El sáb, 28-08-2010 a las 03:44 -0700, Greg escribió:
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The class definition doesn't mean "div2pi can return any type of Floating value", it means "div2pi *will* return any type of floating value".
I would say it like this: div2pi does not return a type of Floating value of its own choosing, it is able to return every type of Floating value (the concrete type is then chosen by the context in each case where div2pi is used).
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If this is right, then my class definition:
class TwoPi a where div2pi :: (Floating b) => a -> b
is essentially impossible to conform to because b is completely untethered to anything else in the code and not all "(Floating b)"'s are created equal.
Actually, it is possible, because of functions like realToFrac, which return a type-class polymorphic value. Unfortunately, I have botched up the example in my post. Sorry for that. Corrected code is below.
Typeclasses provide a mechanism to abstract operations over multiple types, as you mentioned in the thread for my last question. What I'm trying to figure out now is what kinds of types they can be abstracted over. I'm looking to get the result: "((5.6,Foo 9.8),(0.8912676813146139,1.5597184423005745))"
From code that looks kind of like this :
data Foo a = Foo a deriving (Show)
x :: Float x= 5.6
y :: Foo Double y= Foo 9.8
class {-something-} TwoPi {-something-} where div2pi :: {-something-}
instance {-something-} TwoPi Foo where div2pi (Foo b) = b / (2*pi)
instance TwoPi Float where div2pi a = a / (2*pi)
main = do print ((x,y),(div2pi x, div2pi y))
This works: data Foo a = Foo a deriving Show x :: Float x= 5.6 y :: Foo Double y= Foo 9.8 class TwoPi a where div2pi :: (Floating b) => a -> b instance (Real a, Floating a) => TwoPi (Foo a) where div2pi (Foo a) = realToFrac a / (2*pi) instance TwoPi Float where div2pi a = realToFrac a / (2*pi) main = print ((x,y),(div2pi x, div2pi y)) *Main> main ((5.6,Foo 9.8),(0.8912676661364157,1.5597184423005745))
The (Real a) restriction in the instance definition for Foo a is necessary. If a would be Complex Double, for example, there is no way you can sensibly expect a Float return value.
Jürgen
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