Pandora.Paradigm.Primary.Functor.Identity

Documentation

newtype Identity a

Constructors

Identity a

Instances

Covariant Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<$>) :: (a -> b) -> Identity a -> Identity b

comap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

($>) :: Identity a -> b -> Identity b

void :: Identity a -> Identity ()

loeb :: Identity (a <:= Identity) -> Identity a

(<&>) :: Identity a -> (a -> b) -> Identity b

(<$$>) :: Covariant u => (a -> b) -> ((Identity :. u) := a) -> (Identity :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Identity :. u) := a) -> (a -> b) -> (Identity :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Identity :. (u :. v)) := a) -> (a -> b) -> (Identity :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Identity :. (u :. (v :. w))) := a) -> (a -> b) -> (Identity :. (u :. (v :. w))) := b

(.#..) :: (Identity ~ v a, Category v) => v c d -> ((v a :. v b) := c) -> (v a :. v b) := d

(.#...) :: (Identity ~ v a, Identity ~ v b, Category v, Covariant (v a), Covariant (v b)) => v d e -> ((v a :. (v b :. v c)) := d) -> (v a :. (v b :. v c)) := e

(.#....) :: (Identity ~ v a, Identity ~ v b, Identity ~ v c, Category v, Covariant (v a), Covariant (v b), Covariant (v c)) => v e f -> ((v a :. (v b :. (v c :. v d))) := e) -> (v a :. (v b :. (v c :. v d))) := f

(<$$) :: Covariant u => b -> ((Identity :. u) := a) -> (Identity :. u) := b

(<$$$) :: (Covariant u, Covariant v) => b -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b

(<$$$$) :: (Covariant u, Covariant v, Covariant w) => b -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b

($$>) :: Covariant u => ((Identity :. u) := a) -> b -> (Identity :. u) := b

($$$>) :: (Covariant u, Covariant v) => ((Identity :. (u :. v)) := a) -> b -> (Identity :. (u :. v)) := b

($$$$>) :: (Covariant u, Covariant v, Covariant w) => ((Identity :. (u :. (v :. w))) := a) -> b -> (Identity :. (u :. (v :. w))) := b

Applicative Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<*>) :: Identity (a -> b) -> Identity a -> Identity b

apply :: Identity (a -> b) -> Identity a -> Identity b

(*>) :: Identity a -> Identity b -> Identity b

(<*) :: Identity a -> Identity b -> Identity a

forever :: Identity a -> Identity b

(<%>) :: Identity a -> Identity (a -> b) -> Identity b

(<**>) :: Applicative u => ((Identity :. u) := (a -> b)) -> ((Identity :. u) := a) -> (Identity :. u) := b

(<***>) :: (Applicative u, Applicative v) => ((Identity :. (u :. v)) := (a -> b)) -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b

(<****>) :: (Applicative u, Applicative v, Applicative w) => ((Identity :. (u :. (v :. w))) := (a -> b)) -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b

Monad Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Representable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Associated Types

type Representation Identity

Methods

(<#>) :: Representation Identity -> a <:= Identity

tabulate :: (Representation Identity -> a) -> Identity a

index :: Identity a -> Representation Identity -> a

Adjoint Identity Identity ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(-|) :: (Identity a -> b) -> a -> Identity b

(|-) :: (a -> Identity b) -> Identity a -> b

Bindable Identity ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(=<<) :: (a -> Identity b) -> Identity a -> Identity b

Extendable Identity ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<<=) :: (Identity a -> b) -> Identity a -> Identity b

Extractable Identity ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

extract :: Identity a -> a

Comonad Identity ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Pointable Identity ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

point :: a -> Identity a

Covariant_ Identity ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(-<$>-) :: (a -> b) -> Identity a -> Identity b

Traversable Identity ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<<-) :: (Covariant_ u (->) (->), Pointable u (->), Semimonoidal u (:*:) (->) (->)) => (a -> u b) -> Identity a -> u (Identity b)

Category (Lens Identity)

Defined in Pandora.Paradigm.Inventory.Optics

Methods

identity :: Lens Identity a a

(.) :: Lens Identity b c -> Lens Identity a b -> Lens Identity a c

($) :: Lens Identity (Lens Identity a b) (Lens Identity a b)

(#) :: Lens Identity (Lens Identity a b) (Lens Identity a b)

Semigroup a => Semigroup (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

Ringoid a => Ringoid (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(*) :: Identity a -> Identity a -> Identity a

Monoid a => Monoid (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

zero :: Identity a

Quasiring a => Quasiring (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

one :: Identity a

Group a => Group (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

invert :: Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

Supremum a => Supremum (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(\/) :: Identity a -> Identity a -> Identity a

Infimum a => Infimum (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(/\) :: Identity a -> Identity a -> Identity a

Lattice a => Lattice (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Setoid a => Setoid (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Boolean

(!=) :: Identity a -> Identity a -> Boolean

Chain a => Chain (Identity a)

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<=>) :: Identity a -> Identity a -> Ordering

(<) :: Identity a -> Identity a -> Boolean

(<=) :: Identity a -> Identity a -> Boolean

(>) :: Identity a -> Identity a -> Boolean

(>=) :: Identity a -> Identity a -> Boolean

Extendable (Tap ((Stream <:.:> Stream) := (:*:))) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Structure.Some.Stream

Methods

(<<=) :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> Tap ((Stream <:.:> Stream) := (:*:)) b

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Right) (Tap ((Stream <:.:> Stream) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((Stream <:.:> Stream) := (:*:))) ~> Morphing ('Rotate 'Right) (Tap ((Stream <:.:> Stream) := (:*:)))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Left) (Tap ((Stream <:.:> Stream) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((Stream <:.:> Stream) := (:*:))) ~> Morphing ('Rotate 'Left) (Tap ((Stream <:.:> Stream) := (:*:)))

Morphable ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate 'Up) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Up) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate 'Up) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Right)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Right)) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Right)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Left)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Left)) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Left)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Impliable (P_Q_T ((->) :: Type -> Type -> Type) Store Identity source target :: Type)

Defined in Pandora.Paradigm.Inventory.Optics

Associated Types

type Arguments (P_Q_T (->) Store Identity source target) = (args :: Type)

Methods

imply :: Arguments (P_Q_T (->) Store Identity source target)

type Representation Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

type Representation Identity = ()

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) = Tap ((Stream <:.:> Stream) := (:*:))

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) = Tap ((Stream <:.:> Stream) := (:*:))

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Arguments (P_Q_T ((->) :: Type -> Type -> Type) Store Identity source target :: Type)

Defined in Pandora.Paradigm.Inventory.Optics

type Arguments (P_Q_T ((->) :: Type -> Type -> Type) Store Identity source target :: Type) = (source -> target) -> (source -> target -> source) -> Lens Identity source target

type Zipper (Construction Identity) (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type)

Defined in Pandora.Paradigm.Structure.Some.Stream

type Zipper (Construction Identity) (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type) = Tap ((Stream <:.:> Stream) := (:*:))