{- Exercise 3.2 -}

-- version where recursion counts downwards until 0
sum_down :: Integer -> Integer
sum_down n = error "TODO" 

-- version where recursion counts upwards until n
sum_up :: Integer -> Integer
sum_up n = error "TODO" 

-- any solution
fib :: Integer -> Integer
fib n = error "TODO" 

-- efficient version
fib_eff :: Integer -> Integer
fib_eff n = error "TODO" 

{- Exercise 3.3 -}

isDivisible :: Integer -> Integer -> Bool
isDivisible x y = error "TODO, no mod allowed" 

isPrime :: Integer -> Bool
isPrime n = error "TODO" 


{- Tests -}
{- You don't have to understand the Haskell-code in the tests,
   but you can just invoke them after having implemented 
   some exercises -}

-- tests for sum
sums = [0,1,3,6,10,15,21,28,36,45,55]
test_sum_down = map sum_down [0..10] == sums 
  || error "test failed on sum_down"
test_sum_up   = map sum_up [0..10] == sums 
  || error "test failed on sum_up"
test_sum = test_sum_up && test_sum_down

-- tests for fib
fibs = [0,1,1,2,3,5,8,13,21,34]
test_fib = map fib [0 .. 9] == fibs 
  || error "test fib failed"
test_fib_eff = map fib_eff [0 .. 9] == fibs 
  || error "test fib_eff failed"
test_fib_both = test_fib && test_fib_eff

-- tests for primes
primes = [2,3,5,7,11,13,17,19]
test_primes = filter isPrime [0..20] == primes 
  || error "test_primes failed"

-- test for all exercises
test_all = test_primes && test_sum && test_fib_both