In what way is it not a number?

data MyNumber a = MyNum a a
   deriving (Show, Eq)

instance Functor MyNum where
fmap f (MyNum a b) = MyNum (f a) (f b)

instance Applicative MyNum where
pure a = MyNum a a
MyNum f g <*> MyNum a b = MyNum (f a) (g b)

instance (Num a) => Num (MyNum a) where
a + b = pure (+) <*> a <*> b
a - b = pure (-) <*> a <*> b
a * b = pure (*) <*> a <*> b
negate a = pure negate <*> a
abs a = pure abs <*> a
signum = fmap signum
fromInteger = pure . fromInteger

This instance obeys the commutative, distributive, and associative laws, and the multiplicative, and additive identities. (at least, if the numbers it contains satisfy those laws)
How is MyNum not a number?

Sönke Hahn:
btw, I forgot to mention in my first email, but
      fromInteger n = (r, r) where r = fromInteger n
is better than:
      fromInteger n = (fromInteger n, 0)
as you get a lot of corner cases otherwise.

I use fromInteger = pure . fromInteger, which when combined with my Applicative instance, is effectively the same as your: fromInteger n = (r, r) where r = fromInteger n

- Job

On Mon, Oct 5, 2009 at 9:12 AM, Miguel Mitrofanov <miguelimo38@yandex.ru> wrote:

Sönke Hahn wrote:

I used to implement

fromInteger n = (r, r) where r = fromInteger n

, but thinking about it,
fromInteger n = (fromInteger n, 0)

seems very reasonable, too.

Stop pretending something is a number when it's not.

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