Thanks for the comments! On Mon, Feb 12, 2001 at 12:26:35AM +0000, Marcin 'Qrczak' Kowalczyk wrote:
I don't like the fact that there is no Powerful Integer Integer.
Reading this, it occurred to me that you could explictly declare an instance of Powerful Integer Integer and have everything else work.
Then the second argument of (^) is always arbitrary RealIntegral,
Nit: the second argument should be an Integer, not an arbitrary RealIntegral.
class (Real a, Floating a) => RealFrac a where -- lifted directly from Haskell 98 Prelude properFraction :: (Integral b) => a -> (b,a) truncate, round :: (Integral b) => a -> b ceiling, floor :: (Integral b) => a -> b
Should be RealIntegral instead of Integral.
Yes. I'd actually like to make it Integer, and let the user compose with fromInteger herself.
Perhaps RealIntegral should be called Integral, and your Integral should be called somewhat differently.
Perhaps. Do you have suggestions for names? RealIntegral is what naive users probably want, but Integral is what mathematicians would use (and call something like an integral domain).
class (Real a, Integral a) => RealIntegral a where quot, rem :: a -> a -> a quotRem :: a -> a -> (a,a)
-- Minimal definition: toInteger
You forgot toInteger.
Oh, right. I actually had it and then deleted it. On the one hand, it feels very implementation-specific to me, comparable to the decodeFloat routines (which are useful, but not generally applicable). On the other hand, I couldn't think of many examples where I really wouldn't want that operation (other than monadic numbers, that, say, count the number of operations), and I couldn't think of a better place to put it. You'll notice that toRational was similarly missing. My preferred solution might still be the Convertible class I mentioned earlier. Recall it was class Convertible a b where convert :: a -> b maybe with another class like class (Convertible a Integer) => ConvertibleToInteger a where toInteger :: a -> Integer toInteger = convert if the restrictions on instance contexts remain. Convertible a b should indicate that a can safely be converted to b without losing any information and maintaining relevant structure; from this point of view, its use would be strictly limited. (But what's relevant?) I'm still undecided here. Best, Dylan Thurston