向类型类实例添加类约束

我正在尝试实现康托配对函数，作为 通用 Pair 类型类，如下所示：

module Pair (Pair, CantorPair) where

-- Pair interface
class Pair p where
    pi :: a -> a -> p a
    k :: p a -> a
    l :: p a -> a

-- Wrapper for typing
newtype CantorPair a = P { unP :: a }

-- Assume two functions with signatures:
cantorPair :: Integral a => a -> a -> CantorPair a
cantorUnpair :: Integral a => CantorPair a -> (a, a)

-- I need to somehow add an Integral a constraint to this instance,
-- but I can't work out how to do it.
instance Pair CantorPair where
    pi = cantorPair
    k = fst . cantorUnpair
    l = snd . cantorUnpair

如何向实例添加适当的积分约束？ 我隐约感觉我可能需要修改 Pair 接口本身， 但不知道该怎么做。

如果您有权访问类定义，则可以添加Integral的约束pi, k, and l方法。但这有点令人不满意：没有任何说法Integral将成为所有实例的正确约束，并且您毕竟不想仅仅因为没有足够的远见而拒绝某些实例。因此，这是一个概括：我们将允许约束在每个实例中有所不同。

{-# LANGUAGE ConstraintKinds, TypeFamilies #-}
import GHC.Exts

newtype CantorPair a = P { unP :: a }
cantorPair :: Integral a => a -> a -> CantorPair a
cantorUnpair :: Integral a => CantorPair a -> (a, a)
cantorPair = undefined
cantorUnpair = undefined

class Pair p where
    type Ctxt p a :: Constraint
    pi :: Ctxt p a => a -> a -> p a
    k  :: Ctxt p a => p a -> a
    l  :: Ctxt p a => p a -> a

instance Pair CantorPair where
    type Ctxt CantorPair a = Integral a
    pi = cantorPair
    k  = fst . cantorUnpair
    l  = snd . cantorUnpair

-- just for fun
data DataPair a = DataPair a a

instance Pair DataPair where
    type Ctxt DataPair a = ()
    pi = DataPair
    k (DataPair a _) = a
    l (DataPair _ a) = a

-- this one made GHC panic! neat, I get to file a bug
data Unit a = Unit

instance Pair Unit where
    type Ctxt Unit a = a ~ ()
    pi _ _ = Unit
    k _ = ()
    l _ = ()