+
+-- | Monadic versions of any and all. We reimplement them, since there
+-- is no ready-made lifting function for them.
+allM, anyM :: (Monad m) => (a -> m Bool) -> [a] -> m Bool
+allM f = andM . (mapM f)
+anyM f = orM . (mapM f)
+
+mapAccumLM :: (Monad m) => (acc -> x -> m (acc, y)) -> acc -> [x] -> m (acc, [y])
+mapAccumLM _ s [] = return (s, [])
+mapAccumLM f s (x:xs) = do
+ (s', y ) <- f s x
+ (s'', ys) <- mapAccumLM f s' xs
+ return (s'', y:ys)
+
+-- Trace the given string if the given bool is True, do nothing
+-- otherwise.
+traceIf :: Bool -> String -> a -> a
+traceIf True = Trace.trace
+traceIf False = flip const