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:

• Though this module substitutes for monad-transform consisted of elemental(without-lambda-expression) kind of monad, however, this module is unable to substitute for monad-transform consisted of complicated(tangled-with-lambda-expression) kind of monad at all. So this module does not thoroughly make mlt(monad-transformer-library) unnessasary. The range in which this module is helpful is confined to the range that single Monad or Monad with Monadx series (namely Monad2, Monad3, etc) defines.
• In my opinion the above problem 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 function

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

Alias for $.

>>> 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 ->
        y >- \b ->
        a + b
in plus 3 4
:}
7

composite function

(>->) :: (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

Alias for ..

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

Level-1

bind-sequence function

(<<) :: Monad m => m b -> m a -> m b infixr 1

The auguments-flipped function for >>.

Level-2

class Monad m2 => Monad2 m2 where

The Monad2 class defines the Monad functions 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 -> 
 [[0],[1,2]] >>== \y -> 
 (**:) (x ++ show y)
:}
[["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]]

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

Methods

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

Bind function of level-2.

Instances

Monad2 []

Monad2 Maybe

Monad2 (Either e)

bind-sequence function

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

Sequence function of level-2.

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

Bind-cover function made of bind >>== and cover -*, defined as m >-== k = (-*) m >>== k.

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

Bind-cover function made of bind >>== and cover *-, defined as m >-== k = (*-) m >>== k.

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

Sequence-cover function made of sequence >>~ and cover -*, defined as m >-~ k = (-*) m >>~ k.

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

Sequence-cover function made of sequence >>~ and cover *-, defined as m >-~ k = (*-) m >>~ k.

composite function

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

Composite function of level-2.

Level-3

class Monad2 m3 => Monad3 m3 where

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

>>> :{
 -- IO-List-List Monad
 [["a","b"]] ->>== \x ->
 [[0],[1,2]] ->>== \y ->
 print (x,y) >--~
 (***:) (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"]]

Methods

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

Instances

Monad3 []

Monad3 Maybe

Monad3 (Either e)

bind-sequence function

(>>-==) :: (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

(>>>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 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

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

composite function

(>===>) :: (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

class Monad3 m4 => Monad4 m4 where

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 []

Monad4 Maybe

Monad4 (Either e)

bind-sequence function

(>>>>~) :: (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

composite function

(>====>) :: (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

class Monad4 m5 => Monad5 m5 where

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 []

Monad5 Maybe

Monad5 (Either e)

bind-sequence function

(>>>>>~) :: (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

composite function

(>=====>) :: (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