[Haskell-cafe] What is this applicative functor?

[Christopher Allen]

Ah right, I didn't stare hard enough at the Applicative.

If I squint a bit at the results of your Applicative instance it seems
similar to the difference between []'s Applicative and the ZipList
Applicative, except a little crossed up. Sure you already identified
that, sorry I don't have more to offer here.

On Tue, Jan 31, 2017 at 2:36 PM, Joachim Breitner
<mail at joachim-breitner.de> wrote:
> Hi,
>
> good idea, but no. The datatypes are superficially equivalent, but the
> Applicative instance differs:
>
> With NonEmpty’s instance:
>
>> (,) <$> 0 :| [1,2] <*> 3 :| [4,5]
> (0,3) :| [(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)]
>
> with my instance:
>
>> (,) <$> 0 :| [1,2] <*> 3 :| [4,5]
> (0,3) :| [(1,3),(2,3),(0,4),(0,5)]
>
> Greetings,
> Joachim
>
> Am Dienstag, den 31.01.2017, 14:24 -0600 schrieb Christopher Allen:
>> NonEmpty?
>>
>> On Tue, Jan 31, 2017 at 2:22 PM, Joachim Breitner
>> <mail at joachim-breitner.de> wrote:
>> > Hi,
>> >
>> > I recently wrote this applicative functor:
>> >
>> >     data OneStep a = OneStep a [a]
>> >
>> >     instance Functor OneStep where
>> >         fmap f (OneStep o s) = OneStep (f o) (map f s)
>> >
>> >     instance Applicative OneStep where
>> >         pure x = OneStep x []
>> >         OneStep f fs <*> OneStep x xs = OneStep (f x) (map ($x) fs
>> > ++ map f xs)
>> >
>> >     takeOneStep :: OneStep t -> [t]
>> >     takeOneStep (OneStep _ xs) = xs
>> >
>> > This was useful in the context of writing a shrink for QuickCheck,
>> > as
>> > discussed at http://stackoverflow.com/a/41944525/946226.
>> >
>> > Now I wonder: Does this functor have a proper name? Does it already
>> > exist in the libraries somewhere? Should it?
>> >
>> > Greetings,
>> > Joachim
>> >
>> > --
>> > Joachim “nomeata” Breitner
>> >   mail at joachim-breitner.de • https://www.joachim-breitner.de/
>> >   XMPP: nomeata at joachim-breitner.de • OpenPGP-Key: 0xF0FBF51F
>> >   Debian Developer: nomeata at debian.org
>> > _______________________________________________
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>>
>>
> --
> Joachim “nomeata” Breitner
>   mail at joachim-breitner.de • https://www.joachim-breitner.de/
>   XMPP: nomeata at joachim-breitner.de • OpenPGP-Key: 0xF0FBF51F
>   Debian Developer: nomeata at debian.org
>
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-- 
Chris Allen
Currently working on http://haskellbook.com