Re: [Haskell-cafe] Questions about the Functor class and it's use in "Data types à la carte"

Dominic Steinitz dominic.steinitz at
Sun Dec 16 12:28:36 EST 2007

Roberto Zunino wrote:
> Dominic Steinitz wrote:
>> This would give
>> = \x -> bot x
>> and by eta reduction
> This is the point: eta does not hold if seq exists.
>   undefined `seq` 1 == undefined
>   (\x -> undefined x) `seq` 1 == 1

Ok I've never used seq and I've never used unsavePerformIO. Provided my
program doesn't contain these then can I assume that eta reduction holds
and that (.) is categorical composition?

> The "(.) does not form a category" argument should be something like:
>   id . undefined == (\x -> id (undefined x)) /= undefined
> where the last inequation is due to the presence of seq. That is,
> without seq, there is no way to distinguish between undefined and (const
> undefined), so you could use a semantic domain where they coincide. In
> that case, eta does hold.

It would be a pretty odd semantic domain where 1 == undefined. Or
perhaps, I should say not a very useful one.

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