Revised numerical prelude, version 0.02

[Marcin 'Qrczak' Kowalczyk]

Tue, 13 Feb 2001 18:32:21 -0500, Dylan Thurston <dpt@math.harvard.edu> pisze:

> Here's a revision of the numerical prelude.

I like it!

> > 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

These should be SmallIntegral.

> For an instance of RealIntegral a, it is expected that a `quot` b
> will round towards minus infinity and a `div` b will round towards 0.

The opposite.

> > class (Real a) => SmallReal a where
> >     toRational :: a -> Rational
> > class (SmallReal a, RealIntegral a) => SmallIntegral a where
> >     toInteger :: a -> Integer
> 
> These two classes exist to allow convenient conversions, primarily
> between the built-in types.  These classes are "small" in the sense
> that they can be converted to integers (resp. rationals) without loss
> of information.

I find names of these classes unclear: Integer is not small integral,
it's big integral (as opposed to Int)! :-)

Perhaps these classes should be called Real and Integral, with
different names for current Real and Integral. But I don't have
a concrete proposal.

-- 
 __("<  Marcin Kowalczyk * qrczak@knm.org.pl http://qrczak.ids.net.pl/
 \__/
  ^^                      SYGNATURA ZASTĘPCZA
QRCZAK