haskell - 如何在 Haskell 中向 Functor 实例声明添加类约束？

Question

我定义了以下数据类型:

data Probability a = PD { mass :: [(a, Ratio Int)] } 

现在我想写它是 Functor 的一个实例:

collect :: (Eq a, Num b) => [(a, b)] -> [(a, b)]
collect al = map collect' keys where
    keys = nub $ map fst al
    collect' k = (k, sum (map snd (matches k)))
    matches k = filter ((==) k . fst) al

instance (Eq a) => Functor (Probability a) where
    fmap f p = PD (collect $ map (first f) (mass p))

但是，我收到以下错误:

Kind mis-match
The first argument of `Functor' should have kind `* -> *',
but `Probability a' has kind `*'
In the instance declaration for `Functor (Probability a)'

如何添加必要的 Eq a约束？ (我正在使用 GHC 7.4.1)

Answer 1

可悲的是，你不能那样做—— Functor实例必须无限制地接受任何类型的映射函数。

不过，你可以伪造它。

newtype PF a = PF { unPF :: forall r . Eq r => (a -> r) -> Probability r }

instance Functor PF where
  fmap f (PF p) = PF (\mp -> p (mp . f))

在这里，所有将映射到 Probability 的函数已被 PF“推迟” .我们通过“降低”回 Probability 一次性运行它们。如果可能

lowerPF :: Eq a => PF a -> Probability a
lowerPF pf = unPF pf id

并且为了转换一个 Probability成 fmappable PF我们必须“抬起”它

liftPF :: Probability a -> PF a
liftPF p = PF $ \mp -> PD (collect $ map (first mp) (mass p))