Haskell exercises - Chapter 6

My solutions to exercises from Graham Hutton's Programming in Haskell.

Exercise 6.1

import Prelude hiding ( (^) )

(^) :: Int -> Int -> Int
n ^ 0     = 1
n ^ (m+1) = n * (n^m)

Exercise 6.3

import Prelude hiding (and, concat, replicate, (!!), elem)

and :: [Bool] -> Bool
and []     = True
and (b:bs) = b && and bs

concat :: [[a]] -> [a]
concat []       = []
concat (xs:xss) = xs ++ concat xss

replicate :: Int -> a -> [a]
replicate 0     x = []
replicate (n+1) x = x : replicate n x

(!!) :: Integral a => [a] -> n -> a
(!!) (x:xs) 0     = x
(!!) (x:xs) (n+1) = xs !! n

elem :: Eq a => a -> [a] -> Bool
elem x []     = False
elem x (y:ys) = if x == y then True else elem x ys

Exercise 6.4

merge :: Ord a => [a] -> [a] -> [a]
merge xs     []     = xs
merge []     ys     = ys
merge (x:xs) (y:ys) = if x < y then x : merge xs (y:ys) else y : merge (x:xs) ys

Exercise 6.5

halve :: [a] -> ([a], [a])
halve xs = (fsthalf, sndhalf) 
    where fsthalf = take ((length xs) `div` 2) xs
           sndhalf = drop (length fsthalf) xs

msort :: Ord a => [a] -> [a]
msort []  = []
msort [x] = [x]
msort xs  = merge (msort firsthalf) (msort secondhalf)
    where 
        firsthalf = fst halves
        secondhalf = snd halves
        halves = halve xs

Exercise 6.6

import Prelude hiding (sum, take, last)

sum :: Num a => [a] -> a
sum []     = 0
sum (x:xs) = x + sum xs

take :: Int -> [a] -> [a]
take 0     xs     = xs
take (n+1) (x:xs) = x : take n xs

last :: [a] -> a
last [x]    = x
last (x:xs) = last xs