Haskell教堂数字无法打印|应为类型，但T具有种类`f`

Question

我正在关注维基百科上关于如何处理教会字面的指南。根据每篇文章，有一个Haskell代码片段：

链接到维基Here

type Church a = (a -> a) -> a -> a

church :: Integer -> Church Integer
church 0 = \f -> \x -> x
church n = \f -> \x -> f (church (n-1) f x)

unchurch :: Church Integer -> Integer
unchurch cn = cn (+ 1) 0

然而，当我尝试通过GHCI运行它时，我得到了以下错误：

main.hs:3:15: error:
    * Expecting one more argument to `Church'
      Expected a type, but `Church' has kind `* -> *'
    * In the first argument of `Show', namely `Church'
      In the instance declaration for `Show Church'
  |
3 | instance Show Church where

我试着在类型上使用deriving show，而且

instance Show Church Integer where
    show = church

不幸的是，两者都产生了更多的错误。我不确定Church Integer在函数声明中是什么意思，或者这是不是我无法派生show的原因？

如何打印此函数？

Answer 1

惯用的方式是将它定义为一个新类型，a也应该是通用的量化

>> church 10
10

{-# Language GADTs                    #-}
{-# Language InstanceSigs             #-}
{-# Language RankNTypes               #-}
{-# Language ScopedTypeVariables      #-}
{-# Language StandaloneKindSignatures #-}
{-# Language TypeApplications         #-}

import Data.Kind

type    Church :: Type
newtype Church where
 Church :: (forall a. (a -> a) -> (a -> a)) -> Church

church :: Integer -> Church
church n = Church (ch n) where

 ch :: Integer -> forall a. (a -> a) -> (a -> a)
 ch 0 succ zero = zero
 ch n succ zero = succ (ch (n-1) succ zero)

unchurch :: Church -> Integer
unchurch (Church church) = church @Integer (+ 1) 0

instance Show Church where
 show :: Church -> String
 show = show . unchurch