> traverse_ print (sequenceA [ZipList [1,2], ZipList [3,4]])
[1,3]
[2,4]Basically, instead of your example I would like to do something like this:
> cl_map (+) [ZipList [1,2,3], ZipList [4,5,6]]
[5,7,9]
> cl_map (+ 3) [ZipList [1,2,3]]
[4,5,6]
> cl_map max3 [ZipList [1,2], ZipList [3,4], ZipList [5,6]] where max3 x y z = max x (max y z)
[5, 6]
Note: If this doesn't work with ZipList, that's ok - the important part is being able to supply the function at runtime. Also, please don't assume that the function is associative or anything like that - it's an arbitrary function of N parameters.
> (+) <$> ZipList [1,2,3] <*> ZipList [4,5,6]
ZipList {getZipList = [5,7,9]}
> (+3) <$> ZipList [1,2,3]
ZipList {getZipList = [4,5,6]}
> let max3 x y z = max x (max y z)
> max3 <$> ZipList [1,2] <*> ZipList [3,4] <*> ZipList [5,6]
ZipList {getZipList = [5,6]}
> let unsafePlus [x, y] = x + y
> fmap unsafePlus (sequenceA [ZipList [1,2,3], ZipList [4,5,6]])
ZipList {getZipList = [5,7,9]}
> let unsafePlus3 [x] = x + 3
> fmap unsafePlus3 (sequenceA [ZipList [1,2,3]])
ZipList {getZipList = [4,5,6]}
> unsafeMax3 [x, y, z] = x `max` y `max` z
> fmap unsafeMax3 (sequenceA [ZipList [1,2], ZipList [3,4], ZipList [5,6]])
ZipList {getZipList = [5,6]}
cl_map :: ([a] -> b) -> [ZipList a] -> ZipList b
cl_map f = fmap f . sequenceA
> let unwrap x = fromDyn x (error "Type error")
>
> let unsafeGreeting [name, authorized] =
> if unwrap authorized then "Welcome, " ++ unwrap name
> else "UNAUTHORIZED!"
>
> fmap unsafeGreeting (sequenceA [ZipList [toDyn "tome", toDyn "simiones", toDyn "pg"]
> , ZipList [toDyn True, toDyn True, toDyn False]])
ZipList {getZipList = ["Welcome, tome","Welcome, simiones","UNAUTHORIZED!"]}
cl_map :: ([Dynamic] -> b) -> [ZipList Dynamic] -> ZipList b
cl_map f = fmap f . sequenceA
It's nice that Haskell does offer a way to circumvent the type system to write somewhat dynamic code, but it's a shame that in order to write a relatively simple function we need to resort to that.
Note that the type of cl_map is perfectly static. It would be `Integer N => (a_0 ->... a_N -> r) -> [a_0] ->... [a_N] -> [r]` assuming some fictitious syntax.
Steady on! You posed a question and I gave an answer. You weren't happy with that answer. I think it's a bit premature to conclude that "this function can't be written in a simple, safe way in Haskell".
> as the article I linked claims, Haskell's type system can't encode the type of the cl_map function.
Could you say where you see that claim in the article? I can see three mentions of "Haskell" in the body, two of them mentioning that one researcher's particular implementation doesn't handle this case, but not a claim that it can't be done.
> Note that the type of cl_map is perfectly static. It would be `Integer N => (a_0 ->... a_N -> r) -> [a_0] ->... [a_N] -> [r]` assuming some fictitious syntax.
OK, fine, it's a bit clearer now what you are looking for. How about this:
> cl_map (uncurry (+)) ([1,2,3], [4,5,6])
[5,7,9]
> cl_map (+3) [1,2,3]
[4,5,6]
> let max3 (x, y, z) = x `max` y `max` z
> cl_map max3 ([1,2], [3,4], [5,6])
[5,6]
cl_map :: Default Zipper a b => (b -> r) -> a -> [r]
-- Type definition
newtype Zipper a b = Zipper { unZipper :: a -> ZipList b } deriving Functor
-- Instance definition
instance a ~ b => D.Default Zipper [a] b where def = Zipper ZipList
-- These three instances are in principle derivable
instance P.Profunctor Zipper where
dimap f g = Zipper . P.dimap f (fmap g) . unZipper
instance Applicative (Zipper a) where
pure = Zipper . pure . pure
f <*> x = Zipper (liftA2 (<*>) (unZipper f) (unZipper x))
instance PP.ProductProfunctor Zipper where
purePP = pure
(****) = (<*>)
newtype Zipper a b = Zipper { unZipper :: a -> ZipList b } deriving Functor
instance a ~ b => D.Default Zipper [a] b where def = Zipper ZipList