module Exercise_9 where
import Form_9
import Test.QuickCheck
import Control.Monad
import Data.List as List

{- Library -- nicht veraendern! -}

data Tree a =
  Empty |
  Node a (Tree a) (Tree a)
    deriving (Eq, Show)

-- allow QuickCheck to generate arbitrary values of type Tree
instance Arbitrary a => Arbitrary (Tree a) where
  arbitrary = sized tree
    where
    tree 0 = return Empty
    tree n | n > 0 = oneof [return Empty,
      liftM3 Node arbitrary (tree (n `div` 2)) (tree (n `div` 2))]


{- G9.1 -}

-- Modify Form.hs from the lecture


{- G9.2 -}


{- G9.3 -}

showTable :: Form -> String
showTable = undefined


{- H9.1 -}

{- insert proof here -}


{- H9.2 -}

isDnf :: Form -> Bool
isDnf = undefined

pushNot :: Form -> Form
pushNot = undefined

pushAnd :: Form -> Form
pushAnd = undefined

balance :: Form -> Form
balance = undefined

toDnf :: Form -> Form
toDnf = undefined


{- H9.3 -}

treeSum :: Tree Int -> Int
treeSum = undefined

treeMin :: Ord a => a -> Tree a -> a
treeMin = undefined

evens :: Tree Int -> [Int]
evens = undefined


{- H9.4 -}

{-WETT-}
quasiMajorityElems :: Eq a => [a] -> [a]
quasiMajorityElems xs = undefined
{-TTEW-}