[Haskell-cafe] Re: A question about "monad laws"

[Jonathan Cast]

On 11 Feb 2008, at 7:52 AM, Arnar Birgisson wrote:

> Hi all,
>
> On Feb 11, 2008 3:14 PM, apfelmus <apfelmus at quantentunnel.de> wrote:
>> I will be mean by asking the following counter question:
>>
>>    x + (y + z) = (x + y) + z
>>
>> is a mathematical identity. If it is a mathematical identity, a
>> programmer need not care about this law to implement addition + . Can
>> anyone give me an example implementation of addition that violates  
>> this law?
>
> Depends on what you mean by "addition". In general, algebraists call
> any associative and commutative operation on a set "addition", and
> nothing else. From that POV, there is by definition no "addition" that
> violates this law.

I agree.  The Num Double instance should be expelled from the Prelude  
immediately.

jcc

(What?  Haskell has a Float type?)