Re: [Haskell-cafe] Monad laws in presence of bottoms

On 2/21/12 2:17 AM, Roman Cheplyaka wrote:

* Sebastian Fischer [2012-02-21 00:28:13+0100]

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On Mon, Feb 20, 2012 at 7:42 PM, Roman Cheplyaka wrote:

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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