[Haskell-cafe] Monad laws in presence of bottoms
miguelimo38 at yandex.ru
Tue Feb 21 17:27:51 CET 2012
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
>>> 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  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, 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 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.
>  Also a category-theoretic product.
>  Aka: data SmashProduct a b = SmashProduct !a !b
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