DeepControl.Monad

This module enables you to program in Monad for much deeper level than the usual Monad module expresses. You would soon realize exactly what much 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 at all. The range of monad for which this module is effective is confined to the range that the instances of Traversable are defined. This means disappointingly that this module is not effective for not-Traversable monads such as Reader and State.
• In my opinion this imperfection is hard-wired with the ability of GHC on lambda expression; GHC is unable to parse (r->) or ((->) r)　yet. Therefore some fundamental expressions such as (r->)|$> or fmap (r->) are useless, it might be theoretically impossible though.

Documentation

module Control.Monad

Level-0

bind

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

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

>>> Just -< 3
Just 3

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

The auguments-flipped function of -<.

>>> 3 >- Just
Just 3

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

fish

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

The auguments-flipped function of <-<.

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

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

Anologous to ., but the infix preference is low.

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

Level-2

bind

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

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

>>> :{
 -- List-List monad
 [["a","b"]] >>== \x ->   -- (>>==) is the level-2 bind function, analogous to (>>==)
 [[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, Traversable m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b) infixr 1

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

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

cover-bind

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

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

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

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

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

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

cover-sequence

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

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

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

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

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

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

fish

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

The level-2 fish function, analogous to >=>.

Level-3

bind

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

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

>>> :{
 -- IO-List-List monad
 (.*) [["a","b"]] >>>= \x ->   -- (>>>=) is the level-3 bind function, analogous to (>>==)
 (.*) [[0],[1,2]] >>>= \y ->
 (-**) (print (x,y)) >>>~      -- (>>>~) is the level-3 sequence function, analogous to (>>)
 (.***) (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 to (>>==)
 [[0],[1,2]] ->>= \y ->
 print (x,y) >--~         -- (>--~) is a level-3 cover-sequence function, analogous to (>>)
 (.***) (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, Traversable m2, Monad m3, Traversable m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

cover-bind

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

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

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

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

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

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

cover-sequence

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

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

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

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

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

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

fish

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

sequence

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

cover-bind

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cover-sequence

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fish

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fish

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