module SetKreise where

newtype Set a = St [a]

emptySet :: Set a

emptySet = St []

setEmpty :: Set a -> Bool

setEmpty (St []) = True

setEmpty _ = False

inSet :: Eq a => a -> Set a -> Bool

inSet x (St xs) = elem x xs

addSet :: a -> Set a -> Set a

addSet x (St xs) = St (x:xs)

delSet :: Eq a => a -> Set a -> Set a

delSet x (St xs) = St (delete x xs) where

delete _ [] = []

delete x (y:ys) = if x == y then ys else y : delete x ys

subSet :: Eq a => Set a -> Set a -> Bool

subSet (St xs) (St ys) = all (`elem` ys) xs

eqSet :: Eq a => Set a -> Set a -> Bool

eqSet set1 set2 = subSet set1 set2 && subSet set2 set1

-- Auf Mengen uebertragene Listenfunktionen --

filterSet :: (a -> Bool) -> Set a -> Set a

filterSet p (St xs) = St (filter p xs)

mapSet :: (a -> b) -> Set a -> Set b

mapSet f (St xs) = St (map f xs)

allSet :: (a -> Bool) -> Set a -> Bool

allSet p (St xs) = all p xs

anySet :: (a -> Bool) -> Set a -> Bool

anySet p (St xs) = any p xs

setToList (St xs) = xs

-- Anzeigefunktionen --

showSet [] str = showString "{}" str

showSet (x:xs) str = showChar '{' ( shows x ( showl xs str))

where showl [] str = showChar '}' str

showl (x:xs) str = showChar ',' (shows x (showl xs str))

instance (Show a) => Show (Set a) where

showsPrec _ (St s) str = showSet s str