-- ([False,True],[’0’,’1’]) :: ([Bool], [Char])

-- [tail, init, reverse] :: [[a] -> [a]]

palindrome :: [a] -> Bool
palindrome xs = reverse xs == xs

twice :: (a -> a) -> a -> a 
twice f x = f (f x)

length' :: [a] -> Int
length' [] = 0
length' (_:xs) = 1 + length xs

{-
Evaluate length [1,2,3]

length [1,2,3]
= 1 + length [2,3]
= 1 + 1 + length [3]
= 1 + 1 + 1 + length []
= 1 + 1 + 1 + 0
= 3
-}

-- Define and using recursion
and [] = True
and (x:xs) = x && and xs

sum100 :: Int
sum100 = sum [x*x | x <- [1..100]]

pyths :: Int -> [(Int, Int, Int)]
pyths n = [(x,y,z)| x <- [1..n]
                  , y <- [1..n]
                  , z <- [1..n]
                  , x^2 + y^2 == z^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

-- or

safetail''' :: [a] -> [a]
safetail''' [] = []
safetail''' (_:xs) = xs