In hoc signo vinces (Was: Revamping the numeric classes)

[Dylan Thurston]

On Fri, Feb 09, 2001 at 12:55:12PM -0800, William Lee Irwin III wrote:
> class  (Eq a, Show a) => Num a  where
>     (+), (-), (*)   :: a -> a -> a
>     negate          :: a -> a
>     abs, signum     :: a -> a
>     fromInteger     :: Integer -> a
>     fromInt         :: Int -> a -- partain: Glasgow extension
>
> ...  So we have two totally inappropriate operations (fromInteger and
> fromInt), ...

I beg to differ on this point.  One could provide a default
implementation for fromInt(eger) as follows, assuming a 'zero' and
'one', which do obviously fit (they are the additive and
multiplicative units):

  fromInteger n | n < 0 = negate (fromInteger (-n))
  fromInteger n = foldl (+) zero (repeat n one)

(Of course, one could use the algorithm in integer exponentiation to
make this efficient.)

Best,
	Dylan Thurston