ch06_solutions.hs

module ProgrammingInHaskell_Ch06 where

import Prelude hiding (and, concat, elem, last, replicate, sum, take, (!!))

-- Q6a
and :: [Bool] -> Bool
and []     = True
and (x:xs) = x && and xs

-- Q6b
concat :: [[a]] -> [a]
concat []       = []
concat (xs:xss) = xs ++ concat xss

-- Q6c
replicate :: Int -> a -> [a]
replicate 0 _ = []
replicate n x = x : replicate (n-1) x

-- Q6d
(!!) :: [a] -> Int -> a
(!!) (x:xs) 1 = x
(!!) (x:xs) n = (!!) xs (n-1)

-- Q6e
elem :: Eq a => a -> [a] -> Bool
elem e [] = False
elem e (x:xs)
    | e == x    = True
    | otherwise = elem e xs

-- Q7
merge :: Ord a => [a] -> [a] -> [a]
merge xs [] = xs
merge [] ys = ys
merge (x:xs) (y:ys)
    | x < y     = x : merge xs (y:ys)
    | otherwise = y : merge (x:xs) ys

-- Q8
halve :: [a] -> ([a],[a])
halve xs = ((take n xs), (drop n xs))
           where n  = length xs `div` 2

msort :: Ord a => [a] -> [a]
msort []  = []
msort [x] = [x]
msort xs  = merge (msort ys) (msort zs)
            where (ys,zs) = halve xs

-- Q9a
sum :: Num a => [a] -> a
sum []     = 0
sum (x:xs) = x + sum xs

-- Q9b
take :: Int -> [a] -> [a]
take 0 xs     = []
take n (x:xs) = x : take (n-1) xs

-- Q9c
last :: [a] -> a
last (x:[]) = x
last (x:xs) = last xs