类型族无法返回 RankN 类型 - 解决方法还是替代方案？

Question

我正在使用可扩展的记录库玩，我想编写一个函数field，该功能可以根据Symbol密钥是否为Lens或Traversal操作在钥匙列表中。给出了类型的家庭：

type family LensOrTraversal key keys s t a b where
    LensOrTraversal key '[] s t a b = 
        Traversal s t a b
    LensOrTraversal key (key =: val ': xs) s t a b = 
        Lens s t a b
    LensOrTraversal key (foo =: bar ': xs) s t a b = 
        LensOrTraversal key xs s t a b

此代码给我一个错误：

/home/matt/Projects/hash-rekt/src/Data/HashRecord/Internal.hs:433:5: 
error:
    • Illegal polymorphic type: Traversal s t a b
    • In the equations for closed type family ‘LensOrTraversal’
      In the type family declaration for ‘LensOrTraversal’

理想情况下，我希望能够重复使用镜头和遍历的field名称，因为它可以允许您写

>>> let testMap = empty & field @"foo" .~ 'a'
>>> :t testMap
HashRecord '["foo" =: Char]
>>> testMap ^. field @"foo" 
'a'
>>> testMap ^. field @"bar"
Type error
>>> testMap ^? field @"bar"
Nothing

遵循常见的lens成语。我可以提供一个可以执行我想要的fieldTraversal功能，但是如果可能的话，我希望将名称 field超载。您将如何处理这种类型家庭的限制？

Answer 1

lens 是已经是遍历，只有其rank2量词不使用完整的约束(它仅需要Functor，而不是Applicative(。

type Lens s t a b      = ∀ f . Functor f     => (a -> f b) -> s -> f t
type Traversal s t a b = ∀ f . Applicative f => (a -> f b) -> s -> f t

您应该介绍您的类型家庭的层面：

import GHC.Exts (Constraint)
type family FieldOpticConstraint key keys :: (* -> *) -> Constraint where
  FieldOpticConstraint key '[] = Applicative
  FieldOpticConstraint key (key =: val ': xs) = Functor
  FieldOpticConstraint key (_ ': xs) = FieldOpticConstraint key xs

则field不应产生LensOrTraversal，而应始终具有由类型族确定的约束的自定义rank2-签名。