[Haskell-cafe] What is this applicative functor?

[Matt]

Interestingly, neither NEL nor OneStep behave the same as `Product Identity
[]`:

λ> let a = Pair (Identity 0) [1,2]
λ> let b = Pair (Identity 3) [4,5]
λ> (,) <$> a <*> b
Pair (Identity (0,3)) [(1,4),(1,5),(2,4),(2,5)]

So many applicatives!

Matt Parsons

On Tue, Jan 31, 2017 at 3:41 PM, Christopher Allen <cma at bitemyapp.com>
wrote:

> 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
> >> > _______________________________________________
> >> > Haskell-Cafe mailing list
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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
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