> > On 5 Oct 2009, at 21:06, Lennart Augustsson wrote: > > OK, "just pairs" have no arithmetic, but one way of defining > > arithmetic is to treat the pairs as complex numbers. Or as mantissa > > and exponent. Or as something else. So there's nothing wrong, IMO, > > to make pairs an instance of Num if you so desire. (Though I'd > > probably introduce a new type.)
I was looking for one intuitive way of instantiating pairs of numbers as Num. One where i wouldn't have to look in the documentation to remember what (+) does. So considering all these examples of what pairs of numbers could be, i agree with Miguel Mitrofanov: "It's something that should not be done." Two questions remain, i think: 1. How can i have some notion of addition and subtraction for something that i don't want to put in the Num class? That's easy: I could just write a class that defines binary operators (like (+~) and (-~), for example). I don't get the fanciness of (+), but that's okay. 2. How can i use numeric literals to construct values, whose types are not in the Num class? Haskell could provide a class IsNumber (like IsString for string literals). Is that something we would want? BTW, interesting discussion, thanks! Sönke On Monday 05 October 2009 07:24:37 pm Miguel Mitrofanov wrote: > And I agree that sometimes it can be suitable. > > But simply "defining an instance of Num" without a single word on the > problem one > is trying to solve is not just pointless. It's something that should > not be done. > > > > On Mon, Oct 5, 2009 at 6:46 PM, Miguel Mitrofanov <miguelim...@yandex.ru > > > > > wrote: > > > > >>> "Just pairs" have no natural arithmetic upon them. > >> > >> Exactly my point. > >> > >>> BTW. the missing term of M.M. is DUAL NUMBERS. > >> > >> Remembered this already. Thanks anyway. > >> > >> _______________________________________________ > >> Haskell-Cafe mailing list > >> Haskell-Cafe@haskell.org > >> http://www.haskell.org/mailman/listinfo/haskell-cafe > > > > _______________________________________________ > > Haskell-Cafe mailing list > > Haskell-Cafe@haskell.org > > http://www.haskell.org/mailman/listinfo/haskell-cafe > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe > _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
