Copyright | (C) 2015 KONISHI Yohsuke |
---|---|
License | BSD-style (see the LICENSE file in the distribution) |
Maintainer | ocean0yohsuke@gmail.com |
Stability | experimental |
Portability | --- |
Safe Haskell | Safe |
Language | Haskell2010 |
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 make mlt(monad-transformer-library) unnessasary. The range in which this module is helpful is regrettably confined to the range that the instances of deep Monads (namely Monad2, Monad3, etc) define.
- 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->)|$>
orfmap (r->)
are useless. Theoretically it might be impossible though.
- module Control.Monad
- (-<) :: (a -> b) -> a -> b
- (>-) :: a -> (a -> b) -> b
- (>->) :: (a -> b) -> (b -> c) -> a -> c
- (<-<) :: (b -> c) -> (a -> b) -> a -> c
- (<<) :: Monad m => m b -> m a -> m b
- class Monad m2 => Monad2 m2 where
- (>>~) :: (Monad m1, Monad2 m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b)
- (>-==) :: (Monad m1, Monad2 m2) => m1 a -> (a -> m1 (m2 b)) -> m1 (m2 b)
- (->==) :: (Monad m1, Monad2 m2) => m2 a -> (a -> m1 (m2 b)) -> m1 (m2 b)
- (>-~) :: (Monad m1, Monad2 m2) => m1 a -> m1 (m2 b) -> m1 (m2 b)
- (->~) :: (Monad m1, Monad2 m2) => m2 a -> m1 (m2 b) -> m1 (m2 b)
- (>==>) :: (Monad m1, Monad2 m2) => (a -> m1 (m2 b)) -> (b -> m1 (m2 c)) -> a -> m1 (m2 c)
- class Monad2 m3 => Monad3 m3 where
- (>>-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (->>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (>->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (>--==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (->-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (-->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
- (>>>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (->-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (-->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (>>-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (->>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (>->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (>--~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
- (>===>) :: (Monad m1, Monad2 m2, Monad3 m3) => (a -> m1 (m2 (m3 b))) -> (b -> m1 (m2 (m3 c))) -> a -> m1 (m2 (m3 c))
- class Monad3 m4 => Monad4 m4 where
- (>>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b)))
- (>====>) :: (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)))
- class Monad4 m5 => Monad5 m5 where
- (>>>>>~) :: (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))))
- (>=====>) :: (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))))
Documentation
module Control.Monad
Level-0
bind function
(>-) :: a -> (a -> b) -> b infixl 1 Source
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 Source
The auguments-flipped function for
. <-<
>>>
1 >- ((+1) >-> (*2) >-> (+3))
7
(<-<) :: (b -> c) -> (a -> b) -> a -> c infixr 1 Source
Alias for
. .
>>>
((3+) <-< (2*) <-< (1+)) -< 1
7
Level-1
bind-sequence function
Level-2
class Monad m2 => Monad2 m2 where Source
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]
bind-sequence function
(>>~) :: (Monad m1, Monad2 m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b) infixr 1 Source
Sequence function of level-2.
(->==) :: (Monad m1, Monad2 m2) => m2 a -> (a -> m1 (m2 b)) -> m1 (m2 b) infixr 1 Source
Bind-cover function made of bind
and cover >>==
, defined as *-
m >-== k = (*-) m >>== k
.
(->~) :: (Monad m1, Monad2 m2) => m2 a -> m1 (m2 b) -> m1 (m2 b) infixr 1 Source
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 Source
Composite function of level-2.
Level-3
class Monad2 m3 => Monad3 m3 where Source
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"]]
bind-sequence function
(>>-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(->>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(>->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(>--==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(->-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(-->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) infixr 1 Source
(>>>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(->-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(-->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(>>-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(->>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(>->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
(>--~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) infixr 1 Source
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 Source
Level-4
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 Source
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 Source
Level-5
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 Source