[Haskell-cafe] What is this applicative functor?

[Oleg Grenrus]

These instances are quite similar to

https://github.com/ambiata/disorder.hs/blob/ce9ffc1139e32eaa9b82a1a6e2cfeb914d3f705c/disorder-jack/src/Disorder/Jack/Tree.hs#L62-L82

(I wish `disorder-jack` were already on Hackage!)

- Oleg


On 01.02.2017 07:28, David Menendez wrote:
> On Tue, Jan 31, 2017 at 11:55 PM, Joachim Breitner
> <mail at joachim-breitner.de <mailto:mail at joachim-breitner.de>> wrote:
>
>     Hi,
>
>     Am Dienstag, den 31.01.2017, 15:22 -0500 schrieb Joachim Breitner:
>     > 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
>     <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?
>
>     I guess it does not exist, so I am preparing a package for it here:
>     https://github.com/nomeata/haskell-successors
>     <https://github.com/nomeata/haskell-successors>
>
>     The source code contains (in comments) a proof of the Applicative
>     laws.
>
>     My gut feeling says that this does not have a Monad instance that is
>     compatible with the given Applicative instance, but it is too late
>     today to substantiate this feeling. If anyone feels like puzzling: Can
>     you come up with a Monad instance, or (more likely) give good reasons
>     why there cannot be one?
>
>
> How about this?
>
> hd (OneStep x xs) = x
>
> instance Monad OneStep where
>     OneStep x xs >>= f = OneStep y (map (hd . f) xs ++ ys)
>         where
>         OneStep y ys = f x
>
> Not sure if it’s good for anything, but it seems valid and consistent
> based on a preliminary investigation.
>
> -- 
> Dave Menendez <dave at zednenem.com <mailto:dave at zednenem.com>>
> <http://www.eyrie.org/~zednenem/ <http://www.eyrie.org/%7Ezednenem/>>
>
>
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