The questions regarding my first haskell program

Question

The program return all possible combinations of '0' and '1' length N.

addToElement :: String -> String -> String
addToElement element symbol = element ++ symbol

addOneToElement :: String -> String
addOneToElement element = addToElement element "1"                

addZeroToElement :: String -> String
addZeroToElement element = addToElement element "0"                

processListOnce :: [String] -> [String]
processListOnce lst = do
    let s1 = map addOneToElement lst
    let s2 = map addZeroToElement lst 
    s1 ++ s2

processList :: [String] -> Integer -> [String]
processList lst 1 = processListOnce lst
processList lst n = do
             let tmp = processListOnce(lst)
             processList tmp (n - 1)

{-                       
processList2 :: [String] -> Integer -> [String]
processList2 lst n = iterate (map processListOnce) lst !! n
-}

main = do
     let s = processList ["0", "1"] 2
     let ss = show s
     putStrLn ss

It is my first Haskell program so I will be thankful if you help me:

• First of all pls refactore my code Haskell-way. I already know one magic refactring:

   Control.Monad.replicateM n [0,1]
  

  but this solution is not good for studying purposes :)

• Why I can not use ProcessList2 instead ProcessList and get error:

  all_possible_combinations.hs:44:51:
  Couldn't match expected type `[Char]' against inferred type `Char'
  Expected type: [String]]
  Inferred type: [String]
  In the second argument of `iterate', namely `lst'
  In the first argument of `(!!)', namely
   `iterate (map processListOnce) lst'
  

  • Is there any way to skip (not use) the 'tmp' variable in the processList? I have tried, but got the error:

    processList :: [String] -> Integer -> [String]
    processList lst 1 = processListOnce lst
    processList lst n = processList processListOnce(lst) (n - 1)
    
    
    all_possible_combinations.hs:39:32:
    Couldn't match expected type `[String]'
    against inferred type `[String] -> [String]'
    In the first argument of `processList', namely `processListOnce'
    In the expression: processList processListOnce (lst) (n — 1)
    In the definition of `processList':
    processList lst n = processList processListOnce (lst) (n — 1)
    

Thanks in advance.

Answer 1

First of all pls refactore my code Haskell-way. I already know one magic refactring:

Control.Monad.replicateM n [0,1]

but this solution is not good for studying purposes :)

Actually, while I certainly wouldn't expect someone new to Haskell to come up with such a solution, I think that understanding this version would be very good for studying purposes.

The regular replicate function is pretty simple: It creates a list of the same element repeated some number of times. This is also the first step of what replicateM does:

> replicate 2 ["0", "1"]
[["0", "1"], ["0", "1"]]

The second step of what replicateM does is "sequence" the list according to the Monad of the elements, turning something a list of monadic values [m a] into a monadic list of values m [a]. What this does is "combine" the structure of each monadic value in some sense, where the specific meaning of "combine" depends on the specific monad.

As a Monad, lists represent something like trying multiple possibilities. So when we "sequence" the values, that means that at each step, every possibility is tried separately, and all possible results are collected.

So, ["0", "1"] is a monadic value representing trying two different possibilities. [["0", "1"], ["0", "1"]] is a list of that monadic value repeated twice. To sequence that list, we take each possibility from the first element of the list, use it as the head of the result list, then continue until reaching the end. Because each group of possibilities is the same, the final result is all the possible combinations of each possible item:

> replicateM 2 ["0", "1"]
[["0","0"],["0","1"],["1","0"],["1","1"]]

Answer 2

About making it Haskelly, here is a solution that is not pure magic (as the replicateM may be)

onesAndZeroes 0 = [[]]
onesAndZeroes n = [x:xs | x <- [0,1], xs <- onesAndZeroes (n-1)]

Since you are new to haskell, if you don't understand it, it might help to read about list comprehensions.

Answer 3

Is there any way to skip (not use) the 'tmp' variable in the processList? I have tried, but got the error:

This definition has used the wrong precedence. You should write

processList lst n = processList (processListOnce lst) (n - 1)
-- #                            ^                   ^

Why I can not use ProcessList2 instead ProcessList and get error:

processListOnce is already a [String] -> [String] function. If you use map processListOnce it will become a [[String]] -> [[String]] function. Thus, remove the map.

processList2 lst n = iterate processListOnce lst !! n