map is just fold, or is it the other way around :P Is fold enough to have map, filter, and recursion?

map.hs

foldlmap :: (a -> b) -> [a] -> [b]
foldlmap f = foldl (\ a b -> a ++ [f b]) []


foldrmap :: (a -> b) -> [a] -> [b]
foldrmap f = foldr (\ a b -> (f a) : b) []

main :: IO ()
main = do
    print $ foldlmap (*2) [0 .. 5]
    print $ foldrmap (*2) [0 .. 5]