j) = mul2 (Commute j i) -- helper function: i2d :: Int -> Double i2d = fromInteger . toInteger -- finally we can make our definition: instance Mul2 Commute Int Int Int where mul2 (Commute i j) = i * j instance Mul2 Commute Int Double Double where mul2 (Commute i j) = i2d i * j -- note that we don't have to define Mul2 Commute Double Int Double instance Mul Commute Double Double Double where mul2 (Commute i j) = i * j -- we can now test these i :: Int i = 3 d :: Double d = 5 -- now, in ghci: *TryCommute> mul i i 9 *TryCommute> mul i d 15.0 *TryCommute> mul d d 25.0 *TryCommute> mul d i 15.0 Woohoo, even the last one worked. Of course, like so many things, this requires -fallow-overlapping-instances as well as -fallow-undecidable-instances. Interestingly, with -98, Hugs doesn't allow this program, saying: ERROR "TryCommute.hs":23 - Instances are not consistent with dependencies *** This instance : Mul2 Commute a b c *** Conflicts with : Mul2 Commute Int Int Int *** For class : Mul2 a b c d *** Under dependency : b c -> d I'm not entirely sure why.... -- Hal Daume III "Computer science is no more about computers | [EMAIL PROTECTED] than astronomy is about telescopes." -Dijkstra | www.isi.edu/~hdaume On Sat, 14 Dec 2002 [EMAIL PROTECTED] wrote: > I want to use functional dependencies in a way I've not yet seen: to enforce >commutativity. > > I define > > class Mul a b c | a b -> c, b a -> c where mul :: a -> b -> c > > I want > > instance (Mul a b c) => Mul b a c where mul x y = mul y x > > do what I expect: if I can multiply a and b, then I can multiply b and a _and always >have the same type_. In a sense, this makes multiplication commute (in the land of >types). > > For a whole variety of reasons, the many (4 or 5 now) ways I've tried to make this >work have failed, both using Hugs and GHC. > > I mentioned I wanted typed multiplication to commute. Let me explain more >thoroughly: suppose I had > > data Unit u v = Unit u v > > I want (Unit u1 value1) `mul` (Unit u2 value2) to have the same type as (Unit u2 >value2) `mul` (Unit u1 value1). So say u1 :: Int, u2 :: Float, then > > (Unit u1 value1) `mul` (Unit u2 value2) :: (Unit Int (Unit Float blah)) > and > (Unit u2 value2) `mul` (Unit u1 value1) :: (Unit Int (Unit Float blah)) > > I don't care if the result type is Unit Int ... or Unit Float ..., as long as it is >a) consistent and b) inferred and c) enforced. So far, no luck. > > A few other questions: > > What happenned to +m in Hugs? > > In general, if I wanted a fundep to specify that a pair (a, b) determined c >_regardless of the order of a and b_, how could it be done? Why doesn't a b -> c, b >a -> c do this? What I mean is that if I have one of a, b and Int (say) and c a >Float, then I could infer the other of a, b once I have a single instance. > > And a 'bug' report: in the overlapping instance one-liner above, the Mul a b c => >Mul b a c, I can have this in place and write contradictory instances that violate >the fundeps that are not caught in GHC. (Hugs does not allow the overlapping >instances to begin with, even worse.) > > Well, that became a clearinghouse for the frustrations of the last several days. >Sorry. > > Thanks, > Nick > _______________________________________________ > Haskell mailing list > [EMAIL PROTECTED] > http://www.haskell.org/mailman/listinfo/haskell > _______________________________________________ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell
