[Haskell-cafe] Thoughts about redesigning "Num" type class

[DreamApart AtHaskells]

​sorry, didn't realize​
​
​ the subjects​ prefixed with a "[Haskell-Cafe]"



2015-09-07 22:08 GMT+08:00 DreamApart AtHaskells <rnmss.hs at gmail.com>:

> The class Num defines the method functions like (+), (-), (*), negate, ...
> But they are actually different concepts.
>
> We often meet situations that we want an addition for some type, but
> not a multiplication. For example:
>
>     *data* Vec3 = Vec3 Float Float Float
>
> The additive (and subtractive) operation is obvious, but not for a
> multiplication.
>
> *  Note*
>
>     (*) :: a -> a -> a   -- not avaliable for a Vec3
>
>     scale :: Float -> Vec3 -> Vec3
>     dot :: Vec3 -> Vec3 -> Float
>
> We cannot define a (+) alone for a type, so we got many different
> functions
> from different libs, like mappend, mplus, plus, (<+>), (.+.), (+.), which
> all reads
> "plus".
>
> My opinion is that the methods of Num should be seperated into different
> type
> classes, so we don't need to invent a new symbol for a new lib.
>
> A feasible design is:
>
>     *import* Prelude *hiding* ( Num (..), Monoid (..), sum )
>
>     *class* SemiGroup a *where*
>         (+)         :: a -> a -> a
>
>     *class* SemiGroup a => Monoid a *where*
>         zero        :: a
>
>     *class* Monoid a => Group a *where*
>         negate      :: a -> a
>         (-)         :: a -> a -> a
>
>         x - y    = x + negate y
>         negate x = zero - x
>
>     *class* Group a => Ring a *where   *-- not sure about the name ...
>         (*)         :: a -> a -> a
>
>     *class* Ring a => Num a *where*
>         abs         :: a -> a
>         signum      :: a -> a
>         fromInteger :: Integer -> a
>
>     sum :: (Foldable t, Monoid a) => t a -> a
>     sum = foldl' (+) zero
>
>     -- for compatibility
>     mempty = zero
>     mappend = (+)
>     mconcat = sum
>
>
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