Re: [Haskell-cafe] Re: Numeric type classes

On 9/12/06, ajb@spamcop.net wrote:

G'day all.

Quoting Henning Thielemann :

...

More precisely: Can you tell me the difference between numbers and "more complex mathematical objects"?

Yes. A Num is anything which supports the common mathematically- significant operations which are supported by the basic built-in machine types such as Int and Double. It need not _be_ a built-in machine type, but it must support those operations.

And as an example of something which is useful as an instance of num but isn't a number I have a recent experience I can share. I was making an embedded domain specific language for excel spreadsheet formulas recently and found that making my formula datatype an instance of Num had huge pay offs. You write formulas in haskell code and then to turn them into something excel can chew on you only need to show them. I can even use things like Prelude.sum to add up cells. All I really needed was to define Show and Num correctly, neither of which took much mental effort or coding tricks. Now I get tons for free. Jason