Proof Summary for Module Monad

StatusNumberAvg. TimePercent
YES690.6686.25
MAYBE1113.6613.75
TIMEOUT0 0
NO000
TOTAL80
0 start terms are not H-terminating (colored white)

SecondsNumberPercent
56986.25
156986.25
306986.25

Proof timeProof
YES 0.46 mzero :: MonadPlus m => m a
YES 0.4 mzero :: [] a
YES 0.46 mzero :: Maybe a
YES 0.71 mplus :: MonadPlus m => m a -> m a -> m a
YES 0.75 mplus :: [] a -> [] a -> [] a
YES 0.46 mplus :: Maybe a -> Maybe a -> Maybe a
YES 0.73 join :: Monad m => m (m a) -> m a
YES 0.71 join :: [] ([] a) -> [] a
YES 0.44 join :: Maybe (Maybe a) -> Maybe a
YES 0.43 join :: IO (IO a) -> IO a
YES 0.72 msum :: MonadPlus m => [m a] -> m a
YES 0.7 msum :: [[] a] -> [] a
YES 0.68 msum :: [Maybe a] -> Maybe a
MAYBE 1.79 filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
MAYBE 1.71 filterM :: (a -> [] Bool) -> [a] -> [] [a]
YES 0.7 filterM :: (a -> Maybe Bool) -> [a] -> Maybe [a]
YES 0.7 filterM :: (a -> IO Bool) -> [a] -> IO [a]
MAYBE 86.28 mapAndUnzipM :: Monad m => (a -> m (b,c)) -> [a] -> m ([b], [c])
MAYBE 2.12 mapAndUnzipM :: (a -> [] (b,c)) -> [a] -> [] ([b], [c])
MAYBE 47.55 mapAndUnzipM :: (a -> Maybe (b,c)) -> [a] -> Maybe ([b], [c])
YES 0.74 mapAndUnzipM :: (a -> IO (b,c)) -> [a] -> IO ([b], [c])
MAYBE 1.68 zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]
MAYBE 1.58 zipWithM :: (a -> b -> [] c) -> [a] -> [b] -> [] [c]
YES 0.67 zipWithM :: (a -> b -> Maybe c) -> [a] -> [b] -> Maybe [c]
YES 0.72 zipWithM :: (a -> b -> IO c) -> [a] -> [b] -> IO [c]
YES 0.78 zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()
YES 0.82 zipWithM_ :: (a -> b -> [] c) -> [a] -> [b] -> [] ()
YES 0.69 zipWithM_ :: (a -> b -> Maybe c) -> [a] -> [b] -> Maybe ()
YES 0.71 zipWithM_ :: (a -> b -> IO c) -> [a] -> [b] -> IO ()
MAYBE 1.66 foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a
MAYBE 1.58 foldM :: (a -> b -> [] a) -> a -> [b] -> [] a
YES 0.71 foldM :: (a -> b -> Maybe a) -> a -> [b] -> Maybe a
YES 0.78 foldM :: (a -> b -> IO a) -> a -> [b] -> IO a
MAYBE 2.12 foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
MAYBE 2.22 foldM_ :: (a -> b -> [] a) -> a -> [b] -> [] ()
YES 0.76 foldM_ :: (a -> b -> Maybe a) -> a -> [b] -> Maybe ()
YES 0.79 foldM_ :: (a -> b -> IO a) -> a -> [b] -> IO ()
YES 1.39 replicateM :: Monad m => Int -> m a -> m [a]
YES 1.09 replicateM :: Int -> [] a -> [] [a]
YES 1.05 replicateM :: Int -> Maybe a -> Maybe [a]
YES 0.85 replicateM :: Int -> IO a -> IO [a]
YES 1.38 replicateM_ :: Monad m => Int -> m a -> m ()
YES 1.03 replicateM_ :: Int -> [] a -> [] ()
YES 0.85 replicateM_ :: Int -> Maybe a -> Maybe ()
YES 0.9 replicateM_ :: Int -> IO a -> IO ()
YES 0.48 guard :: MonadPlus m => Bool -> m ()
YES 0.46 guard :: Bool -> [] ()
YES 0.44 guard :: Bool -> Maybe ()
YES 0.46 when :: Monad m => Bool -> m () -> m ()
YES 0.44 when :: Bool -> [] () -> [] ()
YES 0.42 when :: Bool -> Maybe () -> Maybe ()
YES 0.44 when :: Bool -> IO () -> IO ()
YES 0.45 unless :: Monad m => Bool -> m () -> m ()
YES 0.45 unless :: Bool -> [] () -> [] ()
YES 0.46 unless :: Bool -> Maybe () -> Maybe ()
YES 0.44 unless :: Bool -> IO () -> IO ()
YES 0.73 liftM :: Monad m => (a -> b) -> (m a -> m b)
YES 0.71 liftM :: (a -> b) -> ([] a -> [] b)
YES 0.46 liftM :: (a -> b) -> (Maybe a -> Maybe b)
YES 0.43 liftM :: (a -> b) -> (IO a -> IO b)
YES 0.73 liftM2 :: Monad m => (a -> b -> c) -> (m a -> m b -> m c)
YES 0.8 liftM2 :: (a -> b -> c) -> ([] a -> [] b -> [] c)
YES 0.46 liftM2 :: (a -> b -> c) -> (Maybe a -> Maybe b -> Maybe c)
YES 0.45 liftM2 :: (a -> b -> c) -> (IO a -> IO b -> IO c)
YES 0.84 liftM3 :: Monad m => (a -> b -> c -> d) -> (m a -> m b -> m c -> m d)
YES 0.76 liftM3 :: (a -> b -> c -> d) -> ([] a -> [] b -> [] c -> [] d)
YES 0.45 liftM3 :: (a -> b -> c -> d) -> (Maybe a -> Maybe b -> Maybe c -> Maybe d)
YES 0.44 liftM3 :: (a -> b -> c -> d) -> (IO a -> IO b -> IO c -> IO d)
YES 0.84 liftM4 :: Monad m => (a -> b -> c -> d -> e) -> (m a -> m b -> m c -> m d -> m e)
YES 0.71 liftM4 :: (a -> b -> c -> d -> e) -> ([] a -> [] b -> [] c -> [] d -> [] e)
YES 0.48 liftM4 :: (a -> b -> c -> d -> e) -> (Maybe a -> Maybe b -> Maybe c -> Maybe d -> Maybe e)
YES 0.47 liftM4 :: (a -> b -> c -> d -> e) -> (IO a -> IO b -> IO c -> IO d -> IO e)
YES 0.83 liftM5 :: Monad m => (a -> b -> c -> d -> e -> f) -> (m a -> m b -> m c -> m d -> m e -> m f)
YES 0.76 liftM5 :: (a -> b -> c -> d -> e -> f) -> ([] a -> [] b -> [] c -> [] d -> [] e -> [] f)
YES 0.47 liftM5 :: (a -> b -> c -> d -> e -> f) -> (Maybe a -> Maybe b -> Maybe c -> Maybe d -> Maybe e -> Maybe f)
YES 0.48 liftM5 :: (a -> b -> c -> d -> e -> f) -> (IO a -> IO b -> IO c -> IO d -> IO e -> IO f)
YES 0.74 ap :: Monad m => m (a -> b) -> m a -> m b
YES 0.71 ap :: [] (a -> b) -> [] a -> [] b
YES 0.45 ap :: Maybe (a -> b) -> Maybe a -> Maybe b
YES 0.49 ap :: IO (a -> b) -> IO a -> IO b