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@@ -75,5 +75,42 @@ treeMap f (Node a left right) = Node (f a) (treeMap f left) (treeMap f right)
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-- defin the foldl function for a tree
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treeFoldl :: (a -> b -> a) -> a -> Tree b -> a
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-treeFoldl f z EmptyTree = z
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+treeFoldl _ z EmptyTree = z
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treeFoldl f z (Node a left right) = treeFoldl f (f (treeFoldl f z left) a) right
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+
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+-- define the foldr function on a tree
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+
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+treeFoldr :: (b -> a -> a) -> a -> Tree b -> a
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+treeFoldr _ z EmptyTree = z
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+treeFoldr f z (Node a left right) = treeFoldr f (f a (treeFoldr f z right)) left
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+
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+-- define a filter function on the tree
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+
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+treeFilter :: (a -> Bool) -> Tree a -> [a]
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+treeFilter f = treeFoldr (\x acc -> if f x then x:acc else acc) []
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+
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+-- define the sumTree using treeFoldr
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+
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+treeSum2 :: (Num a) => Tree a -> a
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+treeSum2 = treeFoldr (+) 0
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+
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+--define a the treeValues function on a tree using the treeFoldr
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+
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+treeValues3 :: Tree a -> [a]
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+treeValues3 = treeFoldr (:) []
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+
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+--define the treeValues unction using the treeFoldl function
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+
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+treeValues4 :: Tree a -> [a]
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+treeValues4 t = treeFoldl (++) [] (treeMap (:[]) t)
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+
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+--define a TrafficLight datatype implementing the equality operations and introducing a (partial) order
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+
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+data TrafficLight = Red | Yellow | Green
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+
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+instance Eq TrafficLight where
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+ Red == red = True
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+ Yellow == Yellow = True
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+ Green == Green = True
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+ _ == _ = False
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+
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