如何在 Haskell 中向 Functor 实例声明添加类约束？

我定义了以下数据类型：

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

现在我想写它是一个实例Functor:

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)'

我怎样才能添加必要的Eq a约束？ （我使用的是 GHC 7.4.1）

可悲的是，你不能这样做——Functor实例必须不受限制地接受任何类型的映射函数。

不过，你可以假装它。

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，所有将被映射的函数Probability已被“推迟”PF。我们通过“降低”回到Probability如果可能

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

为了转换Probability into a fmappable PF我们必须“举起”它

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