A sample revised prelude for numeric classes

[Marcin 'Qrczak' Kowalczyk]

Sun, 11 Feb 2001 22:27:53 -0500, Dylan Thurston <dpt@math.harvard.edu> pisze:

> Reading this, it occurred to me that you could explictly declare an
> instance of Powerful Integer Integer and have everything else work.

No, because it overlaps with Powerful a Integer (the constraint on a
doesn't matter for determining if it overlaps).

> > Then the second argument of (^) is always arbitrary RealIntegral,
> 
> Nit: the second argument should be an Integer, not an arbitrary
> RealIntegral.

Of course not. (2 :: Integer) ^ (i :: Int) makes perfect sense.

> > 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

It is needed for conversions (fromIntegral in particular).

>   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

This requires to write a Convertible instance in addition to
ConvertibleToInteger, where currently mere toInteger in Integral
suffices.

Since Convertible must be defined separately for each pair of types
(otherwise instances would easily overlap), it's not very useful for
numeric conversions. Remember that there are a lot of numeric types
in the FFI: Int8, Word16, CLong, CSize. It does not provide anything
in this area so should not be required to define instances there.

After a proposal is developed, please check how many instances one
has to define to make a type the same powerful as Int, and is it
required to define methods irrelevant to non-mathematical needs.
basAlgPropos fails badly in this criterion.

> Convertible a b should indicate that a can safely be converted to
> b without losing any information and maintaining relevant structure;

So fromInteger does not require Convertible, which is inconsistent
with toInteger. Sorry, I am against Convertible in Prelude - tries
to be too general, which makes it inappropriate.

-- 
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