transducers.hs

type Reducer a r = r -> a -> r

type Transducer a b = forall r. Reducer a r -> Reducer b r

class Conjable f where
    empty :: f a
    conj :: Reducer a (f a)

class Foldable f where
    fold :: Transducer a (f a)


instance Conjable [] where
    empty  = []
    conj xs x = xs ++ [x]

instance Foldable [] where
    fold = foldl

mapping :: (a -> b) -> Transducer b a
mapping f xf xs x = xf xs (f x)

filtering :: (a -> Bool) -> Transducer a a
filtering p xf xs x = if p x then xf xs x else xs

flatMapping :: Foldable f => (a -> f b) -> Transducer b a
flatMapping f xf xs x = fold xf xs (f x)

llist :: (Foldable f, Conjable f) => Transducer b a -> f a -> f b
llist xf xs = fold (xf conj) empty xs

times :: Int -> [Int]
times n = take n (repeat n)

op = flatMapping times . filtering even . mapping (2 ^)

l = llist op [1..10]