DeepControl.Applicative

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.

Documentation

module Control.Applicative

Level-0

bra-ket notation

(|>) :: (a -> b) -> a -> b infixl 4

Alias to $.

>>> (1+) |> 2
3

(<|) :: a -> (a -> b) -> b infixl 4

The auguments-flipped function for |>.

>>> 1 <| (+2)
3 
>>> 1 <|(+)|> 2
3 
>>> 1 <|(+)|> 2 <|(*)|> 3
9

>>> 1 <|(,)|> 2
(1,2)

Level-1

cover notation

(*:) :: Applicative f => a -> f a infixl 6

Alias to pure.

bra-ket notation

(|$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

Alias to <$>.

>>> (1+) |$> [2]
[3]

(<$|) :: Functor f => f a -> (a -> b) -> f b infixl 3

The auguments-flipped function for |$>.

>>> [1] <$| (+2)
[3]

>>> ("<"++)|$> ["a","b"] <$|(++">")
["<a>","<b>"]

(|*>) :: Applicative f => f (a -> b) -> f a -> f b infixl 3

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 -> f (a -> b) -> f b infixl 3

The auguments-flipped function for |*>.

cover-bracket notation

(|*) :: Applicative f => f (a -> b) -> a -> f b infixl 3

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 => a -> f (a -> b) -> f b infixl 3

The auguments-flipped function for |*.

>>> 1 *| [(+2)]
[3]
>>> 1 *| [(+)] |* 2
[3]
>>> 1 *|[(+),(-),(*),(^)]|* 2
[3,-1,2,1]

>>> 1 *|Just (,)|* 2
Just (1,2)

Level-2

cover notation

(**:) :: (Applicative f1, Applicative f2) => a -> f1 (f2 a) infixl 6

Definition: (**:) = (*:) . (*:)

>>> (**:) 1 :: Maybe [Int]
Just [1]

(-*) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 a) infixl 6

Definition: (-*) = ((*:)|$>)

>>> (-*) (Just 1) :: Maybe [Int]
Just [1]

bra-ket notation

(|$>>) :: (Functor f1, Functor f2) => (a -> b) -> f1 (f2 a) -> f1 (f2 b) infixl 4

Definition: (|$>>) = (|$>) . (|$>)

>>> (+1) |$>> [[2]]
[[3]]

(<<$|) :: (Functor f1, Functor f2) => f1 (f2 a) -> (a -> b) -> f1 (f2 b) infixl 3

The auguments-flipped function for |$>>

>>> [[2]] <<$| (+1)
[[3]]

(|*>>) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> f1 (f2 a) -> f1 (f2 b) infixl 3

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) -> f1 (f2 (a -> b)) -> f1 (f2 b) infixl 3

Definition: (<<*|) = liftA2 (<*|)

cover-bracket notation

(|**) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> a -> f1 (f2 b) infixl 3

Definition: f |** x = f |*>> (**:) x

>>> [Just 1] <<$|(+)|** 2
[Just 3]

(**|) :: (Applicative f1, Applicative f2) => a -> f1 (f2 (a -> b)) -> f1 (f2 b) infixl 3

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) => f1 (f2 (a -> b)) -> f1 a -> f1 (f2 b) infixl 3

Definition: f |-* x = f |*>> (-*) x

>>> [Just 1] <<$|(+)|-* [2]
[Just 3]

(|*-) :: (Applicative f1, Applicative f2) => f1 (f2 (a -> b)) -> f2 a -> f1 (f2 b) infixl 3

Definition: f |*- x = f |*>> (*:) x

>>> [Just 1] <<$|(+)|*- Just 2
[Just 3]

(-*|) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 (a -> b)) -> f1 (f2 b) infixl 3

Definition: x -*| f = (-*) x <<*| f

>>> [1] -*|(+)|$>> [Just 2]
[Just 3]

(*-|) :: (Applicative f1, Applicative f2) => f2 a -> f1 (f2 (a -> b)) -> f1 (f2 b) infixl 3

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]

sequence notation

(*>>) :: (Applicative f1, Applicative f2) => f1 (f2 a) -> f1 (f2 b) -> f1 (f2 b) infixl 5

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 a) infixl 5

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]

cover-sequence notation

(-*>) :: (Applicative f1, Applicative f2) => f1 a -> f1 (f2 b) -> f1 (f2 b) infixl 5

Definition: a -*> x = (-*) a *>> x

>>> print 1 -*> (*:) (Just 2)
1
Just 2

(<-*) :: (Applicative f1, Applicative f2) => f1 (f2 b) -> f1 a -> f1 (f2 b) infixl 5

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) => f2 a -> f1 (f2 b) -> f1 (f2 b) infixl 5

Definition: a *-> x = (*:) a *>> x

>>> sequence $ print 1 *-> Just ((*:) 2)
1
Just 2

(<*-) :: (Applicative f1, Applicative f2) => f1 (f2 b) -> f2 a -> f1 (f2 b) infixl 5

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

Level-3

cover notation

(***:) :: (Applicative f1, Applicative f2, Applicative f3) => a -> f1 (f2 (f3 a)) infixl 6

(*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 a)) infixl 6

(-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 a)) infixl 6

(--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 a)) infixl 6

bra-ket notation

(|$>>>) :: (Functor f1, Functor f2, Functor f3) => (a -> b) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) infixl 4

(<<<$|) :: (Functor f1, Functor f2, Functor f3) => f1 (f2 (f3 a)) -> (a -> b) -> f1 (f2 (f3 b)) infixl 3

(|*>>>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) infixl 3

(<<<*|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

cover-bracket notation

(|***) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> a -> f1 (f2 (f3 b)) infixl 3

(|-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 a -> f1 (f2 (f3 b)) infixl 3

(|*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f2 a -> f1 (f2 (f3 b)) infixl 3

(|**-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f3 a -> f1 (f2 (f3 b)) infixl 3

(|--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f2 a) -> f1 (f2 (f3 b)) infixl 3

(|-*-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f1 (f3 a) -> f1 (f2 (f3 b)) infixl 3

(|*--) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 (a -> b))) -> f2 (f3 a) -> f1 (f2 (f3 b)) infixl 3

(***|) :: (Applicative f1, Applicative f2, Applicative f3) => a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(-**|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(*-*|) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(**-|) :: (Applicative f1, Applicative f2, Applicative f3) => f3 a -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(--*|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(-*-|) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f3 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

(*--|) :: (Applicative f1, Applicative f2, Applicative f3) => f2 (f3 a) -> f1 (f2 (f3 (a -> b))) -> f1 (f2 (f3 b)) infixl 3

sequence notation

(*>>>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(<<<*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 a)) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 a)) infixl 5

cover-sequence notation

(*-->) :: (Applicative f1, Applicative f2, Applicative f3) => f2 (f3 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(-*->) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f3 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(--*>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 a) -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(**->) :: (Applicative f1, Applicative f2, Applicative f3) => f3 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(*-*>) :: (Applicative f1, Applicative f2, Applicative f3) => f2 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(-**>) :: (Applicative f1, Applicative f2, Applicative f3) => f1 a -> f1 (f2 (f3 b)) -> f1 (f2 (f3 b)) infixl 5

(<*--) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f2 (f3 a) -> f1 (f2 (f3 b)) infixl 5

(<-*-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 (f3 a) -> f1 (f2 (f3 b)) infixl 5

(<--*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 (f2 a) -> f1 (f2 (f3 b)) infixl 5

(<**-) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f3 a -> f1 (f2 (f3 b)) infixl 5

(<*-*) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f2 a -> f1 (f2 (f3 b)) infixl 5

(<-**) :: (Applicative f1, Applicative f2, Applicative f3) => f1 (f2 (f3 b)) -> f1 a -> f1 (f2 (f3 b)) infixl 5

Level-4

cover notation

(****:) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => a -> f1 (f2 (f3 (f4 a))) infixl 6

(---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 a))) infixl 6

(--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 a))) infixl 6

(-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 a))) infixl 6

(*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 a))) infixl 6

(-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 a))) infixl 6

(*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 a))) infixl 6

(**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 a))) infixl 6

bra-ket notation

(|$>>>>) :: (Functor f1, Functor f2, Functor f3, Functor f4) => (a -> b) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) infixl 4

(<<<<$|) :: (Functor f1, Functor f2, Functor f3, Functor f4) => f1 (f2 (f3 (f4 a))) -> (a -> b) -> f1 (f2 (f3 (f4 b))) infixl 3

(|*>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) infixl 3

(<<<<*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

cover-bracket notation

(|****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> a -> f1 (f2 (f3 (f4 b))) infixl 3

(|-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 a -> f1 (f2 (f3 (f4 b))) infixl 3

(|*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 a -> f1 (f2 (f3 (f4 b))) infixl 3

(|**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f3 a -> f1 (f2 (f3 (f4 b))) infixl 3

(|***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f4 a -> f1 (f2 (f3 (f4 b))) infixl 3

(|--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 3

(|---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b))) infixl 3

(|--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 3

(|-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 3

(|*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 (a -> b)))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 3

(****|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(-***|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(*-**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(**-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(***-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f4 a -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(--**|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(-*-*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(*--*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(*-*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(-**-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(**--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 (f4 a) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(---*|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(--*-|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(-*--|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

(*---|) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (a -> b)))) -> f1 (f2 (f3 (f4 b))) infixl 3

sequence notation

(*>>>>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(<<<<*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 a))) infixl 5

cover-sequence notation

(<---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b))) infixl 5

(<--*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 5

(<-*--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 5

(<*---) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) infixl 5

(<--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f2 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f3 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f3 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<*-*-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<-**-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<**--) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f3 (f4 a) -> f1 (f2 (f3 (f4 b))) infixl 5

(<-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f1 a -> f1 (f2 (f3 (f4 b))) infixl 5

(<*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f2 a -> f1 (f2 (f3 (f4 b))) infixl 5

(<**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f3 a -> f1 (f2 (f3 (f4 b))) infixl 5

(<***-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 (f4 b))) -> f4 a -> f1 (f2 (f3 (f4 b))) infixl 5

(---*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(--*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(-*-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(*--->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(--**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f2 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(-*-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f3 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(*--*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f3 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(*-*->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(-**->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(**-->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 (f4 a) -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(-***>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f1 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(*-**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f2 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(**-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f3 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

(***->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4) => f4 a -> f1 (f2 (f3 (f4 b))) -> f1 (f2 (f3 (f4 b))) infixl 5

Level-5

cover notation

(*****:) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => a -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(----*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 a))) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(---**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 a)) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(--*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(-*--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(*---*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 (f4 a)) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(--***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(-*-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f3 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(*--**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f3 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(*-*-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 (f4 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(-**-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f4 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(**--*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 (f4 a) -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(-****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 a -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(*-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 a -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(**-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 a -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

(***-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 a -> f1 (f2 (f3 (f4 (f5 a)))) infixl 6

bra-ket notation

(|$>>>>>) :: (Functor f1, Functor f2, Functor f3, Functor f4, Functor f5) => (a -> b) -> f1 (f2 (f3 (f4 (f5 a)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 4

(<<<<<$|) :: (Functor f1, Functor f2, Functor f3, Functor f4, Functor f5) => f1 (f2 (f3 (f4 (f5 a)))) -> (a -> b) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 3

(|*>>>>>) :: (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)))) infixl 3

(<<<<<*|) :: (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)))) infixl 3

cover-bracket notation

(|-****) :: (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)))) infixl 3

(|*-***) :: (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)))) infixl 3

(|**-**) :: (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)))) infixl 3

(|***-*) :: (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)))) infixl 3

(|****-) :: (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)))) infixl 3

(|--***) :: (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)))) infixl 3

(|-*-**) :: (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)))) infixl 3

(|*--**) :: (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)))) infixl 3

(|*-*-*) :: (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)))) infixl 3

(|-**-*) :: (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)))) infixl 3

(|**--*) :: (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)))) infixl 3

(|**-*-) :: (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)))) infixl 3

(|*-**-) :: (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)))) infixl 3

(|-***-) :: (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)))) infixl 3

(|***--) :: (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)))) infixl 3

(|---**) :: (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)))) infixl 3

(|--*-*) :: (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)))) infixl 3

(|-*--*) :: (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)))) infixl 3

(|*---*) :: (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)))) infixl 3

(|*--*-) :: (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)))) infixl 3

(|-*-*-) :: (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)))) infixl 3

(|--**-) :: (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)))) infixl 3

(|-**--) :: (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)))) infixl 3

(|*-*--) :: (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)))) infixl 3

(|**---) :: (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)))) infixl 3

(|----*) :: (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)))) infixl 3

(|---*-) :: (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)))) infixl 3

(|--*--) :: (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)))) infixl 3

(|-*---) :: (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)))) infixl 3

(|*----) :: (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)))) infixl 3

(-****|) :: (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)))) infixl 3

(*-***|) :: (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)))) infixl 3

(**-**|) :: (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)))) infixl 3

(***-*|) :: (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)))) infixl 3

(****-|) :: (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)))) infixl 3

(--***|) :: (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)))) infixl 3

(-*-**|) :: (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)))) infixl 3

(*--**|) :: (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)))) infixl 3

(*-*-*|) :: (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)))) infixl 3

(-**-*|) :: (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)))) infixl 3

(**--*|) :: (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)))) infixl 3

(**-*-|) :: (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)))) infixl 3

(*-**-|) :: (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)))) infixl 3

(-***-|) :: (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)))) infixl 3

(***--|) :: (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)))) infixl 3

(---**|) :: (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)))) infixl 3

(--*-*|) :: (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)))) infixl 3

(-*--*|) :: (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)))) infixl 3

(*---*|) :: (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)))) infixl 3

(*--*-|) :: (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)))) infixl 3

(-*-*-|) :: (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)))) infixl 3

(--**-|) :: (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)))) infixl 3

(-**--|) :: (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)))) infixl 3

(*-*--|) :: (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)))) infixl 3

(**---|) :: (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)))) infixl 3

(----*|) :: (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)))) infixl 3

(---*-|) :: (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)))) infixl 3

(--*--|) :: (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)))) infixl 3

(-*---|) :: (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)))) infixl 3

(*----|) :: (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)))) infixl 3

sequence notation

(*>>>>>) :: (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)))) infixl 5

(<<<<<*) :: (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)))) infixl 5

cover-sequence notation

(<----*) :: (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)))) infixl 5

(<---*-) :: (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)))) infixl 5

(<--*--) :: (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)))) infixl 5

(<-*---) :: (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)))) infixl 5

(<*----) :: (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)))) infixl 5

(<---**) :: (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)))) infixl 5

(<--*-*) :: (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)))) infixl 5

(<-*--*) :: (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)))) infixl 5

(<*---*) :: (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)))) infixl 5

(<*--*-) :: (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)))) infixl 5

(<-*-*-) :: (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)))) infixl 5

(<--**-) :: (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)))) infixl 5

(<-**--) :: (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)))) infixl 5

(<*-*--) :: (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)))) infixl 5

(<**---) :: (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)))) infixl 5

(<--***) :: (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)))) infixl 5

(<-*-**) :: (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)))) infixl 5

(<*--**) :: (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)))) infixl 5

(<*-*-*) :: (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)))) infixl 5

(<-**-*) :: (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)))) infixl 5

(<**--*) :: (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)))) infixl 5

(<**-*-) :: (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)))) infixl 5

(<*-**-) :: (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)))) infixl 5

(<-***-) :: (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)))) infixl 5

(<***--) :: (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)))) infixl 5

(<-****) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f1 a -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(<*-***) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f2 a -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(<**-**) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f3 a -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(<***-*) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f4 a -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(<****-) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 (f2 (f3 (f4 (f5 b)))) -> f5 a -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(----*>) :: (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)))) infixl 5

(---*->) :: (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)))) infixl 5

(--*-->) :: (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)))) infixl 5

(-*--->) :: (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)))) infixl 5

(*---->) :: (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)))) infixl 5

(---**>) :: (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)))) infixl 5

(--*-*>) :: (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)))) infixl 5

(-*--*>) :: (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)))) infixl 5

(*---*>) :: (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)))) infixl 5

(*--*->) :: (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)))) infixl 5

(-*-*->) :: (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)))) infixl 5

(--**->) :: (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)))) infixl 5

(-**-->) :: (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)))) infixl 5

(*-*-->) :: (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)))) infixl 5

(**--->) :: (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)))) infixl 5

(--***>) :: (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)))) infixl 5

(-*-**>) :: (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)))) infixl 5

(*--**>) :: (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)))) infixl 5

(*-*-*>) :: (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)))) infixl 5

(-**-*>) :: (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)))) infixl 5

(**--*>) :: (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)))) infixl 5

(**-*->) :: (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)))) infixl 5

(*-**->) :: (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)))) infixl 5

(-***->) :: (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)))) infixl 5

(***-->) :: (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)))) infixl 5

(-****>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f1 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(*-***>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f2 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(**-**>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f3 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(***-*>) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f4 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5

(****->) :: (Applicative f1, Applicative f2, Applicative f3, Applicative f4, Applicative f5) => f5 a -> f1 (f2 (f3 (f4 (f5 b)))) -> f1 (f2 (f3 (f4 (f5 b)))) infixl 5