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? Greetings, Joachim -- Joachim “nomeata” Breitner mail@joachim-breitner.de • https://www.joachim-breitner.de/ XMPP: nomeata@joachim-breitner.de • OpenPGP-Key: 0xF0FBF51F Debian Developer: nomeata@debian.org