3 ms·

Sure it's possible in Haskell. I'm not sure where in that paper you got the impression it isn't. Of course one can't define variadic functions in Haskell, but

• simiones 6y ago
  As far as I can tell, your example calls a unary function on each element of a list of lists. It's solving the variadic part of map, but not the part where I can call an N-ary function with each element of N lists. 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] Can this be done? What is the type of cl_map? 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.
  • tome 6y ago
    The functions in those examples have fixed numbers of arguments, so one would use the original formulation shown by Tyr42. > (+) <$> ZipList [1,2,3] <*> ZipList [4,5,6] ZipList {getZipList = [5,7,9]} > (+3) <$> 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]} If you want to use "functions unknown at runtime that could take any number of arguments" then you'll have to pass the arguments in a list. Of course these can crash at runtime, which Haskellers wouldn't be happy with given an alternative, but hey-ho, let's see where we get. > 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]} So the answer to your question is that cl_map :: ([a] -> b) -> [ZipList a] -> ZipList b cl_map f = fmap f . sequenceA except you don't actually want all the elements of the list to be of the same type, you want them to be of dynamic type, so let's just make them Dynamic. > 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!"]} and the type of cl_map becomes cl_map :: ([Dynamic] -> b) -> [ZipList Dynamic] -> ZipList b cl_map f = fmap f . sequenceA One could polish this up a bit and make a coherent ecosystem out of it, but Haskell programmers hardly ever use Dynamic. We just don't come across the situations where Clojurists seem to think it's necessary.
    • simiones 6y ago
      So in the end, as I claimed initially, this function can't be written in a simple, safe way in Haskell; and as the article I linked claims, Haskell's type system can't encode the type of the cl_map function. 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.
      • tome 6y ago
        > So in the end, as I claimed initially, this function can't be > written in a simple, safe way in Haskell 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] Notice that the function arguments are have different, statically-known types! The type of this miracle function? cl_map :: Default Zipper a b => (b -> r) -> a -> [r] And the implementation? -- 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 (****) = (<*>) Given that the only two lines that actually matter are newtype Zipper a b = Zipper { unZipper :: a -> ZipList b } deriving Functor instance a ~ b => D.Default Zipper [a] b where def = Zipper ZipList and the rest are boiler plate that could be auto-derived, I think this is pretty satisfactory. What do you think?