haskell - 封闭类型族和奇怪的函数类型

Question

抱歉，我想不出更好的问题标题，所以请继续阅读。想象一下，我们有一个封闭的类型族，它将每个类型映射到它对应的 Maybe除了也许自己:

type family Family x where
  Family (Maybe x) = Maybe x
  Family x = Maybe x

我们甚至可以使用该类型族声明一个函数:

doMagic :: a -> Family a
doMagic = undefined

exampleA = doMagic $ Just ()
exampleB = doMagic $ ()

在 GHCi 中使用它表明可以评估此​​函数应用程序的类型:

*Strange> :t exampleA      
exampleA :: Maybe ()       
*Strange> :t exampleB      
exampleB :: Maybe ()       

问题是是否可以提供 doMagic 的任何实现。 undefined 除外的功能?例如，假设我想将每个值包装成 Just构造函数，除了应该保持不变的Maybes，我该怎么做？我尝试使用类型类，但如果不使用封闭类型系列，则无法为 doMagic 函数编写可编译签名，有人可以帮我吗？

Answer 1

您可以使用另一个封闭类型族来区分Maybe x来自 x然后您可以使用另一个类型类来提供 doMagic 的单独实现对于这两种情况。快速而肮脏的版本:

{-# LANGUAGE TypeFamilies, MultiParamTypeClasses,
    FlexibleInstances, UndecidableInstances, ScopedTypeVariables #-}

type family Family x where
  Family (Maybe x) = Maybe x
  Family x = Maybe x

data True
data False

type family IsMaybe x where
  IsMaybe (Maybe x) = True
  IsMaybe x = False


class DoMagic a where
  doMagic :: a -> Family a

instance (DoMagic' (IsMaybe a) a (Family a)) => DoMagic a where
  doMagic = doMagic' (undefined :: IsMaybe a)   


class DoMagic' i a r where
  doMagic' :: i -> a -> r

instance DoMagic' True (Maybe a) (Maybe a) where
  doMagic' _ = id

instance DoMagic' False a (Maybe a) where
  doMagic' _ = Just


exampleA = doMagic $ Just ()
exampleB = doMagic $ ()