On 2008-04-03, Chris Smith <[EMAIL PROTECTED]> 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 -><- _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
