lifting

liftA1 :: forall a b f. Applicative f => (a -> b) -> f a -> f b
liftA1 f a = pure f <*> a
liftA2 :: forall a b c f. Applicative f => (a -> b -> c) -> f a -> f b -> f c
liftA2 f a b = pure f <*> a <*> b
liftM1 :: forall a b m. Monad m => (a -> b) -> m a -> m b
liftM1 f ma = do
  a <- ma
  return (f a)
liftM2 :: forall a b c m. Monad m => (a -> b -> c) -> m a -> m b -> m c
liftM2 f ma mb = do
  a <- ma
  b <- mb
  return (f a b)