-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Provide more deeper level style of programming than the usual Control.xxx modules express
--
-- This module enables more deeper level style of programming than the
-- usual Control.xxx modules express, especially for Applicative and
-- Monad.
@package deepcontrol
@version 0.4.3.0
-- | Signatures for monad operations that require specialized lifting. Each
-- signature has a uniformity property that the lifting should satisfy.
module DeepControl.Monad.Signatures
type CallCC2 m1 m2 a b = ((a -> m1 (m2 b)) -> m1 (m2 a)) -> m1 (m2 a)
type Catch2 e m1 m2 a = m1 (m2 a) -> (e -> m1 (m2 a)) -> m1 (m2 a)
type Listen2 w m1 m2 a = m1 (m2 a) -> m1 (m2 (a, w))
type Pass2 w m1 m2 a = m1 (m2 (a, w -> w)) -> m1 (m2 a)
type CallCC3 m1 m2 m3 a b = ((a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 a))) -> m1 (m2 (m3 a))
type Catch3 e m1 m2 m3 a = m1 (m2 (m3 a)) -> (e -> m1 (m2 (m3 a))) -> m1 (m2 (m3 a))
type Listen3 w m1 m2 m3 a = m1 (m2 (m3 a)) -> m1 (m2 (m3 (a, w)))
type Pass3 w m1 m2 m3 a = m1 (m2 (m3 (a, w -> w))) -> m1 (m2 (m3 a))
type CallCC4 m1 m2 m3 m4 a b = ((a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 a)))) -> m1 (m2 (m3 (m4 a)))
type Catch4 e m1 m2 m3 m4 a = m1 (m2 (m3 (m4 a))) -> (e -> m1 (m2 (m3 (m4 a)))) -> m1 (m2 (m3 (m4 a)))
type Listen4 w m1 m2 m3 m4 a = m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (a, w))))
type Pass4 w m1 m2 m3 m4 a = m1 (m2 (m3 (m4 (a, w -> w)))) -> m1 (m2 (m3 (m4 a)))
type CallCC5 m1 m2 m3 m4 m5 a b = ((a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 a))))) -> m1 (m2 (m3 (m4 (m5 a))))
type Catch5 e m1 m2 m3 m4 m5 a = m1 (m2 (m3 (m4 (m5 a)))) -> (e -> m1 (m2 (m3 (m4 (m5 a))))) -> m1 (m2 (m3 (m4 (m5 a))))
type Listen5 w m1 m2 m3 m4 m5 a = m1 (m2 (m3 (m4 (m5 a)))) -> m1 (m2 (m3 (m4 (m5 (a, w)))))
type Pass5 w m1 m2 m3 m4 m5 a = m1 (m2 (m3 (m4 (m5 (a, w -> w))))) -> m1 (m2 (m3 (m4 (m5 a))))
-- | This module enables you to program in applicative style for more
-- deeper level than the usual Applicative module
-- expresses. You would soon realize exactly what more deeper
-- level means by reading the example codes in order, which are
-- attached on the functions below.
module DeepControl.Applicative
-- | Alias to $.
--
--
-- >>> (1+) |> 2
-- 3
--
(|>) :: (a -> b) -> a -> b
-- | The auguments-flipped function for |>.
--
--
-- >>> 1 <| (+2)
-- 3
--
-- >>> 1 <|(+)|> 2
-- 3
--
-- >>> 1 <|(+)|> 2 <|(*)|> 3
-- 9
--
--
--
-- >>> 1 <|(,)|> 2
-- (1,2)
--
(<|) :: a -> (a -> b) -> b
-- | Alias to pure.
(*:) :: (Applicative f) => a -> f a
-- | Alias to <$>.
--
--
-- >>> (1+) |$> [2]
-- [3]
--
(|$>) :: Functor f => (a -> b) -> f a -> f b
-- | The auguments-flipped function for |$>.
--
--
-- >>> [1] <$| (+2)
-- [3]
--
--
--
-- >>> ("<"++)|$> ["a","b"] <$|(++">")
-- ["<a>","<b>"]
--
(<$|) :: Functor f => f a -> (a -> b) -> f b
-- | Alias to <*>.
--
--
-- >>> [(1+)] |*> [2]
-- [3]
--
--
--
-- >>> [1] <$|(+)|*> [2]
-- [3]
--
-- >>> [1] <$|(+)|*> [0,1,2]
-- [1,2,3]
--
-- >>> [0,1] <$|(+)|*> [2,3] <$|(^)|*> [4,5]
-- [16,32,81,243,81,243,256,1024]
--
--
--
-- >>> foldr (\x acc -> x <$|(:)|*> acc) ((*:) []) [Just 1, Just 2, Just 3]
-- Just [1,2,3]
--
-- >>> foldr (\x acc -> x <$|(:)|*> acc) ((*:) []) [Just 1, Nothing, Just 3]
-- Nothing
--
--
--
-- >>> filter (even <$|(&&)|*> (10 >)) [1..100]
-- [2,4,6,8]
--
-- >>> filter (even <$|(&&)|*> (10 >) <$|(&&)|*> (5 <)) [1..100]
-- [6,8]
--
(|*>) :: Applicative f => f (a -> b) -> f a -> f b
-- | The auguments-flipped function for |*>.
(<*|) :: Applicative f => f a -> f (a -> b) -> f b
-- | Definition: f |* x = f |*> (*:) x
--
--
-- >>> [(1+)] |* 2
-- [3]
--
-- >>> [1] <$|(+)|* 2
-- [3]
--
--
--
-- >>> (,) |$> ["a1","a2"] |* 'b'
-- [("a1",'b'),("a2",'b')]
--
--
--
-- >>> (,,) 'a' |$> ["b1","b2"] |* 'c'
-- [('a',"b1",'c'),('a',"b2",'c')]
--
--
--
-- >>> (,,,) 'a' |$> ["b1","b2"] |* 'c' |* 'd'
-- [('a',"b1",'c','d'),('a',"b2",'c','d')]
--
-- >>> (,,,) 'a' |$> ["b1","b2"] |* 'c' |*> ["d1","d2"]
-- [('a',"b1",'c',"d1"),('a',"b1",'c',"d2"),('a',"b2",'c',"d1"),('a',"b2",'c',"d2")]
--
(|*) :: Applicative f => f (a -> b) -> a -> f b
-- | The auguments-flipped function for |*.
--
--
-- >>> 1 *| [(+2)]
-- [3]
--
-- >>> 1 *| [(+)] |* 2
-- [3]
--
-- >>> 1 *|[(+),(-),(*),(^)]|* 2
-- [3,-1,2,1]
--
--
--
-- >>> 1 *|Just (,)|* 2
-- Just (1,2)
--
(*|) :: Applicative f => a -> f (a -> b) -> f b
-- | Definition: (**:) = (*:) . (*:)
--
--
-- >>> (**:) 1 :: Maybe [Int]
-- Just [1]
--
(**:) :: (Applicative f1, Applicative f2) => a -> f1 (f2 a)
-- | Definition: (-*) = ((*:)|$>)
--
--
-- >>> (-*) (Just 1) :: Maybe [Int]
-- Just [1]
--
(-*) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 a)
-- | Definition: (|$>>) = (|$>) . (|$>)
--
--
-- >>> (+1) |$>> [[2]]
-- [[3]]
--
(|$>>) :: (Functor f1, Functor f2) => (a -> b) -> f1 (f2 a) -> f1 (f2 b)
-- | The auguments-flipped function for |$>>
--
--
-- >>> [[2]] <<$| (+1)
-- [[3]]
--
(<<$|) :: (Functor f1, Functor f2) => f1 (f2 a) -> (a -> b) -> f1 (f2 b)
-- | Definition: (|*>>) = liftA2 (|*>)
--
--
-- >>> [Just 1] <<$|(+)|*>> [Just 2]
-- [Just 3]
--
--
--
-- >>> [Just 1] <<$|(,)|*>> [Just 2]
-- [Just (1,2)]
--
--
--
-- >>> [[1]] <<$|(+)|*>> [[2]] <<$|(-)|*>> [[3]]
-- [[0]]
--
--
--
-- >>> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right (Just 2), Right (Just 3)] :: Either () (Maybe Int)
-- Right (Just 6)
--
-- >>> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right Nothing, Right (Just 3)] :: Either () (Maybe Int)
-- Right Nothing
--
-- >>> foldr (\n acc -> n <<$|(+)|*>> acc) ((**:) 0) [Right (Just 1), Right Nothing, Left ()]
-- Left ()
--
(|*>>) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> f1 (f2 a) -> f1 (f2 b)
-- | Definition: (<<*|) = liftA2 (<*|)
(<<*|) :: (Applicative f1, Applicative f2) => f1 (f2 a) -> f1 (f2 (a -> b)) -> f1 (f2 b)
-- | Definition: f |** x = f |*>> (**:) x
--
--
-- >>> [Just 1] <<$|(+)|** 2
-- [Just 3]
--
(|**) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> a -> f1 (f2 b)
-- | Definition: x **| f = (**:) x <<*| f
--
--
-- >>> 1 **|(+)|$>> [Just 2]
-- [Just 3]
--
--
--
-- >>> 1 **|[Just (+)]|** 2
-- [Just 3]
--
-- >>> 1 **|[Just (+), Just (-), Just (*), Nothing]|** 2
-- [Just 3,Just (-1),Just 2,Nothing]
--
(**|) :: (Applicative f1, Applicative f2) => a -> f1 (f2 (a -> b)) -> f1 (f2 b)
-- | Definition: f |-* x = f |*>> (-*) x
--
--
-- >>> [Just 1] <<$|(+)|-* [2]
-- [Just 3]
--
(|-*) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> f1 a -> f1 (f2 b)
-- | Definition: f |*- x = f |*>> (*:) x
--
--
-- >>> [Just 1] <<$|(+)|*- Just 2
-- [Just 3]
--
(|*-) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> f2 a -> f1 (f2 b)
-- | Definition: x -*| f = (-*) x <<*| f
--
--
-- >>> [1] -*|(+)|$>> [Just 2]
-- [Just 3]
--
(-*|) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 (a -> b)) -> f1 (f2 b)
-- | Definition: x *-| f = (*:) x <<*| f
--
--
-- >>> Just 1 *-|(+)|$>> [Just 2]
-- [Just 3]
--
-- >>> Just 1 *-|[Just (+)]|** 2
-- [Just 3]
--
-- >>> Just 1 *-|[Just (+)]|*- Just 2
-- [Just 3]
--
-- >>> [1] -*|[Just (+)]|*- Just 2
-- [Just 3]
--
-- >>> [1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2
-- [Just 3,Just (-1),Just 2,Nothing]
--
-- >>> [1,2] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2
-- [Just 3,Just (-1),Just 2,Nothing,Just 4,Just 0,Just 4,Nothing]
--
--
--
-- >>> print 1 -*|return [\_ _ -> 3]|-* print 2
-- 1
-- 2
-- [3]
--
(*-|) :: (Applicative f1, Applicative f2) => f2 a -> f1 (f2 (a -> b)) -> f1 (f2 b)
-- | Definition: (*>>) = liftA2 (*>)
--
--
-- >>> sequence $ Just (print 1) *>> (**:) 2
-- 1
-- Just 2
--
--
--
-- >>> (-*) (print 1) *>> return (Just 2)
-- 1
-- Just 2
--
(*>>) :: (Applicative f1, Applicative f2) => f1 (f2 a) -> f1 (f2 b) -> f1 (f2 b)
-- | Definition: (<<*) = liftA2 (<*)
--
--
-- >>> sequence $ (**:) 2 <<* Just (print 1)
-- 1
-- Just 2
--
-- >>> sequence $ Just (print 1) *>> (**:) 3 <<* Just (print 2)
-- 1
-- 2
-- Just 3
--
--
--
-- >>> sequence $ [putStr "1", putStr "2"] *>> (**:) 0 <<* [putStr "3", putStr "4"]
-- 13142324[0,0,0,0]
--
(<<*) :: (Applicative f1, Applicative f2) => f1 (f2 a) -> f1 (f2 b) -> f1 (f2 a)
-- | Definition: a -*> x = (-*) a *>> x
--
--
-- >>> print 1 -*> (*:) (Just 2)
-- 1
-- Just 2
--
(-*>) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 b) -> f1 (f2 b)
-- | Definition: x <-* a = x <<* (-*) a
--
--
-- >>> (*:) (Just 2) <-* print 1
-- 1
-- Just 2
--
-- >>> print 1 -*> (*:) (Just 3) <-* print 2
-- 1
-- 2
-- Just 3
--
-- >>> print 1 -*> (*:) (Just 3) <*- Nothing
-- 1
-- Nothing
--
(<-*) :: (Applicative f1, Applicative f2) => f1 (f2 b) -> f1 a -> f1 (f2 b)
-- | Definition: a *-> x = (*:) a *>> x
--
--
-- >>> sequence $ print 1 *-> Just ((*:) 2)
-- 1
-- Just 2
--
(*->) :: (Applicative f1, Applicative f2) => f2 a -> f1 (f2 b) -> f1 (f2 b)
-- | Definition: x <*- a = x <<* (*:) a
--
--
-- >>> sequence $ Just ((*:) 2) <*- print 1
-- 1
-- Just 2
--
-- >>> sequence $ print 1 *-> Just ((*:) 3) <*- print 2
-- 1
-- 2
-- Just 3
--
-- >>> sequence $ print 1 *-> Just ((*:) 3) <-* Nothing
-- Nothing
--
(<*-) :: (Applicative f1, Applicative f2) => f1 (f2 b) -> f2 a -> f1 (f2 b)
(***:) :: (Applicative f1, Applicative f2, Applicative f3) => a -> f1 (f2 (f3 a))
(*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 a))
(-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 a))
(--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 a))
(|$>>>) :: (Functor f1, Functor f2, Functor f3) => (a -> b) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 b))
(<<<$|) :: (Functor f1, Functor f2, Functor f3) => f1 (f2 (f3 a)) -> (a -> b) -> f1 (f2 (f3 b))
(|*>>>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 b))
(<<<*|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(|***) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> a -> f1 (f2 (f3 b))
(|-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 a -> f1 (f2 (f3 b))
(|*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f2 a -> f1 (f2 (f3 b))
(|**-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f3 a -> f1 (f2 (f3 b))
(|--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f2 a) -> f1 (f2 (f3 b))
(|-*-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f3 a) -> f1 (f2 (f3 b))
(|*--) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f2 (f3 a) -> f1 (f2 (f3 b))
(***|) :: (Applicative f1, Applicative f2, Applicative f3) => a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(-**|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(*-*|) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(**-|) :: (Applicative f1, Applicative f2, Applicative f3) => f3 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(--*|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(-*-|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f3 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(*--|) :: (Applicative f1, Applicative f2, Applicative f3) => f2 (f3 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b))
(*>>>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(<<<*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 a))
(*-->) :: (Applicative f1, Applicative f2, Applicative f3) => f2 (f3 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(-*->) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f3 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(--*>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(**->) :: (Applicative f1, Applicative f2, Applicative f3) => f3 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(*-*>) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(-**>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b))
(<*--) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f2 (f3 a) -> f1 (f2 (f3 b))
(<-*-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 (f3 a) -> f1 (f2 (f3 b))
(<--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 (f2 a) -> f1 (f2 (f3 b))
(<**-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f3 a -> f1 (f2 (f3 b))
(<*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f2 a -> f1 (f2 (f3 b))
(<-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 a -> f1 (f2 (f3 b))
(****:) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => a -> f1 (f2 (f3 (f4 a)))
(---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 a)))
(--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 a)))
(-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 a)))
(*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 a)))
(-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 a)))
(*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 a)))
(**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 a)))
(|$>>>>) :: (Functor f1, Functor f2, Functor f3, Functor f4) => (a -> b) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b)))
(<<<<$|) :: (Functor f1, Functor f2, Functor f3, Functor f4) => f1 (f2 (f3 (f4 a))) -> (a -> b) -> f1 (f2 (f3 (f4 b)))
(|*>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b)))
(<<<<*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(|****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> a -> f1 (f2 (f3 (f4 b)))
(|-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 a -> f1 (f2 (f3 (f4 b)))
(|*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 a -> f1 (f2 (f3 (f4 b)))
(|**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f3 a -> f1 (f2 (f3 (f4 b)))
(|***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f4 a -> f1 (f2 (f3 (f4 b)))
(|--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 b)))
(|-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 b)))
(|*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 b)))
(|*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 b)))
(|-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 b)))
(|**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 b)))
(|---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b)))
(|--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(|-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(|*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(****|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(-***|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(*-**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(**-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(***-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f4 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(--**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(-*-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(*--*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(*-*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(-**-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(**--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(---*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(--*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(-*--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(*---|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b)))
(*>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(<<<<*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 a)))
(<---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b)))
(<--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(<-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(<*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b)))
(<--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 b)))
(<-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 b)))
(<*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 b)))
(<*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 b)))
(<-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 b)))
(<**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 b)))
(<-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 a -> f1 (f2 (f3 (f4 b)))
(<*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 a -> f1 (f2 (f3 (f4 b)))
(<**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f3 a -> f1 (f2 (f3 (f4 b)))
(<***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f4 a -> f1 (f2 (f3 (f4 b)))
(---*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(--*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(-*-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(*--->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(--**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(-*-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(*--*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(*-*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(-**->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(**-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(-***>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(*-**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(**-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(***->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f4 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b)))
(*****:) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => a -> f1 (f2 (f3 (f4 (f5 a))))
(----*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 a))))
(---**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 a))))
(--*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a))))
(-*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a))))
(*---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a))))
(--***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 a))))
(-*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 a))))
(*--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 a))))
(*-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 a))))
(-**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 a))))
(**--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 a))))
(-****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 a -> f1 (f2 (f3 (f4 (f5 a))))
(*-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 a -> f1 (f2 (f3 (f4 (f5 a))))
(**-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 a -> f1 (f2 (f3 (f4 (f5 a))))
(***-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 a -> f1 (f2 (f3 (f4 (f5 a))))
(|$>>>>>) :: (Functor f1, Functor f2, Functor f3, Functor f4, Functor f5) => (a -> b) -> f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 b))))
(<<<<<$|) :: (Functor f1, Functor f2, Functor f3, Functor f4, Functor f5) => f1 (f2 (f3 (f4 (f5 a)))) -> (a -> b) -> f1 (f2 (f3 (f4 (f5 b))))
(|*>>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 b))))
(<<<<<*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(|-****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 a -> f1 (f2 (f3 (f4 (f5 b))))
(|*-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 a -> f1 (f2 (f3 (f4 (f5 b))))
(|**-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f3 a -> f1 (f2 (f3 (f4 (f5 b))))
(|***-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f4 a -> f1 (f2 (f3 (f4 (f5 b))))
(|****-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f5 a -> f1 (f2 (f3 (f4 (f5 b))))
(|--***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|-*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|*--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|*-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|-**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|**--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|**-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f3 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|*-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|-***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|***--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f4 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(|---**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|--*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|-*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|*---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|*--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|-*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|--**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|-**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|*-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|**---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f3 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(|----*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(|---*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(|--*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(|-*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(|*----) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f2 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(-****|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 a -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-***|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 a -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(**-**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 a -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(***-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 a -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(****-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f5 a -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(--***|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*-**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*--**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-*-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-**-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(**--*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(**-*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f5 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-**-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f5 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-***-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f5 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(***--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 (f5 a) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(---**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(--*-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*--*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*---*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*--*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*-*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(--**-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-**--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-*--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(**---|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(----*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(---*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f5 a))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(--*--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*---|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*----|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 (a -> b))))) -> f1 (f2 (f3 (f4 (f5 b))))
(*>>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(<<<<<*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 a))))
(<----*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(<---*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(<--*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(<-*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(<*----) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b))))
(<---**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<--*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<-*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<*---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<*--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<-*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<--**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<-**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<*-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<**---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f3 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b))))
(<--***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<-*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<*--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<*-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<-**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<**--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<**-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f3 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<*-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<-***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<***--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f4 (f5 a) -> f1 (f2 (f3 (f4 (f5 b))))
(<-****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 a -> f1 (f2 (f3 (f4 (f5 b))))
(<*-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 a -> f1 (f2 (f3 (f4 (f5 b))))
(<**-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f3 a -> f1 (f2 (f3 (f4 (f5 b))))
(<***-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f4 a -> f1 (f2 (f3 (f4 (f5 b))))
(<****-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f5 a -> f1 (f2 (f3 (f4 (f5 b))))
(----*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(---*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(--*-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*--->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*---->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 (f5 a))) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(---**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(--*-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*--*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*---*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*--*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*-*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(--**->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-**-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-*-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(**--->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 (f5 a)) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(--***>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-*-**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*--**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-*-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-**-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(**--*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(**-*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f5 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-**->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f5 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-***->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f5 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(***-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 (f5 a) -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(-****>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(*-***>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(**-**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(***-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
(****->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f5 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b))))
-- | This module is made of Traversable, distilling most
-- function names polluted with action kind of concepts into
-- crystalized(static) ones.
module DeepControl.Commutative
-- | [], Maybe, Either, Except and Writer are all commutative each other.
-- So these monads can be deepened to Monad2, Monad3, Monad4 and Monad5.
class (Functor c) => Commutative c
-- | This method is equivalent for sequenceA except the
-- name. The only difference is the name "commute", that is to say from
-- which no action kind of concepts smell.
--
--
-- >>> commute $ Just [1]
-- [Just 1]
--
-- >>> commute $ [Just 1]
-- Just [1]
--
--
--
-- >>> commute $ Right (Just 1)
-- Just (Right 1)
--
-- >>> commute $ Just (Right 1)
-- Right (Just 1)
--
commute :: (Commutative c, Applicative f) => c (f a) -> f (c a)
-- | Do fmap f then commute, equivalent for
-- traverse.
cmap :: (Applicative f, Commutative c) => (a -> f b) -> c a -> f (c b)
-- | The auguments-flipped function for cmap, equivalent
-- for for.
cfor :: (Applicative f, Commutative c) => c a -> (a -> f b) -> f (c b)
-- | This function may be used as a value for fmap in a
-- Functor instance, provided that commute is defined.
-- (Using fmapDefault with a Commutative instance will
-- result in infinite recursion.)
fmapDefault :: Commutative t => (a -> b) -> t a -> t b
-- | This function may be used as a value for foldMap in a
-- Foldable instance.
foldMapDefault :: (Commutative t, Monoid m) => (a -> m) -> t a -> m
-- | sink2 = (commute|$>) . commute
--
--
-- >>> sink2 $ Right (Just [1])
-- Just [Right 1]
--
sink2 :: (Commutative m1, Applicative m2, Applicative m3) => m1 (m2 (m3 a)) -> m2 (m3 (m1 a))
-- | float2 = commute . (commute|$>)
--
--
-- >>> float2 $ Just [Right 1]
-- Right (Just [1])
--
float2 :: (Applicative m1, Commutative m2, Commutative m3) => m2 (m3 (m1 a)) -> m1 (m2 (m3 a))
-- | sink3 = (sink2|$>) . commute
--
--
-- >>> sink3 $ Right [Just [1]]
-- [Just [Right 1]]
--
sink3 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4) => m1 (m2 (m3 (m4 a))) -> m2 (m3 (m4 (m1 a)))
-- | float3 = commute . (float2|$>)
--
--
-- >>> float3 $ [Just [Right 1]]
-- Right [Just [1]]
--
float3 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4) => m2 (m3 (m4 (m1 a))) -> m1 (m2 (m3 (m4 a)))
sink4 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4, Applicative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m2 (m3 (m4 (m5 (m1 a))))
float4 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5) => m2 (m3 (m4 (m5 (m1 a)))) -> m1 (m2 (m3 (m4 (m5 a))))
sink5 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4, Applicative m5, Applicative m6) => m1 (m2 (m3 (m4 (m5 (m6 a))))) -> m2 (m3 (m4 (m5 (m6 (m1 a)))))
float5 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5, Commutative m6) => m2 (m3 (m4 (m5 (m6 (m1 a))))) -> m1 (m2 (m3 (m4 (m5 (m6 a)))))
instance DeepControl.Commutative.Commutative GHC.Base.Maybe
instance DeepControl.Commutative.Commutative []
instance GHC.Base.Monoid w => DeepControl.Commutative.Commutative (Control.Monad.Trans.Writer.Lazy.Writer w)
instance DeepControl.Commutative.Commutative (Data.Either.Either a)
instance DeepControl.Commutative.Commutative (Control.Monad.Trans.Except.Except e)
instance DeepControl.Commutative.Commutative (Control.Applicative.Const m)
instance GHC.Base.Functor DeepControl.Commutative.Id
instance GHC.Base.Applicative DeepControl.Commutative.Id
-- | 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.
--
module DeepControl.Monad
-- | Anologous for $, but (-<) is left associative.
--
--
-- >>> Just -< 3
-- Just 3
--
(-<) :: (a -> b) -> a -> b
-- | 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
--
(>-) :: a -> (a -> b) -> b
-- | The auguments-flipped function for <-<.
--
--
-- >>> 1 >- ((+1) >-> (*2) >-> (+3))
-- 7
--
(>->) :: (a -> b) -> (b -> c) -> a -> c
-- | Anologous for ., but the infix preference is low.
--
--
-- >>> ((3+) <-< (2*) <-< (1+)) -< 1
-- 7
--
(<-<) :: (b -> c) -> (a -> b) -> a -> c
-- | 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]
--
(>>==) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> (a -> m1 (m2 b)) -> m1 (m2 b)
-- | The level-2 sequence function, analogous for >>.
--
-- Definition: m >>~ f = m >>== \_ -> f
(>>~) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b)
-- | A level-2 cover-bind function, analogous for
-- >>=.
--
-- Definition: m >-== f = (-*) m >>== f
(>-==) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> (a -> m1 (m2 b)) -> m1 (m2 b)
-- | 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)
-- | A level-2 cover-sequence function, analogous for
-- >>.
--
-- Definition: m >-~ f = (-*) m >>~ f
(>-~) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> m1 (m2 b) -> m1 (m2 b)
-- | 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)
-- | The level-2 composite function, analogous for
-- >=>.
(>==>) :: (Monad m1, Monad m2, Commutative m2) => (a -> m1 (m2 b)) -> (b -> m1 (m2 c)) -> a -> m1 (m2 c)
-- | 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"]]
--
(>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b))
(>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b))
(>===>) :: (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))
(>>>>==) :: (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)))
(>>>>~) :: (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)))
(--->==) :: (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)))
(-->-==) :: (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)))
(->--==) :: (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)))
(>---==) :: (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)))
(-->>==) :: (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)))
(->->==) :: (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)))
(>-->==) :: (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)))
(>->-==) :: (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)))
(->>-==) :: (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)))
(>>--==) :: (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)))
(->>>==) :: (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)))
(>->>==) :: (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)))
(>>->==) :: (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)))
(>>>-==) :: (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)))
(--->~) :: (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)))
(-->-~) :: (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)))
(->--~) :: (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)))
(>---~) :: (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)))
(-->>~) :: (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)))
(->->~) :: (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)))
(>-->~) :: (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)))
(>->-~) :: (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)))
(->>-~) :: (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)))
(>>--~) :: (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)))
(->>>~) :: (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)))
(>->>~) :: (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)))
(>>->~) :: (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)))
(>>>-~) :: (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)))
(>====>) :: (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)))
(>>>>>==) :: (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))))
(>>>>>~) :: (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))))
(---->==) :: (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))))
(--->-==) :: (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))))
(-->--==) :: (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))))
(->---==) :: (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))))
(>----==) :: (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))))
(--->>==) :: (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))))
(-->->==) :: (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))))
(->-->==) :: (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))))
(>--->==) :: (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))))
(>-->-==) :: (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))))
(->->-==) :: (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))))
(-->>-==) :: (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))))
(->>--==) :: (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))))
(>->--==) :: (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))))
(>>---==) :: (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))))
(-->>>==) :: (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))))
(->->>==) :: (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))))
(>-->>==) :: (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))))
(>->->==) :: (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))))
(->>->==) :: (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))))
(>>-->==) :: (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))))
(>>->-==) :: (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))))
(>->>-==) :: (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))))
(->>>-==) :: (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))))
(>>>--==) :: (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))))
(->>>>==) :: (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))))
(>->>>==) :: (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))))
(>>->>==) :: (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))))
(>>>->==) :: (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))))
(>>>>-==) :: (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))))
(---->~) :: (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))))
(--->-~) :: (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))))
(-->--~) :: (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))))
(->---~) :: (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))))
(>----~) :: (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))))
(--->>~) :: (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))))
(-->->~) :: (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))))
(->-->~) :: (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))))
(>--->~) :: (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))))
(>-->-~) :: (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))))
(->->-~) :: (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))))
(-->>-~) :: (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))))
(->>--~) :: (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))))
(>->--~) :: (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))))
(>>---~) :: (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))))
(-->>>~) :: (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))))
(->->>~) :: (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))))
(>-->>~) :: (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))))
(>->->~) :: (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))))
(->>->~) :: (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))))
(>>-->~) :: (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))))
(>>->-~) :: (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))))
(>->>-~) :: (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))))
(->>>-~) :: (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))))
(>>>--~) :: (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))))
(->>>>~) :: (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))))
(>->>>~) :: (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))))
(>>->>~) :: (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))))
(>>>->~) :: (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))))
(>>>>-~) :: (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))))
(>=====>) :: (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))))
-- | This module enables you to program in Monad-Morphic style for more
-- deeper level than the usual Control.Monad.Morph module
-- expresses. You would realize exactly what more deeper
-- level means by reading the example codes, which are attached
-- on the page bottom.
module DeepControl.Monad.Morph
-- | Alias to hoist.
(|>|) :: (Monad m, MFunctor t) => (forall a. m a -> n a) -> t m b -> t n b
-- | Equivalent to (|>|) with the arguments flipped.
(|<|) :: (Monad m, MFunctor t) => t m b -> (forall a. m a -> n a) -> t n b
(|>>|) :: (Monad m, Monad (t2 m), MFunctor t1, MFunctor t2) => (forall a. m a -> n a) -> t1 (t2 m) b -> t1 (t2 n) b
(|<<|) :: (Monad m, Monad (t2 m), MFunctor t1, MFunctor t2) => t1 (t2 m) b -> (forall a. m a -> n a) -> t1 (t2 n) b
(|>>>|) :: (Monad m, Monad (t3 m), Monad (t2 (t3 m)), MFunctor t1, MFunctor t2, MFunctor t3) => (forall a. m a -> n a) -> t1 (t2 (t3 m)) b -> t1 (t2 (t3 n)) b
(|<<<|) :: (Monad m, Monad (t3 m), Monad (t2 (t3 m)), MFunctor t1, MFunctor t2, MFunctor t3) => t1 (t2 (t3 m)) b -> (forall a. m a -> n a) -> t1 (t2 (t3 n)) b
(|>>>>|) :: (Monad m, Monad (t4 m), Monad (t3 (t4 m)), Monad (t2 (t3 (t4 m))), MFunctor t1, MFunctor t2, MFunctor t3, MFunctor t4) => (forall a. m a -> n a) -> t1 (t2 (t3 (t4 m))) b -> t1 (t2 (t3 (t4 n))) b
(|<<<<|) :: (Monad m, Monad (t4 m), Monad (t3 (t4 m)), Monad (t2 (t3 (t4 m))), MFunctor t1, MFunctor t2, MFunctor t3, MFunctor t4) => t1 (t2 (t3 (t4 m))) b -> (forall a. m a -> n a) -> t1 (t2 (t3 (t4 n))) b
(|>>>>>|) :: (Monad m, Monad (t5 m), Monad (t4 (t5 m)), Monad (t3 (t4 (t5 m))), Monad (t2 (t3 (t4 (t5 m)))), MFunctor t1, MFunctor t2, MFunctor t3, MFunctor t4, MFunctor t5) => (forall a. m a -> n a) -> t1 (t2 (t3 (t4 (t5 m)))) b -> t1 (t2 (t3 (t4 (t5 n)))) b
(|<<<<<|) :: (Monad m, Monad (t5 m), Monad (t4 (t5 m)), Monad (t3 (t4 (t5 m))), Monad (t2 (t3 (t4 (t5 m)))), MFunctor t1, MFunctor t2, MFunctor t3, MFunctor t4, MFunctor t5) => t1 (t2 (t3 (t4 (t5 m)))) b -> (forall a. m a -> n a) -> t1 (t2 (t3 (t4 (t5 n)))) b
-- | This module enables you to program in Monad-Transformer style for more
-- deeper level than the usual Control.Monad.Trans module
-- expresses. You would realize exactly what more deeper
-- level means by reading the example codes, which are attached
-- on the page bottom.
module DeepControl.Monad.Trans
-- | The class of monad transformers. Instances should satisfy the
-- following laws, which state that lift is a monad
-- transformation:
--
--
class MonadTrans (t :: (* -> *) -> * -> *)
-- | Lift a computation from the argument monad to the constructed monad.
lift :: (MonadTrans t, Monad m) => m a -> t m a
-- | Alias to lift
liftT :: (Monad m, MonadTrans t) => m a -> t m a
liftTT :: (Monad m, Monad (t1 m), MonadTrans t, MonadTrans t1) => m a -> t (t1 m) a
liftTTT :: (Monad m, Monad (t1 (t2 m)), Monad (t2 m), MonadTrans t, MonadTrans t1, MonadTrans t2) => m a -> t (t1 (t2 m)) a
liftTTTT :: (Monad m, Monad (t1 (t2 (t3 m))), Monad (t2 (t3 m)), Monad (t3 m), MonadTrans t, MonadTrans t1, MonadTrans t2, MonadTrans t3) => m a -> t (t1 (t2 (t3 m))) a
liftTTTTT :: (Monad m, Monad (t1 (t2 (t3 (t4 m)))), Monad (t2 (t3 (t4 m))), Monad (t3 (t4 m)), Monad (t4 m), MonadTrans t, MonadTrans t1, MonadTrans t2, MonadTrans t3, MonadTrans t4) => m a -> t (t1 (t2 (t3 (t4 m)))) a
class (Monad (TransDown t1), MonadTrans t1) => MonadTransDown t1 where type family TransDown t1 :: * -> *
type M t1 = TransDown t1
class (MonadTransDown t1) => MonadTransCover t1
(|*|) :: (MonadTransCover t1, Monad m1) => (TransDown t1) a -> t1 m1 a
-- | Required only for MonadTransFold2 and
-- MonadTransFold3
class MonadTrans_ t
trans :: (MonadTrans_ t, Monad m) => m ((TransDown t) a) -> t m a
untrans :: (MonadTrans_ t, Monad m) => t m a -> m ((TransDown t) a)
class MonadTrans2 t
liftT2 :: (MonadTrans2 t, Monad m1, Monad m2) => m1 (m2 a) -> t m1 m2 a
liftTT2 :: (Monad m1, Monad (t2 m1 m2), Monad m2, MonadTrans t1, MonadTrans2 t2) => m1 (m2 a) -> t1 (t2 m1 m2) a
liftTTT2 :: (Monad m1, Monad (t1 (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t2 m1 m2)) a
liftTTTT2 :: (Monad m1, Monad (t1 (t1' (t2 m1 m2))), Monad (t1' (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t1' (t2 m1 m2))) a
liftTTTTT2 :: (Monad m1, Monad (t1 (t1' (t1'' (t2 m1 m2)))), Monad (t1' (t1'' (t2 m1 m2))), Monad (t1'' (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans t1'', MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t1' (t1'' (t2 m1 m2)))) a
class (MonadTrans (Trans2Down t2), MonadTrans2 t2) => MonadTrans2Down t2 where type family Trans2Down t2 :: (* -> *) -> * -> *
type M_ t2 = TransDown (T_ t2)
type T_ t2 = Trans2Down t2
-- | Following property holds.
--
--
-- untransfold2 . transfold2 == id
--
class (MonadTrans (T_ t), MonadTrans2 t) => MonadTransFold2 t
transfold2 :: (MonadTransFold2 t, Monad m1, Monad (t2 m1), MonadTrans_ t2) => t m1 (TransDown t2) a -> (T_ t) (t2 m1) a
untransfold2 :: (MonadTransFold2 t, Monad m1, Monad (t2 m1), MonadTrans_ t2) => (T_ t) (t2 m1) a -> t m1 (TransDown t2) a
class (MonadTransCover (Trans2Down t2)) => MonadTransCover2 t2
(|-*|) :: (MonadTransCover2 t2, Monad m1, Monad m2) => (Trans2Down t2) m1 a -> t2 m1 m2 a
(|*-|) :: (MonadTransCover2 t2, Monad m1, Monad m2) => (Trans2Down t2) m2 a -> t2 m1 m2 a
(|**|) :: (Monad m1, Monad m2, MonadTransCover2 t2) => (M_ t2) a -> t2 m1 m2 a
trans2 :: (Monad m, Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2) => m ((TransDown t1) ((TransDown t2) a)) -> t2 (t1 m) a
untrans2 :: (Monad m, Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2) => t2 (t1 m) a -> m ((TransDown t1) ((TransDown t2) a))
class MonadTrans3 t
liftT3 :: (MonadTrans3 t, Monad m1, Monad m2, Monad m3) => m1 (m2 (m3 a)) -> t m1 m2 m3 a
liftTT3 :: (Monad m1, Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t3 m1 m2 m3) a
liftTTT3 :: (Monad m1, Monad (t1 (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t3 m1 m2 m3)) a
liftTTTT3 :: (Monad m1, Monad (t1 (t1' (t3 m1 m2 m3))), Monad (t1' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t1' (t3 m1 m2 m3))) a
liftTTTTT3 :: (Monad m1, Monad (t1 (t1' (t1'' (t3 m1 m2 m3)))), Monad (t1' (t1'' (t3 m1 m2 m3))), Monad (t1'' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans t1'', MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t1' (t1'' (t3 m1 m2 m3)))) a
class (MonadTrans2 (Trans3Down t3), MonadTrans3 t3) => MonadTrans3Down t3 where type family Trans3Down t3 :: (* -> *) -> (* -> *) -> * -> *
type M__ t3 = M_ (Trans3Down t3)
type T__ t3 = T_ (Trans3Down t3)
-- | Following property holds.
--
--
-- untransfold3 . transfold3 == id
--
class (MonadTrans (T__ t), MonadTrans3 t) => MonadTransFold3 t
transfold3 :: (MonadTransFold3 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3) => t m1 (TransDown t2) (TransDown t3) a -> (T__ t) (t3 (t2 m1)) a
untransfold3 :: (MonadTransFold3 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3) => (T__ t) (t3 (t2 m1)) a -> t m1 (TransDown t2) (TransDown t3) a
class (MonadTransCover2 (Trans3Down t3)) => MonadTransCover3 t3
(|--*|) :: (MonadTransCover3 t3, Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m1 m2 a -> t3 m1 m2 m3 a
(|-*-|) :: (MonadTransCover3 t3, Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m1 m3 a -> t3 m1 m2 m3 a
(|*--|) :: (MonadTransCover3 t3, Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m2 m3 a -> t3 m1 m2 m3 a
(|***|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (M__ t3) a -> t3 m1 m2 m3 a
(|-**|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m1 a -> t3 m1 m2 m3 a
(|*-*|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m2 a -> t3 m1 m2 m3 a
(|**-|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m3 a -> t3 m1 m2 m3 a
trans3 :: (Monad m, Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3) => m ((TransDown t1) ((TransDown t2) ((TransDown t3) a))) -> t3 (t2 (t1 m)) a
untrans3 :: (Monad m, Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3) => t3 (t2 (t1 m)) a -> m ((TransDown t1) ((TransDown t2) ((TransDown t3) a)))
class MonadTrans4 t
liftT4 :: (MonadTrans4 t, Monad m1, Monad m2, Monad m3, Monad m4) => m1 (m2 (m3 (m4 a))) -> t m1 m2 m3 m4 a
class (MonadTrans3 (Trans4Down t4), MonadTrans4 t4) => MonadTrans4Down t4 where type family Trans4Down t4 :: (* -> *) -> (* -> *) -> (* -> *) -> * -> *
type M___ t4 = M__ (Trans4Down t4)
type T___ t4 = T__ (Trans4Down t4)
type T2__ t4 = Trans3Down (Trans4Down t4)
-- | Following property holds.
--
--
-- untransfold4 . transfold4 == id
--
class (MonadTrans (T___ t), MonadTrans4 t) => MonadTransFold4 t
transfold4 :: (MonadTransFold4 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), Monad (t4 (t3 (t2 m1))), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3, MonadTrans t4, MonadTrans_ t4) => t m1 (TransDown t2) (TransDown t3) (TransDown t4) a -> (T___ t) (t4 (t3 (t2 m1))) a
untransfold4 :: (MonadTransFold4 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), Monad (t4 (t3 (t2 m1))), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3, MonadTrans t4, MonadTrans_ t4) => (T___ t) (t4 (t3 (t2 m1))) a -> t m1 (TransDown t2) (TransDown t3) (TransDown t4) a
class (MonadTransCover3 (Trans4Down t4)) => MonadTransCover4 t4
(|---*|) :: (MonadTransCover4 t4, Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m2 m3 a -> t4 m1 m2 m3 m4 a
(|--*-|) :: (MonadTransCover4 t4, Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m2 m4 a -> t4 m1 m2 m3 m4 a
(|-*--|) :: (MonadTransCover4 t4, Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m3 m4 a -> t4 m1 m2 m3 m4 a
(|*---|) :: (MonadTransCover4 t4, Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m2 m3 m4 a -> t4 m1 m2 m3 m4 a
(|****|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (M___ t4) a -> t4 m1 m2 m3 m4 a
(|--**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m2 a -> t4 m1 m2 m3 m4 a
(|-*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m3 a -> t4 m1 m2 m3 m4 a
(|-**-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m4 a -> t4 m1 m2 m3 m4 a
(|*-*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m2 m4 a -> t4 m1 m2 m3 m4 a
(|**--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m3 m4 a -> t4 m1 m2 m3 m4 a
(|*--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m2 m3 a -> t4 m1 m2 m3 m4 a
(|-***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m1 a -> t4 m1 m2 m3 m4 a
(|*-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m2 a -> t4 m1 m2 m3 m4 a
(|**-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m3 a -> t4 m1 m2 m3 m4 a
(|***-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m4 a -> t4 m1 m2 m3 m4 a
trans4 :: (Monad m, Monad (t3 (t2 (t1 m))), Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3, MonadTrans_ t4) => m ((TransDown t1) ((TransDown t2) ((TransDown t3) ((TransDown t4) a)))) -> t4 (t3 (t2 (t1 m))) a
untrans4 :: (Monad m, Monad (t3 (t2 (t1 m))), Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3, MonadTrans_ t4) => t4 (t3 (t2 (t1 m))) a -> m ((TransDown t1) ((TransDown t2) ((TransDown t3) ((TransDown t4) a))))
class MonadTrans5 t
liftT5 :: (MonadTrans5 t, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => m1 (m2 (m3 (m4 (m5 a)))) -> t m1 m2 m3 m4 m5 a
class (MonadTrans4 (Trans5Down t5), MonadTrans5 t5) => MonadTrans5Down t5 where type family Trans5Down t5 :: (* -> *) -> (* -> *) -> (* -> *) -> (* -> *) -> * -> *
type M____ t5 = M___ (Trans5Down t5)
type T____ t5 = T___ (Trans5Down t5)
type T2___ t5 = T2__ (Trans5Down t5)
type T3___ t5 = Trans4Down (Trans5Down t5)
-- | Following property holds.
--
--
-- untransfold5 . transfold5 == id
--
class (MonadTrans (T____ t), MonadTrans5 t) => MonadTransFold5 t
transfold5 :: (MonadTransFold5 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), Monad (t4 (t3 (t2 m1))), Monad (t5 (t4 (t3 (t2 m1)))), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3, MonadTrans t4, MonadTrans_ t4, MonadTrans t5, MonadTrans_ t5) => t m1 (TransDown t2) (TransDown t3) (TransDown t4) (TransDown t5) a -> (T____ t) (t5 (t4 (t3 (t2 m1)))) a
untransfold5 :: (MonadTransFold5 t, Monad m1, Monad (t2 m1), Monad (t3 (t2 m1)), Monad (t4 (t3 (t2 m1))), Monad (t5 (t4 (t3 (t2 m1)))), MonadTrans t2, MonadTrans_ t2, MonadTrans t3, MonadTrans_ t3, MonadTrans t4, MonadTrans_ t4, MonadTrans t5, MonadTrans_ t5) => (T____ t) (t5 (t4 (t3 (t2 m1)))) a -> t m1 (TransDown t2) (TransDown t3) (TransDown t4) (TransDown t5) a
class (MonadTransCover4 (Trans5Down t5)) => MonadTransCover5 t5
(|----*|) :: (MonadTransCover5 t5, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m3 m4 a -> t5 m1 m2 m3 m4 m5 a
(|---*-|) :: (MonadTransCover5 t5, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m3 m5 a -> t5 m1 m2 m3 m4 m5 a
(|--*--|) :: (MonadTransCover5 t5, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|-*---|) :: (MonadTransCover5 t5, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|*----|) :: (MonadTransCover5 t5, Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m2 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|---**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m2 m3 a -> t5 m1 m2 m3 m4 m5 a
(|--*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m2 m4 a -> t5 m1 m2 m3 m4 m5 a
(|-*--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m3 m4 a -> t5 m1 m2 m3 m4 m5 a
(|*---*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m3 m4 a -> t5 m1 m2 m3 m4 m5 a
(|*--*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m3 m5 a -> t5 m1 m2 m3 m4 m5 a
(|*-*--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|**---|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|--***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m1 m2 a -> t5 m1 m2 m3 m4 m5 a
(|-*-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m1 m3 a -> t5 m1 m2 m3 m4 m5 a
(|*--**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m2 m3 a -> t5 m1 m2 m3 m4 m5 a
(|*-*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m2 m4 a -> t5 m1 m2 m3 m4 m5 a
(|**--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m3 m4 a -> t5 m1 m2 m3 m4 m5 a
(|**-*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m3 m5 a -> t5 m1 m2 m3 m4 m5 a
(|***--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m4 m5 a -> t5 m1 m2 m3 m4 m5 a
(|-****|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m1 a -> t5 m1 m2 m3 m4 m5 a
(|*-***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m2 a -> t5 m1 m2 m3 m4 m5 a
(|**-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m3 a -> t5 m1 m2 m3 m4 m5 a
(|***-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m4 a -> t5 m1 m2 m3 m4 m5 a
(|****-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m5 a -> t5 m1 m2 m3 m4 m5 a
trans5 :: (Monad m, Monad (t4 (t3 (t2 (t1 m)))), Monad (t3 (t2 (t1 m))), Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3, MonadTrans_ t4, MonadTrans_ t5) => m ((TransDown t1) ((TransDown t2) ((TransDown t3) ((TransDown t4) ((TransDown t5) a))))) -> t5 (t4 (t3 (t2 (t1 m)))) a
untrans5 :: (Monad m, Monad (t4 (t3 (t2 (t1 m)))), Monad (t3 (t2 (t1 m))), Monad (t2 (t1 m)), Monad (t1 m), MonadTrans_ t1, MonadTrans_ t2, MonadTrans_ t3, MonadTrans_ t4, MonadTrans_ t5) => t5 (t4 (t3 (t2 (t1 m)))) a -> m ((TransDown t1) ((TransDown t2) ((TransDown t3) ((TransDown t4) ((TransDown t5) a)))))
-- | Monads in which IO computations may be embedded. Any monad
-- built by applying a sequence of monad transformers to the IO
-- monad will be an instance of this class.
--
-- Instances should satisfy the following laws, which state that
-- liftIO is a transformer of monads:
--
--
class Monad m => MonadIO (m :: * -> *)
-- | Lift a computation from the IO monad.
liftIO :: MonadIO m => IO a -> m a
instance DeepControl.Monad.Trans.MonadTransDown Control.Monad.Trans.List.ListT
instance DeepControl.Monad.Trans.MonadTransDown Control.Monad.Trans.Maybe.MaybeT
instance DeepControl.Monad.Trans.MonadTransDown (Control.Monad.Trans.Except.ExceptT e)
instance GHC.Base.Monoid w => DeepControl.Monad.Trans.MonadTransDown (Control.Monad.Trans.RWS.Lazy.RWST r w s)
instance DeepControl.Monad.Trans.MonadTransDown (Control.Monad.Trans.Reader.ReaderT r)
instance DeepControl.Monad.Trans.MonadTransDown (Control.Monad.Trans.State.Lazy.StateT s)
instance DeepControl.Monad.Trans.MonadTransCover Control.Monad.Trans.List.ListT
instance DeepControl.Monad.Trans.MonadTransCover Control.Monad.Trans.Maybe.MaybeT
instance DeepControl.Monad.Trans.MonadTransCover (Control.Monad.Trans.Except.ExceptT e)
instance GHC.Base.Monoid w => DeepControl.Monad.Trans.MonadTransCover (Control.Monad.Trans.RWS.Lazy.RWST r w s)
instance DeepControl.Monad.Trans.MonadTransCover (Control.Monad.Trans.Reader.ReaderT s)
instance DeepControl.Monad.Trans.MonadTransCover (Control.Monad.Trans.State.Lazy.StateT s)
instance DeepControl.Monad.Trans.MonadTrans_ Control.Monad.Trans.List.ListT
instance DeepControl.Monad.Trans.MonadTrans_ Control.Monad.Trans.Maybe.MaybeT
instance DeepControl.Monad.Trans.MonadTrans_ (Control.Monad.Trans.Except.ExceptT e)
-- | This module enables you to deal with deep monads in any
-- monad-transformer.
module DeepControl.Monad.Trans.Identity
newtype IdentityT2 f1 f2 a
IdentityT2 :: f1 (f2 a) -> IdentityT2 f1 f2 a
[runIdentityT2] :: IdentityT2 f1 f2 a -> f1 (f2 a)
mapIdentityT2 :: (m1 (m2 a) -> n1 (n2 b)) -> IdentityT2 m1 m2 a -> IdentityT2 n1 n2 b
liftCallCC2 :: CallCC2 m1 m2 a b -> CallCC (IdentityT2 m1 m2) a b
liftCatch2 :: Catch2 e m1 m2 a -> Catch e (IdentityT2 m1 m2) a
newtype IdentityT3 f1 f2 f3 a
IdentityT3 :: f1 (f2 (f3 a)) -> IdentityT3 f1 f2 f3 a
[runIdentityT3] :: IdentityT3 f1 f2 f3 a -> f1 (f2 (f3 a))
mapIdentityT3 :: (m1 (m2 (m3 a)) -> n1 (n2 (n3 b))) -> IdentityT3 m1 m2 m3 a -> IdentityT3 n1 n2 n3 b
liftCallCC3 :: CallCC3 m1 m2 m3 a b -> CallCC (IdentityT3 m1 m2 m3) a b
liftCatch3 :: Catch3 e m1 m2 m3 a -> Catch e (IdentityT3 m1 m2 m3) a
newtype IdentityT4 f1 f2 f3 f4 a
IdentityT4 :: f1 (f2 (f3 (f4 a))) -> IdentityT4 f1 f2 f3 f4 a
[runIdentityT4] :: IdentityT4 f1 f2 f3 f4 a -> f1 (f2 (f3 (f4 a)))
mapIdentityT4 :: (m1 (m2 (m3 (m4 a))) -> n1 (n2 (n3 (n4 b)))) -> IdentityT4 m1 m2 m3 m4 a -> IdentityT4 n1 n2 n3 n4 b
liftCallCC4 :: CallCC4 m1 m2 m3 m4 a b -> CallCC (IdentityT4 m1 m2 m3 m4) a b
liftCatch4 :: Catch4 e m1 m2 m3 m4 a -> Catch e (IdentityT4 m1 m2 m3 m4) a
newtype IdentityT5 f1 f2 f3 f4 f5 a
IdentityT5 :: f1 (f2 (f3 (f4 (f5 a)))) -> IdentityT5 f1 f2 f3 f4 f5 a
[runIdentityT5] :: IdentityT5 f1 f2 f3 f4 f5 a -> f1 (f2 (f3 (f4 (f5 a))))
mapIdentityT5 :: (m1 (m2 (m3 (m4 (m5 a)))) -> n1 (n2 (n3 (n4 (n5 b))))) -> IdentityT5 m1 m2 m3 m4 m5 a -> IdentityT5 n1 n2 n3 n4 n5 b
liftCallCC5 :: CallCC5 m1 m2 m3 m4 m5 a b -> CallCC (IdentityT5 m1 m2 m3 m4 m5) a b
liftCatch5 :: Catch5 e m1 m2 m3 m4 m5 a -> Catch e (IdentityT5 m1 m2 m3 m4 m5) a
instance (Data.Traversable.Traversable f1, Data.Traversable.Traversable f2, Data.Traversable.Traversable f3, Data.Traversable.Traversable f4, Data.Traversable.Traversable f5) => Data.Traversable.Traversable (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5)
instance (Data.Foldable.Foldable f1, Data.Foldable.Foldable f2, Data.Foldable.Foldable f3, Data.Foldable.Foldable f4, Data.Foldable.Foldable f5) => Data.Foldable.Foldable (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5)
instance GHC.Show.Show (f1 (f2 (f3 (f4 (f5 a))))) => GHC.Show.Show (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5 a)
instance GHC.Read.Read (f1 (f2 (f3 (f4 (f5 a))))) => GHC.Read.Read (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5 a)
instance GHC.Classes.Ord (f1 (f2 (f3 (f4 (f5 a))))) => GHC.Classes.Ord (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5 a)
instance GHC.Classes.Eq (f1 (f2 (f3 (f4 (f5 a))))) => GHC.Classes.Eq (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5 a)
instance (GHC.Base.Functor f1, GHC.Base.Functor f2, GHC.Base.Functor f3, GHC.Base.Functor f4, GHC.Base.Functor f5) => GHC.Base.Functor (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5)
instance (Data.Traversable.Traversable f1, Data.Traversable.Traversable f2, Data.Traversable.Traversable f3, Data.Traversable.Traversable f4) => Data.Traversable.Traversable (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4)
instance (Data.Foldable.Foldable f1, Data.Foldable.Foldable f2, Data.Foldable.Foldable f3, Data.Foldable.Foldable f4) => Data.Foldable.Foldable (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4)
instance GHC.Show.Show (f1 (f2 (f3 (f4 a)))) => GHC.Show.Show (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4 a)
instance GHC.Read.Read (f1 (f2 (f3 (f4 a)))) => GHC.Read.Read (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4 a)
instance GHC.Classes.Ord (f1 (f2 (f3 (f4 a)))) => GHC.Classes.Ord (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4 a)
instance GHC.Classes.Eq (f1 (f2 (f3 (f4 a)))) => GHC.Classes.Eq (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4 a)
instance (GHC.Base.Functor f1, GHC.Base.Functor f2, GHC.Base.Functor f3, GHC.Base.Functor f4) => GHC.Base.Functor (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4)
instance (Data.Traversable.Traversable f1, Data.Traversable.Traversable f2, Data.Traversable.Traversable f3) => Data.Traversable.Traversable (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3)
instance (Data.Foldable.Foldable f1, Data.Foldable.Foldable f2, Data.Foldable.Foldable f3) => Data.Foldable.Foldable (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3)
instance GHC.Show.Show (f1 (f2 (f3 a))) => GHC.Show.Show (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3 a)
instance GHC.Read.Read (f1 (f2 (f3 a))) => GHC.Read.Read (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3 a)
instance GHC.Classes.Ord (f1 (f2 (f3 a))) => GHC.Classes.Ord (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3 a)
instance GHC.Classes.Eq (f1 (f2 (f3 a))) => GHC.Classes.Eq (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3 a)
instance (GHC.Base.Functor f1, GHC.Base.Functor f2, GHC.Base.Functor f3) => GHC.Base.Functor (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3)
instance (Data.Traversable.Traversable f1, Data.Traversable.Traversable f2) => Data.Traversable.Traversable (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2)
instance (Data.Foldable.Foldable f1, Data.Foldable.Foldable f2) => Data.Foldable.Foldable (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2)
instance GHC.Show.Show (f1 (f2 a)) => GHC.Show.Show (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2 a)
instance GHC.Read.Read (f1 (f2 a)) => GHC.Read.Read (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2 a)
instance GHC.Classes.Ord (f1 (f2 a)) => GHC.Classes.Ord (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2 a)
instance GHC.Classes.Eq (f1 (f2 a)) => GHC.Classes.Eq (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2 a)
instance (GHC.Base.Functor f1, GHC.Base.Functor f2) => GHC.Base.Functor (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2)
instance DeepControl.Commutative.Commutative f => DeepControl.Commutative.Commutative (Control.Monad.Trans.Identity.IdentityT f)
instance DeepControl.Monad.Trans.MonadTransDown Control.Monad.Trans.Identity.IdentityT
instance DeepControl.Monad.Trans.MonadTransCover Control.Monad.Trans.Identity.IdentityT
instance (DeepControl.Commutative.Commutative f1, DeepControl.Commutative.Commutative f2) => DeepControl.Commutative.Commutative (DeepControl.Monad.Trans.Identity.IdentityT2 f1 f2)
instance (GHC.Base.Applicative m1, GHC.Base.Applicative m2) => GHC.Base.Applicative (DeepControl.Monad.Trans.Identity.IdentityT2 m1 m2)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2) => GHC.Base.Monad (DeepControl.Monad.Trans.Identity.IdentityT2 m1 m2)
instance (GHC.Base.Alternative m1, GHC.Base.Alternative m2) => GHC.Base.Alternative (DeepControl.Monad.Trans.Identity.IdentityT2 m1 m2)
instance (GHC.Base.MonadPlus m1, GHC.Base.Alternative m2, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2) => GHC.Base.MonadPlus (DeepControl.Monad.Trans.Identity.IdentityT2 m1 m2)
instance DeepControl.Monad.Trans.MonadTrans2 DeepControl.Monad.Trans.Identity.IdentityT2
instance (Control.Monad.IO.Class.MonadIO m1, GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2) => Control.Monad.IO.Class.MonadIO (DeepControl.Monad.Trans.Identity.IdentityT2 m1 m2)
instance DeepControl.Monad.Trans.MonadTrans2Down DeepControl.Monad.Trans.Identity.IdentityT2
instance DeepControl.Monad.Trans.MonadTransFold2 DeepControl.Monad.Trans.Identity.IdentityT2
instance DeepControl.Monad.Trans.MonadTransCover2 DeepControl.Monad.Trans.Identity.IdentityT2
instance (DeepControl.Commutative.Commutative f1, DeepControl.Commutative.Commutative f2, DeepControl.Commutative.Commutative f3) => DeepControl.Commutative.Commutative (DeepControl.Monad.Trans.Identity.IdentityT3 f1 f2 f3)
instance (GHC.Base.Applicative m1, GHC.Base.Applicative m2, GHC.Base.Applicative m3) => GHC.Base.Applicative (DeepControl.Monad.Trans.Identity.IdentityT3 m1 m2 m3)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3) => GHC.Base.Monad (DeepControl.Monad.Trans.Identity.IdentityT3 m1 m2 m3)
instance (GHC.Base.Alternative m1, GHC.Base.Alternative m2, GHC.Base.Alternative m3) => GHC.Base.Alternative (DeepControl.Monad.Trans.Identity.IdentityT3 m1 m2 m3)
instance (GHC.Base.MonadPlus m1, GHC.Base.Alternative m2, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Alternative m3, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3) => GHC.Base.MonadPlus (DeepControl.Monad.Trans.Identity.IdentityT3 m1 m2 m3)
instance DeepControl.Monad.Trans.MonadTrans3 DeepControl.Monad.Trans.Identity.IdentityT3
instance (Control.Monad.IO.Class.MonadIO m1, GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3) => Control.Monad.IO.Class.MonadIO (DeepControl.Monad.Trans.Identity.IdentityT3 m1 m2 m3)
instance DeepControl.Monad.Trans.MonadTrans3Down DeepControl.Monad.Trans.Identity.IdentityT3
instance DeepControl.Monad.Trans.MonadTransFold3 DeepControl.Monad.Trans.Identity.IdentityT3
instance DeepControl.Monad.Trans.MonadTransCover3 DeepControl.Monad.Trans.Identity.IdentityT3
instance (DeepControl.Commutative.Commutative f1, DeepControl.Commutative.Commutative f2, DeepControl.Commutative.Commutative f3, DeepControl.Commutative.Commutative f4) => DeepControl.Commutative.Commutative (DeepControl.Monad.Trans.Identity.IdentityT4 f1 f2 f3 f4)
instance (GHC.Base.Applicative m1, GHC.Base.Applicative m2, GHC.Base.Applicative m3, GHC.Base.Applicative m4) => GHC.Base.Applicative (DeepControl.Monad.Trans.Identity.IdentityT4 m1 m2 m3 m4)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4) => GHC.Base.Monad (DeepControl.Monad.Trans.Identity.IdentityT4 m1 m2 m3 m4)
instance (GHC.Base.Alternative m1, GHC.Base.Alternative m2, GHC.Base.Alternative m3, GHC.Base.Alternative m4) => GHC.Base.Alternative (DeepControl.Monad.Trans.Identity.IdentityT4 m1 m2 m3 m4)
instance (GHC.Base.MonadPlus m1, GHC.Base.Alternative m2, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Alternative m3, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Alternative m4, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4) => GHC.Base.MonadPlus (DeepControl.Monad.Trans.Identity.IdentityT4 m1 m2 m3 m4)
instance DeepControl.Monad.Trans.MonadTrans4 DeepControl.Monad.Trans.Identity.IdentityT4
instance (Control.Monad.IO.Class.MonadIO m1, GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4) => Control.Monad.IO.Class.MonadIO (DeepControl.Monad.Trans.Identity.IdentityT4 m1 m2 m3 m4)
instance DeepControl.Monad.Trans.MonadTrans4Down DeepControl.Monad.Trans.Identity.IdentityT4
instance DeepControl.Monad.Trans.MonadTransFold4 DeepControl.Monad.Trans.Identity.IdentityT4
instance DeepControl.Monad.Trans.MonadTransCover4 DeepControl.Monad.Trans.Identity.IdentityT4
instance (DeepControl.Commutative.Commutative f1, DeepControl.Commutative.Commutative f2, DeepControl.Commutative.Commutative f3, DeepControl.Commutative.Commutative f4, DeepControl.Commutative.Commutative f5) => DeepControl.Commutative.Commutative (DeepControl.Monad.Trans.Identity.IdentityT5 f1 f2 f3 f4 f5)
instance (GHC.Base.Applicative m1, GHC.Base.Applicative m2, GHC.Base.Applicative m3, GHC.Base.Applicative m4, GHC.Base.Applicative m5) => GHC.Base.Applicative (DeepControl.Monad.Trans.Identity.IdentityT5 m1 m2 m3 m4 m5)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4, GHC.Base.Monad m5, DeepControl.Commutative.Commutative m5) => GHC.Base.Monad (DeepControl.Monad.Trans.Identity.IdentityT5 m1 m2 m3 m4 m5)
instance (GHC.Base.Alternative m1, GHC.Base.Alternative m2, GHC.Base.Alternative m3, GHC.Base.Alternative m4, GHC.Base.Alternative m5) => GHC.Base.Alternative (DeepControl.Monad.Trans.Identity.IdentityT5 m1 m2 m3 m4 m5)
instance (GHC.Base.MonadPlus m1, GHC.Base.Alternative m2, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Alternative m3, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Alternative m4, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4, GHC.Base.Alternative m5, GHC.Base.Monad m5, DeepControl.Commutative.Commutative m5) => GHC.Base.MonadPlus (DeepControl.Monad.Trans.Identity.IdentityT5 m1 m2 m3 m4 m5)
instance DeepControl.Monad.Trans.MonadTrans5 DeepControl.Monad.Trans.Identity.IdentityT5
instance (Control.Monad.IO.Class.MonadIO m1, GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4, GHC.Base.Monad m5, DeepControl.Commutative.Commutative m5) => Control.Monad.IO.Class.MonadIO (DeepControl.Monad.Trans.Identity.IdentityT5 m1 m2 m3 m4 m5)
instance DeepControl.Monad.Trans.MonadTrans5Down DeepControl.Monad.Trans.Identity.IdentityT5
instance DeepControl.Monad.Trans.MonadTransFold5 DeepControl.Monad.Trans.Identity.IdentityT5
instance DeepControl.Monad.Trans.MonadTransCover5 DeepControl.Monad.Trans.Identity.IdentityT5
-- | This module extended Except monad of mtl(monad-transformer-library).
module DeepControl.Monad.Trans.Except
throwError2 :: (MonadError e m2, Applicative m1) => e -> m1 (m2 a)
catchError2 :: (MonadError e m2, Commutative m1, Applicative m1, Commutative m2, Applicative m2) => Catch2 e m1 m2 a
throwError3 :: (MonadError e m3, Applicative m1, Applicative m2) => e -> m1 (m2 (m3 a))
catchError3 :: (MonadError e m3, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3) => Catch3 e m1 m2 m3 a
throwError4 :: (MonadError e m4, Applicative m1, Applicative m2, Applicative m3) => e -> m1 (m2 (m3 (m4 a)))
catchError4 :: (MonadError e m4, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4) => Catch4 e m1 m2 m3 m4 a
throwError5 :: (MonadError e m5, Applicative m1, Applicative m2, Applicative m3, Applicative m4) => e -> m1 (m2 (m3 (m4 (m5 a))))
catchError5 :: (MonadError e m5, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4, Commutative m5, Applicative m5) => Catch5 e m1 m2 m3 m4 m5 a
-- | This module extended Writer monad of mtl(monad-transformer-library).
module DeepControl.Monad.Trans.Writer
listen2 :: (MonadWriter w m2, Applicative m1) => m1 (m2 a) -> m1 (m2 (a, w))
pass2 :: (MonadWriter w m2, Applicative m1) => m1 (m2 (a, w -> w)) -> m1 (m2 a)
listen3 :: (MonadWriter w m3, Applicative m1, Applicative m2) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (a, w)))
pass3 :: (MonadWriter w m3, Applicative m1, Applicative m2) => m1 (m2 (m3 (a, w -> w))) -> m1 (m2 (m3 a))
listen4 :: (MonadWriter w m4, Applicative m1, Applicative m2, Applicative m3) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (a, w))))
pass4 :: (MonadWriter w m4, Applicative m1, Applicative m2, Applicative m3) => m1 (m2 (m3 (m4 (a, w -> w)))) -> m1 (m2 (m3 (m4 a)))
listen5 :: (MonadWriter w m5, Applicative m1, Applicative m2, Applicative m3, Applicative m4) => m1 (m2 (m3 (m4 (m5 a)))) -> m1 (m2 (m3 (m4 (m5 (a, w)))))
pass5 :: (MonadWriter w m5, Applicative m1, Applicative m2, Applicative m3, Applicative m4) => m1 (m2 (m3 (m4 (m5 (a, w -> w))))) -> m1 (m2 (m3 (m4 (m5 a))))
module DeepControl.Arrow
newtype Kleisli2 m1 m2 a b
Kleisli2 :: (a -> m1 (m2 b)) -> Kleisli2 m1 m2 a b
[runKleisli2] :: Kleisli2 m1 m2 a b -> a -> m1 (m2 b)
newtype Kleisli3 m1 m2 m3 a b
Kleisli3 :: (a -> m1 (m2 (m3 b))) -> Kleisli3 m1 m2 m3 a b
[runKleisli3] :: Kleisli3 m1 m2 m3 a b -> a -> m1 (m2 (m3 b))
newtype Kleisli4 m1 m2 m3 m4 a b
Kleisli4 :: (a -> m1 (m2 (m3 (m4 b)))) -> Kleisli4 m1 m2 m3 m4 a b
[runKleisli4] :: Kleisli4 m1 m2 m3 m4 a b -> a -> m1 (m2 (m3 (m4 b)))
newtype Kleisli5 m1 m2 m3 m4 m5 a b
Kleisli5 :: (a -> m1 (m2 (m3 (m4 (m5 b))))) -> Kleisli5 m1 m2 m3 m4 m5 a b
[runKleisli5] :: Kleisli5 m1 m2 m3 m4 m5 a b -> a -> m1 (m2 (m3 (m4 (m5 b))))
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2) => Control.Category.Category (DeepControl.Arrow.Kleisli2 m1 m2)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2) => Control.Arrow.Arrow (DeepControl.Arrow.Kleisli2 m1 m2)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3) => Control.Category.Category (DeepControl.Arrow.Kleisli3 m1 m2 m3)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3) => Control.Arrow.Arrow (DeepControl.Arrow.Kleisli3 m1 m2 m3)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4) => Control.Category.Category (DeepControl.Arrow.Kleisli4 m1 m2 m3 m4)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4) => Control.Arrow.Arrow (DeepControl.Arrow.Kleisli4 m1 m2 m3 m4)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4, GHC.Base.Monad m5, DeepControl.Commutative.Commutative m5) => Control.Category.Category (DeepControl.Arrow.Kleisli5 m1 m2 m3 m4 m5)
instance (GHC.Base.Monad m1, GHC.Base.Monad m2, DeepControl.Commutative.Commutative m2, GHC.Base.Monad m3, DeepControl.Commutative.Commutative m3, GHC.Base.Monad m4, DeepControl.Commutative.Commutative m4, GHC.Base.Monad m5, DeepControl.Commutative.Commutative m5) => Control.Arrow.Arrow (DeepControl.Arrow.Kleisli5 m1 m2 m3 m4 m5)