Fusion.hs

data Term a b where
    Map :: (a -> b) -> Term a b
    Filter :: (a -> Maybe a) -> Term a (Maybe a)

fuseMap :: Term a b -> Term b c -> Term a c
fuseMap (Map f ) (Map g) = Map $ g . f

filterFuse :: Term a (Maybe a) -> Term a b ->  Term a (Maybe b)
filterFuse (Filter p) (Map f ) = Map (\x -> p x >>= Just . f)

fuseFilter :: Term a b -> Term b (Maybe b) -> Term a (Maybe b)
fuseFilter (Map f) (Filter p) = Map $ p . f

-- infix syntax
(||) = fuseMap
(>|) = filterFuse
(|>) = fuseFilter

filter p = Filter $ \x -> case p x of
                            True -> Just x
                            _ -> Nothing

map :: (a -> b) -> Term a b
map = Map

run :: Term a b -> [a] -> [b]
run (Map f) xs = fmap f xs

-- example
run (map (+1) || map (^2) |> filter even) [1..6] ==> [Just 4,Nothing,Just 16,Nothing,Just 36,Nothing]




-- This is a chain of list operations

(map (+1) || map (^2) |> filter even) 

-- It reduces down to a single pass
Map (\x ->  case (even ((x+1)^2)) of
                      True -> Just x
                      _ -> Nothing )