DeepControl.Monad

This module enables you to program in Monad for more deeper level than the usual Monad module expresses. You would soon realize exactly what more deeper level means by reading the example codes in order, which are attached on the Monadx(Monad, Monad, etc) classes below.

Note:

• This module never makes mtl(monad-transformer-library) unnessasary. The range in which this module is helpful is regrettably confined to the range of deep monads (namely Monad, Monad, etc).
• In my opinion this bad confinement is hard-wired with the ability of the compiler, that is to say GHC doesn't parse (r->) or ((->) r) as a data constructor; thus some fundamental expressions such as (r->)|$> or fmap (r->) are useless. Theoretically it might be impossible though.

Documentation

module Control.Monad

Level-0

bind

(-<) :: (a -> b) -> a -> b infixl 1

Anologous for $, but (-<) is left associative.

>>> Just -< 3
Just 3

(>-) :: a -> (a -> b) -> b infixl 1

The auguments-flipped function for -<.

>>> 3 >- Just
Just 3

>>> :{
let plus :: Int -> Int -> Int
    plus x y = 
        x >- \a ->  -- (>-) is the level-0 bind function, analogous for (>>=)
        y >- \b ->
        a + b
in plus 3 4
:}
7

composite

(>->) :: (a -> b) -> (b -> c) -> a -> c infixr 1

The auguments-flipped function for <-<.

>>> 1 >- ((+1) >-> (*2) >-> (+3))
7

(<-<) :: (b -> c) -> (a -> b) -> a -> c infixr 1

Anologous for ., but the infix preference is low.

>>> ((3+) <-< (2*) <-< (1+)) -< 1
7

Level-2

bind

(>>==) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> (a -> m1 (m2 b)) -> m1 (m2 b) infixr 1

The level-2 bind function, analogous for >>=.

>>> :{
 -- List-List monad
 [["a","b"]] >>== \x ->   -- (>>==) is the level-2 bind function, analogous for (>>=)
 [[0],[1,2]] >>== \y -> 
 (**:) (x ++ show y)
:}
[["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]]

>>> :{
 let lengthM :: [Int] -> Maybe Int      -- (->)-Maybe monad
     lengthM [] = Nothing
     lengthM xs = Just (length xs) 
     averageM :: [Int] -> Maybe Double  -- (->)-Maybe monad
     averageM = 
         (-*) sum >>== \s ->
         lengthM >>== \l ->
         (**:) (fromIntegral s / fromIntegral l)
 in [averageM [10, 25, 70], averageM []]
:}
[Just 35.0,Nothing]

sequence

(>>~) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b) infixr 1

The level-2 sequence function, analogous for >>.

Definition: m >>~ f = m >>== \_ -> f

cover-bind

(>-==) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> (a -> m1 (m2 b)) -> m1 (m2 b) infixr 1

A level-2 cover-bind function, analogous for >>=.

Definition: m >-== f = (-*) m >>== f

(->==) :: (Monad m1, Monad m2, Commutative m2) => m2 a -> (a -> m1 (m2 b)) -> m1 (m2 b) infixr 1

A level-2 cover-bind function, analogous for >>=.

Definition: m ->== f = (*:) m >>== f

cover-sequence

(>-~) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> m1 (m2 b) -> m1 (m2 b) infixr 1

A level-2 cover-sequence function, analogous for >>.

Definition: m >-~ f = (-*) m >>~ f

(->~) :: (Monad m1, Monad m2, Commutative m2) => m2 a -> m1 (m2 b) -> m1 (m2 b) infixr 1

A level-2 cover-sequence function, analogous for >>.

Definition: m ->~ f = (*:) m >>~ f

composite

(>==>) :: (Monad m1, Monad m2, Commutative m2) => (a -> m1 (m2 b)) -> (b -> m1 (m2 c)) -> a -> m1 (m2 c) infixr 1

The level-2 composite function, analogous for >=>.

Level-3

bind

(>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

The level-3 bind function, analogous for >>=.

>>> :{
 -- IO-List-List monad
 (*:) [["a","b"]] >>>== \x ->   -- (>>>==) is the level-3 bind function, analogous for (>>=)
 (*:) [[0],[1,2]] >>>== \y ->
 (-**) (print (x,y)) >>>~       -- (>>>~) is the level-3 sequence function, analogous for (>>)
 (***:) (x ++ show y)
:}
("a",0)
("a",1)
("a",2)
("b",0)
("b",1)
("b",2)
[["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]]

This messy code above can be neatly rewritten to the code below by grace of the cover functions.

>>> :{
 -- IO-List-List monad
 [["a","b"]] ->>== \x ->   -- (->>==) is a level-3 cover-bind function, analogous for (>>=)
 [[0],[1,2]] ->>== \y ->
 print (x,y) >--~          -- (>--~) is a level-3 cover-sequence function, analogous for (>>)
 (***:) (x ++ show y)
:}
("a",0)
("a",1)
("a",2)
("b",0)
("b",1)
("b",2)
[["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]]

sequence

(>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

cover-bind

(>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

cover-sequence

(>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

composite

(>===>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => (a -> m1 (m2 (m3 b))) -> (b -> m1 (m2 (m3 c))) -> a -> m1 (m2 (m3 c)) infixr 1

Level-4

bind

(>>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

sequence

(>>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

cover-bind

(--->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m4 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

cover-sequence

(--->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m4 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

composite

(>====>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => (a -> m1 (m2 (m3 (m4 b)))) -> (b -> m1 (m2 (m3 (m4 c)))) -> a -> m1 (m2 (m3 (m4 c))) infixr 1

Level-5

bind

(>>>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

sequence

(>>>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

cover-bind

(---->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m5 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>----==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>--->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

cover-sequence

(---->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m5 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>----~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>--->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

composite

(>=====>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => (a -> m1 (m2 (m3 (m4 (m5 b))))) -> (b -> m1 (m2 (m3 (m4 (m5 c))))) -> a -> m1 (m2 (m3 (m4 (m5 c)))) infixr 1