haskell - 将 Data.Constraint.Forall 与等式约束一起使用

Question

假设我有一个这样的函数:

{-# LANGUAGE ScopedTypeVariables #-}

class C a where

foo :: forall f a b. (C (f a), C (f b)) => f a -> f b
foo = _

现在，如果我想将 a 和 b 的范围移动到 foo 类型中类型类约束的右侧(假设，因为我想使用 foo 来实现需要在 a 和 b 中实现多态的类型类方法)，它可以完成使用 Data.Constraint.Forall 进行一些跑腿工作:

{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ConstraintKinds, TypeOperators #-}
import Data.Constraint
import Data.Constraint.Forall

foo' :: forall f. (ForallF C f) => forall a b. f a -> f b
foo' = helper
  where
    helper :: forall a b. f a -> f b
    helper = case (instF :: ForallF C f :- C (f a)) of
        Sub Dict -> case (instF :: ForallF C f :- C (f b)) of
            Sub Dict -> foo

现在，我的问题是，假设我将函数更改为涉及类型相等的函数:

{-# LANGUAGE TypeFamilies, ScopedTypeVariables #-}

type family F a :: * -> *

bar :: forall f g a b. (F (f a) ~ g a, F (f b) ~ g b) => f a -> f b
bar = _

有没有办法使上述技术适应这一点？

这是我尝试过的:

{-# LANGUAGE TypeFamilies, ScopedTypeVariables #-}
{-# LANGUAGE ConstraintKinds, TypeOperators #-}
import Data.Constraint
import Data.Constraint.Forall

type F'Eq f g x = F (f x) ~ g x

bar' :: forall f g. (Forall (F'Eq f g)) => forall a b. f a -> f b
bar' = helper
  where
    helper :: forall a b. f a -> f b
    helper = case (inst :: Forall (F'Eq f g) :- F'Eq f g a) of
        Sub Dict -> case (inst :: Forall (F'Eq f g) :- F'Eq f g b) of
            Sub Dict -> bar

但是(毫不奇怪)由于不饱和类型同义词而失败:

Type synonym ‘F'Eq’ should have 3 arguments, but has been given 2

In an expression type signature: Forall (F'Eq f g) :- F'Eq f g a

In the expression: (inst :: Forall (F'Eq f g) :- F'Eq f g a)

Answer 1

您可以使用一个类:

{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}

class (F (f x) ~ g x) => F'Eq f g x
instance (F (f x) ~ g x) => F'Eq f g x

bar' :: forall f g. (Forall (F'Eq f g)) => forall a b. f a -> f b
bar' = helper
  where
    helper :: forall a b. f a -> f b
    helper = case (inst :: Forall (F'Eq f g) :- F'Eq f g a) of
        Sub Dict -> case (inst :: Forall (F'Eq f g) :- F'Eq f g b) of
            Sub Dict -> bar