[Haskell-cafe] adding the elements of two lists

[Chris Smith]

Jerzy Karczmarczuk <jerzy.karczmarczuk at unicaen.fr> wrote:
> Le 26/03/2012 02:41, Chris Smith a écrit :
>> Of course there are rings for which it's possible to represent the
>> elements as lists.  Nevertheless, there is definitely not one that
>> defines (+) = zipWith (+), as did the one I was responding to.
>
> What?
>
> The additive structure does not define a ring.
> The multiplication can be a Legion, all different.

I'm not sure I understand what you're saying there.  If you were
asking about why there is no ring on [a] that defines (+) = zipWith
(+), then here's why.  By that definition, you have [1,2,3] + [4,5] =
[5,7].  But also [1,2,42] + [4,5] = [5,7].  Addition by [4,5] is not
one-to-one, so [4,5] cannot be invertible.

-- 
Chris Smith