On Mon, Feb 12, 2001 at 12:26:35AM +0000, Marcin 'Qrczak' Kowalczyk wrote:
I must say I like it. It has a good balance between generality and usefulness / convenience.
Modulo a few details, see below.
class (Num a, Additive b) => Powerful a b where (^) :: a -> b -> a instance (Num a) => Powerful a (Positive Integer) where a ^ 0 = one a ^ n = reduceRepeated (*) a n instance (Fractional a) => Powerful a Integer where a ^ n | n < 0 = recip (a ^ (negate n)) a ^ n = a ^ (positive n)
I don't like the fact that there is no Powerful Integer Integer. Since the definition on negative exponents really depends on the first type but can be polymorphic wrt. any Integral exponent, I would make other instances instead:
instance RealIntegral b => Powerful Int b instance RealIntegral b => Powerful Integer b instance (Num a, RealIntegral b) => Powerful (Ratio a) b instance Powerful Float Int instance Powerful Float Integer instance Powerful Float Float instance Powerful Double Int instance Powerful Double Integer instance Powerful Double Double
OK, I'm slow. I finally understand your point here. I might leave off a few cases, and simplify this to instance Powerful Int Int instance Powerful Integer Integer instance (Num a, SmallIntegral b) => Powerful (Ratio a) b instance Powerful Float Float instance Powerful Double Double instance Powerful Complex Complex (where "SmallIntegral" is a class that contains toInteger; "small" in the sense that it fits inside an Integer.) All of these call one of 3 functions: postivePow :: (Num a, SmallIntegral b) => a -> b -> a integerPow :: (Fractional a, SmallIntegral b) => a -> b -> a analyticPow :: (Floating a) => a -> a -> a (These 3 functions might be in a separate module from the Prelude.) Consequences: you cannot, e.g., raise a Double to an Integer power without an explicit conversion or calling a different function (or declaring your own instance). Is this acceptable? I think it might be: after all, you can't multiply a Double by an Integer either... You then have one instance declaration per type, just as for the other classes. Opinions? I'm still not very happy. Best, Dylan Thurston