set

module Set (
Set,
empty,
insert,
delete,
--isEmpty,
--isElement,
--card,
--intersection,
--union,
--diff,
--show
) where

data Set a = Empty | S a (Set a) deriving(Eq,Show)

empty :: Set a
empty = Empty

-- insert an element in the set wenn nicht vorhanden
insert :: a -> Set a -> Set a
insert x s = S x s

-- removes an element from the set
--delete empty s = s
delete b (S x xs) = if' (b == x) (delete b xs) (S x (delete b (xs)))
delete b Empty = Empty

if' True x _ = x
if' False _ y = y
--is the set an empty set
isEmpty :: Set a -> Bool
isEmpty Empty = True
isEmpty _ = False

-- is a Element in the set
--isElement :: a -> Set a -> Bool
isElement b (S x xs) = if' (b == x) (True) (isElement b xs)
isElement _ Empty = False

-- the number of elements in the set
card :: Set a -> Int
card a = card' a 0 where
	card' (S a s) x = card' s (x+1)
	card' Empty x = x

--The intersection of two set
--intersection :: Set a -> Set a -> Set a

--the union of two sets
--union :: Set a -> Set a -> Set a

--the difference of two sets
--diff :: Set a -> Set a -> Set a

--show :: Set a -> String