Solutions for Real World Haskell-chp03

Ref:http://typedef.me/blog/2011/01/25/real_world_haskell_solutions_chapter_3/
Exercises on P.60
1. Write the converse of fromList for the List type: a function that takes a List a and generates a [a].

-- file: ch03/ListADT.hs
data List a = Cons a (List a)
        | Nil
        deriving (Show)

fromList (x:xs) = Cons x (fromList xs)
fromList [] = Nil


toList (Cons x xs) = x: (toList xs)
toList Nil = []

2. Define a tree type that has only one constructor, like our Java example. Instead of the Empty constructor, use the Maybe type to refer to a node's children.

-- file:ch03/tree.hs
--data Tree a = Node a (Tree a) (Tree a)
--          | Empty
--          deriving (Show)

data  Tree a  = Node  a (Maybe (Tree a)) (Maybe (Tree a))
             deriving (Show)

Exercises on P. 69-70
1. Write a function that computes the number of elements in a list. To test it, ensure that it gives the same answers as the standard length function.

-- file ch03/myLength.hs

myLength :: [a] -> Int
myLength (x:xs) = if null xs
                then 1
        else 1 + myLength xs
myLength _ = 0

myLength2 [] = 0
myLength2 (_:xs) = 1 + myLength2 xs


myLength3 :: [a] -> Int
myLength3 (x:xs)
           | null xs = 1
        | otherwise = 1 + myLength3 xs
myLength3 _ = 0

3. Write a function that computes the mean of a list.

-- file: ch03/myMean.hs
myMean :: [Double] -> Double
myMean xs = if null xs
               then 0
        else mySum xs / fromIntegral (length xs)

mySum :: [Double] -> Double
mySum (x:xs) = x + mySum xs
mySum [] = 0

4. Turn a list into a palindrome; i.e., it should read the same both backward and forward.

-- file:ch03/myPalindrome.hs
myPalindrome :: [Int]-> [Int]
myPalindrome (x:xs) = [x] ++ (myPalindrome xs) ++ [x]
myPalindrome [] = []