[simiones]

I replied to the parent as well, but not only is the solution the parent showed significantly more complex than the CL version, I'm not even sure it actually does what I asked.

More explicitly, the expression there seems to rely on knowing the arity of the function and the number of lists at compile time. Basically, I was asking for a function cl_map such that:

    cl_map foo [xs:[ys:[zs:...]]] = foo <$> xs <*> ys <*> zs <*> ...

Edit: found a paper explaining that this is not possible in Haskell, and showing how the problem is solved in Typed Scheme: https://www2.ccs.neu.edu/racket/pubs/esop09-sthf.pdf

[tome]

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 that's a more fundamental difference from Clojure, not a "code pattern that [is] safe and easy to do with dynamic typing, but impossible with simple type systems or more complex with more advanced type system."

    > traverse_ print (sequenceA [ZipList [1,2], ZipList [3,4]])
    [1,3]
    [2,4]

[simiones]

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]

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]

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]

> 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?

[simiones]

First of all, thank you for bearing with me this long!

Still, you haven't written exactly the function I was asking for. You require a manual, compile-time step of transforming the N-ary function to a unary function taking a tuple. Still, it's impressive that this can define variable-length, variable-type tuples. Unfortunately I am not able at all to follow your solution, as it's using too many types that I'm not familiar with, and it seems to require some external packages, so I can't easily try it out in an online compiler to understand it better (as I have been doing so far).

Either way, I would say we are well outside the limits of an easy to understand way of specifying this kind of function - even if you are only showing 2 lines of code, it seems that your definition requires, outside of lists and functions (the objects we intended to work with): ZipList, Default, Functor, Profunctor, ProductProfunctor, Applicative, and a helper type. Even if these were derivable, someone seeking to write this function would still need to be aware of all of these types, some of which are not even part of the standard library; and of the way they work together to magically produce the relatively simple task they had set out to do.

> Could you say where you see that claim in the article?

The claim is presented implicitly: for one, they conjecture that, were Haskell or SML to "pragmatically support" such a feature, it would be used more often (offering as argument the observation that both Haskell's and SML's standard libraries define functions that differ only in the arity of their arguments, such as zipWith/zipWith3 in Haskell). This implies that, to their knowledge, it is not pragmatically possible to implement this in Haskell.

Similarly, given that in their "Related Works" section they don't identify any complete implementation of variadic polymorphism, it can be assumed that they claim at least not to have found one.