simple add function for natural number

add.hs

{-# LANGUAGE OverloadedStrings #-}

-- 半加器
bitAdd :: String -> String -> (String, String)

-- 1 + n
bitAdd "1" "2" = ("0", "3")
bitAdd "1" "1" = ("0", "2")
bitAdd "1" "3" = ("0", "4")
bitAdd "1" "4" = ("0", "5")
bitAdd "1" "5" = ("0", "6")
bitAdd "1" "6" = ("0", "7")
bitAdd "1" "7" = ("0", "8")
bitAdd "1" "8" = ("0", "9")
bitAdd "1" "9" = ("1", "0")

-- 2 + 
bitAdd "2" "2" = ("0", "4")
bitAdd "2" "3" = ("0", "5")
bitAdd "2" "4" = ("0", "6")
bitAdd "2" "5" = ("0", "7")
bitAdd "2" "6" = ("0", "8")
bitAdd "2" "7" = ("0", "9")
bitAdd "2" "8" = ("1", "0")
bitAdd "2" "9" = ("1", "1")

-- 3 + n
bitAdd "3" "3" = ("0", "6")
bitAdd "3" "4" = ("0", "7")
bitAdd "3" "5" = ("0", "8")
bitAdd "3" "6" = ("0", "9")
bitAdd "3" "7" = ("1", "0")
bitAdd "3" "8" = ("1", "1")
bitAdd "3" "9" = ("1", "2")

-- 4 + n
bitAdd "4" "4" = ("0", "8")
bitAdd "4" "5" = ("0", "9")
bitAdd "4" "6" = ("1", "0")
bitAdd "4" "7" = ("1", "1")
bitAdd "4" "8" = ("1", "2")
bitAdd "4" "9" = ("1", "3")

-- 5 + n
bitAdd "5" "5" = ("1", "0")
bitAdd "5" "6" = ("1", "1")
bitAdd "5" "7" = ("1", "2")
bitAdd "5" "8" = ("1", "3")
bitAdd "5" "9" = ("1", "4")

-- 6 + n
bitAdd "6" "6" = ("1", "2")
bitAdd "6" "7" = ("1", "3")
bitAdd "6" "8" = ("1", "4")
bitAdd "6" "9" = ("1", "5")

-- 7 + n
bitAdd "7" "7" = ("1", "4")
bitAdd "7" "8" = ("1", "5")
bitAdd "7" "9" = ("1", "6")

-- 8 + n
bitAdd "8" "8" = ("1", "6")
bitAdd "8" "9" = ("1", "7")

-- 9 + n
bitAdd "9" "9" = ("1", "8")

-- 0 + n

bitAdd "0" a = ("0", a)

-- 加法交换律
bitAdd a b = bitAdd b a


fullAdd :: String -> String -> (String, String)
fullAdd a b
  | (length a == 1) && (length b == 1) = a `bitAdd` b
  | length a == 0 = ("0", b)
  | length b == 0 = ("0", a)
  | otherwise =
      let (carry, sum) = [last a] `bitAdd` [last b] in
      let (subCarry, subSum) = fullAdd (init a) (init b)
        in let (lastCarry, totalSum) = fullAdd carry subSum in
          (
            case (subCarry, lastCarry) of 
              ("1", "0") -> "1"
              ("0", "1") -> "1"
              ("1", "1") -> "2"
              ("0", "0") -> "0"
            , totalSum ++ sum)

add :: String -> String -> String
add a b
  | (length a == 0) || (length b == 0) = "NaN"
  | a == "0" = b
  | b == "0" = a
  | otherwise = let (carry, sum) = fullAdd a b in case carry of
      "1" -> "1" ++ sum
      "0" -> sum

main = print ("9944" `add` "22")