On 2/21/12 2:17 AM, Roman Cheplyaka wrote:
* Sebastian Fischer<[email protected]> [2012-02-21 00:28:13+0100]
On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyaka<[email protected]> 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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