Haskell迭代参数类型不匹配，为什么？

Question

I have a function appendLetters :: [[Char]] -> [[Char]] . When I try to call this function in with iterate like this: iterate appendLetters [""] , ghci tells me:

Couldn't match type '[Char]' with 'Char'  
Expected type: [Char] -> [Char]  
  Actual type: [[Char]] -> [[Char]]  
In the first argument of 'iterate', namely 'appendLetters'  
In the second argument of 'genericTake', namely  
  '(iterate appendLetters [""])'  
In the expression: genericTake n (iterate appendLetters [""]) 

Couldn't match expected type 'Char' with actual type `[Char]'  
In the expression: ""  
In the second argument of 'iterate', namely '[""]'  
In the second argument of 'genericTake', namely  
  '(iterate appendLetters [""])'  

Failed, modules loaded: none.

Why does iterate expect to have these argument types? How can I make it work?

Thanks in advance.

Edit: Full code:

wordsOfLength :: [Char] -> Integer -> [[Char]]  
wordsOfLength alphabet n = genericTake n ( iterate appendLetters [""] ) where appendLetters words = [ atFirst ++ [letter] | atFirst <- words , letter <- alphabet ]  

Explanation: wordsOfLength should take an alphabet and create all words of length n over this alphabet. This is a homework assignment and I don't want to get help with solving the task itself, but only with the iterate function.

Answer 1

The expression

iterate appendLetters [""]

has type [[[Char]]] ( iterate :: (a -> a) -> a -> [a] , and in your case a == [[Char]] ). So the result of genericTake will have the same type. But your wordsOfLength function has the output type [[Char]] , which causes the type mismatch.

Intuitively, you are returning a list (over lengths) of lists (of possible words), where words are lists themselves, so it's [[[Char]]] .