Sixth group session

Set.hs

module Set where

-- Menge als Funktion?!
type Set a = a -> Bool

-- empty
empty :: Set Int -- Int -> Bool
empty _ = False
-- empty x = const False x
-- empty   = const False
-- const :: a -> b -> a
-- const x y = x

-- Set Int :: Int -> Bool
-- s :: Int -> Bool
-- v :: Int
-- => s v :: Bool
isElem :: Set Int -> Int -> Bool
isElem = id
-- isElem s = s
-- isElem s v = s v

insert :: Set Int -> Int -> Set Int
insert s v = s'
 where
   s' :: Set Int -- Int -> Bool
   s' w | w == v    = True
        | otherwise = s w

remove :: Set Int -> Int -> Set Int
remove s v = s'
 where
   s' :: Set Int -- Int -> Bool
   s' w | w == v    = False
        | otherwise = s w

-- Set Int -> Set Int -> (Int -> Bool)
-- (Int -> Bool) -> (Int -> Bool) -> (Int -> Bool)
union :: Set Int -> Set Int -> Set Int
union = lift (||)
-- union s1 s2 = lift (||) s1 s2
-- union s1 s2 = s'
 -- where
   -- s' = s1 v || s2 v

intersection :: Set Int -> Set Int -> Set Int
intersection = lift (&&)
-- intersection s1 s2 = lift (&&) s1 s2
-- intersection s1 s2 = s'
 -- where
 --   s' = s1 v && s2 v


-- lift :: (Bool -> Bool -> Bool)
--      -> Set Int
--      -> Set Int
--      -> Set Int
lift :: (b -> b -> b)
     -> (a -> b)
     -> (a -> b)
     -> a
     -> b
lift op s1 s2 v = s1 v `op` s2 v

complement :: Set Int -> Set Int
complement s v = not (s v)
-- complement s = not . s
-- compmement = (not .)

difference :: Set Int -> Set Int -> Set Int
difference s1 = intersection s1 . complement
-- difference s1 s2 =
--   intersection s1 (complement s2)
-- difference s1 s2 = a'
 -- where
   -- a' :: Int -> Bool
   -- a' v = s1 v && not (s2 v)

-- listToSet :: [Int] -> Int -> Bool
listToSet :: [Int] -> Set Int
listToSet xs = s'
 where
   s' v = v `elem` xs
   -- s' = (`elem` xs)

----- Kurze Wiederholung des Arrays
type Array a = Int -> a

emptyArray i =
  error ("Access to non-initialized component " ++ show i)

getIndex :: Array a -> Int -> a
-- Array a :: Int -> a
-- arr :: Array a, i :: Int
-- arr i :: a
getIndex = id
-- getIndex a = a
-- getIndex a i = a i

-- (Int -> a) -> Int -> a -> (Int -> a)
putIndex :: Array a -> Int -> a -> Array a
putIndex a i v = a'
  where
   a' j | i == j    = v
        | otherwise = a j

removeIndex :: Array a -> Int -> Array a
removeIndex a i = a'
 where
   a' j | i == j    = emptyArray j
        | otherwise = a j