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. Note: all braket-cover notation for Level-4 and Level-5 is not written yet.

Documentation

module Control.Applicative

Level-0

bra-ket notation

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

Alias for $.

>>> (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 5

Alias for pure.

bra-ket notation

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

Alias for <$>.

>>> (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 for <*>.

>>> [(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 |*>.

braket-cover notation

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

Combination consisted of ket |*> and cover *:, defined as f |* x = f |*> ((*:) x).

>>> [(1+)] |* 2
[3]
>>> [1] <$|(+)|* 2
[3]
>>> [1] <$|(+)|* 2 <$|(*)|* 3
[9]

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

(*|) :: 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 5

Combination consisted of cover *: twice, defined as (**:) = (*:) . (*:).

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

Alias for *:.

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

Combination consisted of cover *: and ket |$>, defined as (-*) = ((*:)|$>).

bra-ket notation

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

Combination consisted of cover |$> twice, defined as (|$>>) = (|$>) . (|$>).

>>> (+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

The lifted function of |*>, defined as (|*>>) = 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

The auguments-flipped function for |*>>.

braket-cover notation

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

Combination consisted of ket |*>> and cover **:, defined as f |** x = f |*>> ((**:) x).

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

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

The auguments-flipped function for |**.

>>> 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

Combination consisted of ket |*>> and cover -*, defined as f |-* x = f |*>> ((-*) x).

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

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

Combination consisted of ket |*>> and cover *-, defined as 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

The auguments-flipped function for |-*.

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

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

The auguments-flipped function for |*-.

>>> 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]
>>> [0,1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2
[Just 2,Just 3,Just (-2),Just (-1),Just 0,Just 2,Nothing,Nothing]

Level-3

cover notation

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

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

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

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

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

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

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

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

braket-cover 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) => a -> f1 (f2 (f3 (a -> b))) -> 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) => 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

Level-4

cover notation

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

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

Level-5

cover notation

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

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