{- Exercise 2.2 -}

-- values from the exercise sheet
baseAttack :: Integer
baseAttack = 3
baseDefense :: Integer
baseDefense = 4

-- intermediate functions, identified by your functional decomposition
-- change names, types and definitions

totalAttack :: Integer -> Integer
totalAttack x = error "write the defining equation here"

-- main function: calculateDamage

-- calculateDamage :: uncomment this line and write the correct type
calculateDamage = error "write the defining equation here"


{- Exercise 2.3 -}

-- 1.)

square :: Integer -> Integer
square n = error "square not yet defined" 


-- 2.)

-- factorial from the lecture
fact :: Integer -> Integer
fact n = if n > 0 then n * fact (n - 1) else 1

binom_fd :: Integer -> Integer -> Integer
binom_fd n k = error "binom_fd not yet defined" 

binom_dc :: Integer -> Integer -> Integer
binom_dc n k = error "binom_dc not yet defined" 


{- Tests -}

-- the following functions can be run in ghci to test your implementations

test_square = if square 3 == 3^2 then True else error "test on square failed"

-- tests for binomials 
test_binom_fd = if binom_fd 3 2 == 3 then True else error "test on binom_fd failed"
test_binom_dc = if binom_dc 3 2 == 3 then True else error "test on binom_dc failed"

-- a test for all parts of exercise 2.3: invoke test_ex_2_3 in ghci
test_ex_2_3 = test_square && test_binom_fd && test_binom_dc