[Haskell-cafe] Monad laws in presence of bottoms

[MigMit]

Ehm... why exactly don't domain products form domains?

On 21 Feb 2012, at 19:44, wren ng thornton wrote:

> On 2/21/12 2:17 AM, Roman Cheplyaka wrote:
>> * Sebastian Fischer<fischer at nii.ac.jp>  [2012-02-21 00:28:13+0100]
>>> On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyaka<roma at ro-che.info>  wrote:
>>> 
>>>> Is there any other interpretation in which the Reader monad obeys the
>>>> laws?
>>> 
>>> 
>>> If "selective strictness" (the  seq  combinator) would exclude function
>>> types, the difference between  undefined  and  \_ ->  undefined  could not
>>> be observed. This reminds me of the different language levels used by the
>>> free theorem generator [1] and the discussions whether  seq  should have a
>>> type-class constraint..
>> 
>> It's not just about functions. The same holds for the lazy Writer monad,
>> for instance.
> 
> That's a similar sort of issue, just about whether undefined == (undefined,undefined) or not. If the equality holds then tuples would be domain products[1], but domain products do not form domains! In order to get a product which does form a domain, we'd need to use the smash product[2] instead. Unfortunately we can't have our cake and eat it too (unless we get rid of bottom entirely).
> 
> Both this issue and the undefined == (\_ -> undefined) issue come down to whether we're allowed to eta expand functions or tuples/records. While this is a well-studies topic, I don't know that anyone's come up with a really pretty answer to the dilemma.
> 
> 
> [1] Also a category-theoretic product.
> 
> [2] Aka: data SmashProduct a b = SmashProduct !a !b
> 
> -- 
> Live well,
> ~wren
> 
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