module LibraryFunctions where

-- 1
sum :: (Foldable t, Num a) => t a -> a
sum = foldr (+) 0

-- 2
product :: (Foldable t, Num a) => t a -> a
product = foldr (*) 0

-- 3
elem :: (Foldable t, Eq a) => a -> t a -> Bool
elem needle = foldr (\x b -> b || (needle == x)) False

-- 4
minimum :: (Foldable t, Ord a) => t a -> Maybe a
minimum = foldr f Nothing
    where f x Nothing = Just x
          f x (Just y)
            | x > y = Just x
            | otherwise = Just y

-- 5
maximum :: (Foldable t, Ord a) => t a -> Maybe a
maximum = foldr f Nothing
    where f x Nothing = Just x
          f x (Just y)
            | x < y = Just x
            | otherwise = Just y

-- 6
null :: (Foldable t) => t a -> Bool
null f = LibraryFunctions.length f == 0

-- 7
length :: (Foldable t) => t a -> Int
length = foldr (\_ l -> l + 1) 0

-- 8
toList :: (Foldable t) => t a -> [a]
toList = foldr (:) []

-- 9
-- | Combine the elements of a structure using a monoid.
--
fold :: (Foldable t, Monoid m) => t m -> m
fold = LibraryFunctions.foldMap id

-- 10
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m
foldMap f t = foldr (\x m -> mappend (f x) m) mempty t