On Sat, 2007-08-18 at 19:26 +0000, DavidA wrote:
Hi,
I am trying to implement quadratic fields Q(sqrt d). These are numbers of the form a + b sqrt d, where a and b are rationals, and d is an integer.
In an earlier attempt, I tried data QF = QF Integer Rational Rational (see http://www.polyomino.f2s.com/david/haskell/hs/QuadraticField.hs.txt) The problem with this approach is that it's not really type-safe: I can attempt to add a + b sqrt 2 to c + d sqrt 3, whereas this should be a type error because 2 /= 3.
So I thought I'd have a go at doing it with phantom types. In effect I'd be using phantom types to simulate dependent types. Here's the code:
{-# OPTIONS_GHC -fglasgow-exts #-}
import Data.Ratio
class IntegerType a where value :: Integer
data Two instance IntegerType Two where value = 2
data Three instance IntegerType Three where value = 3
data QF d = QF Rational Rational deriving (Eq)
instance IntegerType d => Show (QF d) where show (QF a b) = show a ++ " + " ++ show b ++ " sqrt " ++ show value
instance IntegerType d => Num (QF d) where QF a b + QF a' b' = QF (a+a') (b+b') negate (QF a b) = QF (-a) (-b) QF a b * QF c d = QF (a*c + b*d*value) (a*d + b*c) fromInteger n = QF (fromInteger n) 0
The problem is, this doesn't work. GHC complains: The class method `value' mentions none of the type variables of the class IntegerType a When checking the class method: value :: Integer In the class declaration for `IntegerType'
Is what I'm trying to do reasonable? If no, what should I be doing instead? If yes, why doesn't GHC like it?
When you write 'value' how is GHC supposed to know what instance you want? The typical trick is to add what could be called a phantom argument to propagate the type. I.e. class IntegerType a where value :: a -> Integer instance IntegerType Two where value _ = 2 value (undefined :: Two) == 2