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(Monad2, Monad3, etc) classes below.

Note:

• This module never makes mlt(monad-transformer-library) unnessasary. The range in which this module is helpful is regrettably confined to the range of deep monads (namely Monad2, Monad3, 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

class Monad m2 => Monad2 m2 where

The Monad2 class defines the bind function for level-2 types m1 (m2 a) such as [[a]], Maybe [a], Either () (Maybe a), a -> [b], IO [a], etc.

>>> :{
 -- 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]

Minimal complete definition

(>>==)

Methods

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

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

Instances

Monad2 []

Methods

(>>==) :: Monad m1 => m1 [a] -> (a -> m1 [b]) -> m1 [b]

Monad2 Maybe

Methods

(>>==) :: Monad m1 => m1 (Maybe a) -> (a -> m1 (Maybe b)) -> m1 (Maybe b)

Monad2 (Either e)

Methods

(>>==) :: Monad m1 => m1 (Either e a) -> (a -> m1 (Either e b)) -> m1 (Either e b)

Monad2 (Except e)

Methods

(>>==) :: Monad m1 => m1 (Except e a) -> (a -> m1 (Except e b)) -> m1 (Except e b)

Monoid w => Monad2 (Writer w)

Methods

(>>==) :: Monad m1 => m1 (Writer w a) -> (a -> m1 (Writer w b)) -> m1 (Writer w b)

sequence

(>>~) :: (Monad m1, Monad2 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, Monad2 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, Monad2 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, Monad2 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, Monad2 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, Monad2 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

class Monad2 m3 => Monad3 m3 where

The Monad3 class defines the bind function for level-3 types m1 (m2 (m3 a).

>>> :{
 -- 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 with 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"]]

Minimal complete definition

(>>>==)

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

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

Instances

Monad3 []

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 [a]) -> (a -> m1 (m2 [b])) -> m1 (m2 [b])

Monad3 Maybe

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (Maybe a)) -> (a -> m1 (m2 (Maybe b))) -> m1 (m2 (Maybe b))

Monad3 (Either e)

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (Either e a)) -> (a -> m1 (m2 (Either e b))) -> m1 (m2 (Either e b))

Monad3 (Except e)

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (Except e a)) -> (a -> m1 (m2 (Except e b))) -> m1 (m2 (Except e b))

Monoid w => Monad3 (Writer w)

Methods

(>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (Writer w a)) -> (a -> m1 (m2 (Writer w b))) -> m1 (m2 (Writer w b))

sequence

(>>>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

cover-bind

(>>-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(->>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(>->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(>--==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(->-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

(-->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1

cover-sequence

(>--~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(->-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(-->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(>>-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(->>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

(>->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1

composite

(>===>) :: (Monad m1, Monad2 m2, Monad3 m3) => (a -> m1 (m2 (m3 b))) -> (b -> m1 (m2 (m3 c))) -> a -> m1 (m2 (m3 c)) infixr 1

Level-4

bind

class Monad3 m4 => Monad4 m4 where

Minimal complete definition

(>>>>==)

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

Instances

Monad4 []

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 [a])) -> (a -> m1 (m2 (m3 [b]))) -> m1 (m2 (m3 [b]))

Monad4 Maybe

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (Maybe a))) -> (a -> m1 (m2 (m3 (Maybe b)))) -> m1 (m2 (m3 (Maybe b)))

Monad4 (Either e)

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (Either e a))) -> (a -> m1 (m2 (m3 (Either e b)))) -> m1 (m2 (m3 (Either e b)))

Monad4 (Except e)

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (Except e a))) -> (a -> m1 (m2 (m3 (Except e b)))) -> m1 (m2 (m3 (Except e b)))

Monoid w => Monad4 (Writer w)

Methods

(>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (Writer w a))) -> (a -> m1 (m2 (m3 (Writer w b)))) -> m1 (m2 (m3 (Writer w b)))

sequence

(>>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

cover-bind

(--->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m4 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) infixr 1

cover-sequence

(--->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m4 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(-->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

(>>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) infixr 1

composite

(>====>) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (a -> m1 (m2 (m3 (m4 b)))) -> (b -> m1 (m2 (m3 (m4 c)))) -> a -> m1 (m2 (m3 (m4 c))) infixr 1

Level-5

bind

class Monad4 m5 => Monad5 m5 where

Minimal complete definition

(>>>>>==)

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (m5 a)))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

Instances

Monad5 []

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 [a]))) -> (a -> m1 (m2 (m3 (m4 [b])))) -> m1 (m2 (m3 (m4 [b])))

Monad5 Maybe

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (Maybe a)))) -> (a -> m1 (m2 (m3 (m4 (Maybe b))))) -> m1 (m2 (m3 (m4 (Maybe b))))

Monad5 (Either e)

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (Either e a)))) -> (a -> m1 (m2 (m3 (m4 (Either e b))))) -> m1 (m2 (m3 (m4 (Either e b))))

Monad5 (Except e)

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (Except e a)))) -> (a -> m1 (m2 (m3 (m4 (Except e b))))) -> m1 (m2 (m3 (m4 (Except e b))))

Monoid w => Monad5 (Writer w)

Methods

(>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (Writer w a)))) -> (a -> m1 (m2 (m3 (m4 (Writer w b))))) -> m1 (m2 (m3 (m4 (Writer w b))))

sequence

(>>>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 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, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m5 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>----==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>--->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 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, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m5 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>----~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(--->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>--->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(-->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>-->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(->>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

(>>>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) infixr 1

composite

(>=====>) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (a -> m1 (m2 (m3 (m4 (m5 b))))) -> (b -> m1 (m2 (m3 (m4 (m5 c))))) -> a -> m1 (m2 (m3 (m4 (m5 c)))) infixr 1