[Haskell-cafe] Reifying case expressions [was: Re: On stream processing, and a new release of timeplot coming]

[Eugene Kirpichov]

On Tue, Dec 27, 2011 at 7:23 AM, Sebastian Fischer <fischer at nii.ac.jp>wrote:

> 2011/12/26 Eugene Kirpichov <ekirpichov at gmail.com>
>
>> Whoa. Sebastian, you're my hero — I've been struggling with defining
>> Arrow for ListTransformer for a substantial time without success, and here
>> you got it, dramatically simpler than I thought it could be done (I was
>> using explicit queues).
>>
>
> This stuff is tricky. I noticed that my Applicative instance did not
> satisfy all required laws. I think I could fix this by changing the
> implementation of pure to
>
>     pure x = Put x $ pure x
>
> in analogy to the ZipList instance. At least, QuickCheck does not complain
> anymore (I did not write proofs).
>
> The original definition of `pure` was inspired by Chris Smith's post on
> the connection of Category/Applicative and Arrow:
>
>
> http://cdsmith.wordpress.com/2011/08/13/arrow-category-applicative-part-iia/
>
> However, even with the fixed Applicative instance, the Arrow instance does
> not satisfy all laws. ListTransformer seems to be a type that has valid
> Category and Applicative instances which do not give rise to a valid Arrow
> instance as outlined by Chris. One of his additional axioms relating
> Category and Applicative does not hold.
>
> I have extended the (corrected) code with QuickCheck tests:
>
>     https://gist.github.com/1521467
>
Thanks, I'll take a look.


>
>  I wonder if now this datatype of yours is isomorphic to StreamSummary b
>> r -> StreamSummary a r.
>>
>
> Not sure what you mean here. StreamSummary seems to be the same as
> ListConsumer but I don't see how functions from consumers to consumers are
> list transformers, i.e., functions from lists to lists.
>
Well. They are isomorphic, if list transformers are represented as
functions from lists. I'm assuming they could be with the other
representation too.

type ListT a b = forall r . ([b] -> r) -> ([a] -> r)

there :: ([a] -> [b]) -> ListT a b
there as2bs bs2r = bs2r . as2bs

back :: ListT a b -> ([a] -> [b])
back f = f id


>
> Sebastian
>



-- 
Eugene Kirpichov
Principal Engineer, Mirantis Inc. http://www.mirantis.com/
Editor, http://fprog.ru/
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