It kind of seems like there should be fold-like things to match some and many. foldrAlt :: Alternative f => (a -> b -> b) -> b -> f a -> f b foldrAlt c n m = foldr1Alt c n m <|> pure n foldr1Alt :: Alternative f => (a -> b -> b) -> b -> f a -> f b foldr1Alt c n m = c <$> m <*> foldrAlt c n m foldlMP' :: MonadPlus f => (b -> a -> b) -> b -> f a -> f b foldlMP' f b m = foldl1MP' f b m <|> pure b foldl1MP' :: MonadPlus f => (b -> a -> b) -> b -> f a -> f b foldl1MP' f b m = m >>= \r -> let !b' = f b r in foldlMP' f b' m --These look a bit iffy foldlAlt :: Alternative f => (b -> a -> b) -> b -> f a -> f b foldlAlt f b m = ($ b) <$> foldrAlt (\x r acc -> r (f acc x)) id m foldl1Alt :: Alternative f => (b -> a -> b) -> b -> f a -> f b foldl1Alt f b m = ($ b) <$> foldr1Alt (\x r acc -> r (f acc x)) id m Do these or similar exist somewhere? If not, should they exist somewhere? I'm particularly interested in whether either of these will be fast, or will admit a fast implementation, for attoparsec parsers. Thanks, David Feuer