[Haskell-cafe] Monad laws in presence of bottoms
wren ng thornton
wren at freegeek.org
Tue Feb 21 16:44:27 CET 2012
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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