Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)

On 5 Oct 2009, at 21:06, Lennart Augustsson wrote:

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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.

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On Mon, Oct 5, 2009 at 6:46 PM, Miguel Mitrofanov

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wrote:

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"Just pairs" have no natural arithmetic upon them.

Exactly my point.

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BTW. the missing term of M.M. is DUAL NUMBERS.

Remembered this already. Thanks anyway.

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