On Tue, Jan 31, 2017 at 11:55 PM, Joachim Breitner 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. 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 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