Haskell - 容器和實例declration的容器

Question

來自Haskell新手的簡短版本：假設我有一個Container容器，其中Container有* -> *種類。我希望把他們到另一個容器中，仍然使第二容器的原始類的實例像：

data Container2 a container = Container2 (container a) 

instance Container (Conrainer2 a) where ... 

但看來這是不可能的，因爲GHC總是產生類似的錯誤：

Kind mis-match 

    The first argument of `Container' should have kind `* -> *', 
    but `Container2 a' has kind `(* -> *) -> *' 

是否可以解決這個問題？

長版：我用下面的代碼建模Java中的迭代器接口玩弄：

module Main where 

data NextResult a iter = Stop | More a (iter a) 

class Iter iter where 
    next :: iter a -> NextResult a iter 

-- Convert iterator to a list 
toList :: (Iter c) => c a -> [a] 
toList iter = case next iter of 
    Stop -> [] 
    More value iter2 -> value : toList iter2 

-- List itself is iterator 
instance Iter [] where 
    next [] = Stop 
    next (x:xs) = More x xs 

main = let iter = [1,2,3,4,5] in print $ toList iter 

隨着GHC 7.4.1本編譯並打印預期1 2 3 4 5。現在我想定義一個從函數和迭代器構造新迭代器的變換迭代器。對於我添加了以下幾行：

data TransformedIter from to iter = TransformedIter (from->to) (iter from) 

instance Iter (TransformedIter from to) where 
    next (TransformedIter f iter) = case next iter of 
    Stop -> Stop 
    More value iter2 -> More (f value) (TransformedIter f iter2) 

但生成該錯誤：

Main.hs:21:16: 
    Kind mis-match 
    The first argument of `Iter' should have kind `* -> *', 
    but `TransformedIter from to' has kind `(* -> *) -> *' 
    In the instance declaration for `Iter (TransformedIter from to)' 

我想變通方法，但結果總是一種或另一種類型錯誤。那麼如何在Haskell中對這種轉換進行建模呢？

更新

我誤解了實例聲明的工作原理。根據該建議，下面我翻TransformedIter類型的順序，並結束了：

module Main where 

data NextResult a iter = Stop | More a (iter a) 

class Iter iter where 
    next :: iter a -> NextResult a iter 

toList :: (Iter c) => c a -> [a] 
toList iter = case next iter of 
    Stop -> [] 
    More value iter2 -> value : toList iter2 

instance Iter [] where 
    next [] = Stop 
    next (x:xs) = More x xs 

main = let iter = [1,2,3,4,5] in print $ toList iter 

data TransformedIter iter from to = TransformedIter (from->to) (iter from) 

instance Iter (TransformedIter iter from) where 
    next (TransformedIter f iter) = case next iter of 
    Stop -> Stop 
    More value iter2 -> More (f value) (TransformedIter f iter2) 

但是所產生另一個錯誤：

Main.hs:22:40: 
    No instance for (Iter iter) 
     arising from a use of `next' 
    In the expression: next iter 
    In the expression: 
     case next iter of { 
     Stop -> Stop 
     More value iter2 -> More (f value) (TransformedIter f iter2) } 
    In an equation for `next': 
     next (TransformedIter f iter) 
      = case next iter of { 
       Stop -> Stop 
       More value iter2 -> More (f value) (TransformedIter f iter2) } 

我改變了實例聲明：

instance Iter (Iter iter => TransformedIter iter from) where 

這產生了另一個錯誤：

Main.hs:21:10: 
    Illegal instance declaration for `Iter 
             (Iter iter => TransformedIter iter from)' 
     (All instance types must be of the form (T a1 ... an) 
     where a1 ... an are *distinct type variables*, 
     and each type variable appears at most once in the instance head. 
     Use -XFlexibleInstances if you want to disable this.) 
    In the instance declaration for `Iter (Iter iter => 
              TransformedIter iter from)' 

我加-XFlexibleInstances

後，我得到了：

Main.hs:21:10: 
    Illegal polymorphic or qualified type: 
     Iter iter => TransformedIter iter from 
    In the instance declaration for `Iter (Iter iter => 
              TransformedIter iter from)' 

所以我還沒有看到如何聲明TransformedIter是Iter項目的一個實例。任何線索？

更新2

使用GADTs GHC擴展我設法確定TransformedIter：

module Main where 

data NextResult a iter = Stop | More a (iter a) 

class Iter iter where 
    next :: iter a -> NextResult a iter 

toList :: (Iter c) => c a -> [a] 
toList iter = case next iter of 
    Stop -> [] 
    More value iter2 -> value : toList iter2 

instance Iter [] where 
    next [] = Stop 
    next (x:xs) = More x xs 

data TransformedIter iter from to where 
    TransformedIter :: Iter iter => 
        (from->to) -> (iter from) -> TransformedIter iter from to 

instance Iter (TransformedIter iter from) where 
    next (TransformedIter f iter) = case next iter of 
    Stop -> Stop 
    More value iter2 -> More (f value) (TransformedIter f iter2) 

twice = (*) 2 

main = let iter = TransformedIter twice [1,2,3,4,5] in print $ toList iter 

，編譯並打印預期的2 4 6 8 10，但確實需要這種擴展？

Answer 1

答案被J. Abrahamson在評論中給出的，現在我終於在不使用任何GHC擴展（我用錯了語法方面的實例聲明先前）工作的版本：

module Main where 

data NextResult a iter = Stop | More a (iter a) 

class Iter iter where 
    next :: iter a -> NextResult a iter 

toList :: (Iter c) => c a -> [a] 
toList iter = case next iter of 
    Stop -> [] 
    More value iter2 -> value : toList iter2 

instance Iter [] where 
    next [] = Stop 
    next (x:xs) = More x xs 

data TransformedIter iter from to = TransformedIter (from->to) (iter from) 

instance Iter iter => Iter (TransformedIter iter from) where 
    next (TransformedIter f iter) = case next iter of 
    Stop -> Stop 
    More value iter2 -> More (f value) (TransformedIter f iter2) 

twice = (*) 2 

main = let iter = TransformedIter twice [1,2,3,4,5] in print $ toList iter 

，打印2 4 6 8 10