Haskell exercises - Chapter 4

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


Exercise 4.1

halve :: [a] -> ([a], [a])
halve xs
  | len `mod` 2 == 0 = (take (len `div` 2) xs, drop (len `div` 2) xs)
  | otherwise = (xs, [])
  where len = length xs

Exercise 4.2
a)

safetail :: [a] -> [a]
safetail xs = if null xs then [] else tail xs

b)

safetail :: [a] -> [a]
safetail xs | null xs   = []
            | otherwise = tail xs

c)

safetail :: [a] -> [a]
safetail [] = []
safetail xs = tail xs

Exercise 4.3

(||) :: Bool -> Bool -> Bool

First method:

(||) True  True  = True
(||) True  False = True
(||) False True  = True
(||) False False = False

Second method:

(||) False False = False
(||) _    _     = True

Third method:

(||) False q = q
(||) True  _ = True

A variation of the 3rd method:

(||) True _ = True
(||) _    q = q

Fourth method:

(||) p q | p == q    = p
         | otherwise = True

Exercise 4.4

(&&) :: Bool -> Bool -> Bool
p && q = if p 
              then 
                  if q then True else False
              else
                  False

Exercise 4.5

(&&) :: Bool -> Bool -> Bool
p && q = if p then q else False

Exercise 4.6

mult :: Num a => a -> (a -> (a -> a))
mult = \x -> (\y -> (\z -> x * y * z))