类型族不能返回RankN类型-变通方法还是替代方法？

Question

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

/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’

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

它遵循常用的lens习惯用法。我可以提供一个fieldtraversal函数来执行我想要的操作，但是如果可能的话，我更希望重载field这个名称。您将如何克服类型族的这种限制？

Answer 1

一个透镜已经是一个遍历，只是它的Rank2量词没有使用完整的约束（它只需要functor，而不需要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

正是在这个约束的级别上,您应该引入您的类型族：

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不应生成lensortraversal，而应始终生成具有由类型族确定的约束的自定义Rank2-signature。