变量参数函数上的 fmap

Question

我想在变量参数函数上定义fmap：

type family VarArg (args :: [*]) e where
VarArg '[] e = e
VarArg (a ': as) e = a -> VarArg as e
mapVarArg :: forall args e e'
. (e -> e') -> VarArg args e -> VarArg args e'
mapVarArg f = _

这是我找到的最接近的解决方案：

mapVarArg :: forall args e e' . VarArgIso args
=> (e -> e') -> VarArg args e -> VarArg args e'
mapVarArg f = (^. Lens.from varArgIso) . fmap f . (^. varArgIso @args)
data VarArgD (args :: [*]) e where
DNil  :: e -> VarArgD '[] e
DCons :: (a -> VarArgD as e) -> VarArgD (a ': as) e
class VarArgIso (args :: [*]) where
varArgIso :: Iso' (VarArg args e) (VarArgD args e)
instance VarArgIso '[] where
varArgIso = iso DNil ((DNil x) -> x)
instance VarArgIso as => VarArgIso (a ': as) where
varArgIso = iso (f -> DCons ((^. varArgIso) . f)) ((DCons f) -> ((^. Lens.from varArgIso) . f))
instance Functor (VarArgD args) where
fmap f (DNil a)  = DNil (f a)
fmap f (DCons g) = DCons (fmap f . g)

是否有更简单的解决方案，或者没有额外VarArgIso约束的解决方案？

Answer 1

我认为如果没有额外的类约束，非模板解决方案是不可能的。有一个简单且大概高效的实现，具有重叠的实例：

class VarArg a b c d where
mapVarArg :: (a -> b) -> c -> d
instance (a ~ c, b ~ d) => VarArg a b c d where
mapVarArg = id
instance {-# overlapping #-} (VarArg a b c2 d2, c1 ~ d1) =>
VarArg a b (c1 -> c2) (d1 -> d2) where
mapVarArg f g = mapVarArg f . g

如果将overlapping替换为incoherent，它通常也适用于多态/约束函数作为参数：

> mapVarArg (+100) (+) 0 0
100

但是，对于incoherent实例，部分应用的mapVarArg-s 往往具有不可用的推断类型。

> let foo = mapVarArg (+100) (+)
> :t foo
foo :: (Num (a -> a -> a), Num a) => a -> a -> a