import Data.List hiding (group)

-- sq x returns the square of x
-- sq :: Integer -> Integer
sq :: Integer -> Integer
sq x = x*x

-- absolute x returns the absolute value of x
absolute :: Integer -> Integer
absolute x | x >= 0 = x
absolute x | x < 0  = -x

absolute' :: Integer -> Integer
absolute' x
    | x >= 0 = x
    | x < 0  = -x

absolute'' :: Integer -> Integer
absolute'' x
    | x >= 0    = x
    | otherwise = -x

absolute''' :: Integer -> Integer
absolute''' x = if x>=0 then x else -x

absolute'''' :: Double -> Double
absolute'''' x = sqrt (x^2)

-- evaluation by substitution
--   sq 5
--   absolute (-4)

-- power x n returns x to the power n
power :: Integer -> Integer -> Integer
power x 0         = 1
power x n | n < 0 = error "n is negative"
power x n         = x * (power x (n-1))

-- repli n s returns n copies of s as a string
repli :: Integer -> String -> String
repli 0 s = ""
repli n s = s ++ (repli (n-1) s)

-- regions n computes the number of regions formed by n lines
regions :: Integer -> Integer
regions 0 = 1
regions n = n + regions (n-1)

-- group n xs divides xs up into groups of length n
group :: Integer -> String -> [String]
group n "" = []
group n s = [genericTake n s] ++ group n (genericDrop n s)