[Haskell-cafe] adding the elements of two lists

[Chris Smith]

Jerzy Karczmarczuk <jerzy.karczmarczuk at unicaen.fr> wrote:
> Le 26/03/2012 01:51, Chris Smith a écrit :
>
>>     instance (Num a) => Num [a] where
>>         xs + ys = zipWith (+) xs ys
>>
>> You can do this in the sense that it's legal Haskell... but it is a bad idea [...]

> It MIGHT be a ring or not. The "real problem" is that one should not confuse
> structural and algebraic (in the "classical" sense) properties of your
> objects.

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.  By the
time you get a ring structure back by some *other* set of rules,
particularly for multiplication, the result will so clearly not be
anything like a general Num instance for lists that it's silly to even
be having this discussion.

-- 
Chris Smith