[Haskell-cafe] Re: Function Precedence
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
> 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
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