After rereading page 2 of McBride and Paterson's Functional Pearl,
"Applicative programming with effects", I think you are just reinventing
Control.Applicative. The problem is that the default Applicative
instance for [] is wrong, being a direct product rather than a direct sum.
If [] were not already an instance of Applicative, you could easily
define it as:
import Control.Applicative
data MyList a = Nil | (:::) a (MyList a) deriving (Read,Show,Eq,Ord)
infixr 5 :::
-- same as []
instance Functor MyList where
fmap f Nil = Nil
fmap f (x ::: xs) = f x ::: fmap f xs
-- different from [], sum rather than product
instance Applicative MyList where
pure x = x ::: Nil
(<*>) (f ::: fs) (x ::: xs) = f x ::: (fs <*> xs)
(<*>) _ _ = Nil
x = (1::Int) ::: 3 ::: 5 ::: 7 ::: 3 ::: Nil
y = (6::Int) ::: 9 ::: 3 ::: 1 ::: 4 ::: Nil
z = (2::Int) ::: 4 ::: 0 ::: 8 ::: 2 ::: Nil
test = (,,) <$> x <*> y <*> z
> test
(:::) (1,6,2) ((:::) (3,9,4) ((:::) (5,3,0) ((:::) (7,1,8) ((:::)
(3,4,2) Nil))))
Alternately, you could write a newtype for [] and give it the zippy
instance for Applicative.
Job Vranish wrote:
I was needing a way to zip generic data structures together today and
was very annoyed to find that there is no Zippable class, or variant
there of.
So I made my own:
class (Foldable f, Functor f) => Zippable f where
fmaps :: (Foldable g) => g (a -> b) -> f a -> f b
fmaps' :: [a -> b] -> f a -> f b -- to save a step on instance
implementation
zipWith :: (a -> b -> c) -> f a -> f b -> f c
zip :: f a -> f b -> f (a, b)
unzip :: f (a, b) -> (f a, f b)
fmaps fs a = fmaps' (toList fs) a
fmaps' fs a = fmaps fs a
zipWith f a b = fmaps (fmap f a) b
zip = zipWith (,)
unzip a = (fmap fst a, fmap snd a)
instance Zippable [] where
fmaps' (fx:fs) (x:xs) = fx x : fmaps' fs xs
fmaps' _ _ = []
--The fmaps function is also quite handy as a replacment for zipWith3,
zipWith4, etc...
--For example:
x = [1, 3, 5, 7, 3]
y = [6, 9, 3, 1, 4]
z = [2, 4, 0, 8, 2]
test = fmap (,,) x `fmaps` y `fmaps` z
-- > [(1,6,2),(3,9,4),(5,3,0),(7,1,8),(3,4,2)]
--you can also throw in a functor instance to remove the dependency on
the Functor class, but it
-- might not be worth it:
instance (Zippable f) => Functor f where
fmap f a = fmaps (repeat f) a
Is there any good reason that there isn't something like this in the
standard libraries? Or, as far as I can tell, on hackage?
If not, then maybe I'll stick it on hackage.
- Job Vranish
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