Aaron Denney wnoise at ofb.net
Mon Apr 7 07:36:59 EDT 2008

```On 2008-04-03, Chris Smith <cdsmith at twu.net> wrote:
> Hans Aberg wrote:
>> This problem is not caused by defining f+g, but by defining numerals as
>> constants.
>
> Yup.  So the current (Num thing) is basically:
>
> 1. The type thing is a ring
> 2. ... with signs and absolute values
> 3. ... along with a natural homomorphism from Z into thing
> 4. ... and with Eq and Show.
>
> If one wanted to be perfectly formally correct, then each of 2-4 could be
> split out of Num.  For example, 2 doesn't make sense for polynomials or n
> by n square matrices.  4 doesn't make sense for functions.  3 doesn't
> make sense for square matrices of dimension greater than 1.  And, this
> quirk about 2(x+y) can be seen as an argument for not wanting it in the
> case of functions, either.  I'm not sure I find the argument terribly
> compelling, but it is there anyway.

Just a nit, but 3 seems to make perfect sense for square matrices -- n
gets mapped onto I_d for any dimension d.

fromInteger (n*m) == fromInteger n * fromInteger m
fromInteger (n+m) == fromInteger n + fromInteger m

--
Aaron Denney
-><-

```