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

Bindable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

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

join :: ((Identity :. Identity) := a) -> Identity a

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

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

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

Distributive Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

distribute :: Covariant u => ((u :. Identity) := a) -> (Identity :. u) := a

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

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

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

Extendable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

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

duplicate :: Identity a -> (Identity :. Identity) := a

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

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

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

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

Extractable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

extract :: a <:= Identity

Comonad Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Pointable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

point :: a :=> Identity

pass :: Identity ()

Monad Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

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

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

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

Traversable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(->>) :: (Pointable u, Applicative u) => Identity a -> (a -> u b) -> (u :. Identity) := b

traverse :: (Pointable u, Applicative u) => (a -> u b) -> Identity a -> (u :. Identity) := b

sequence :: (Pointable u, Applicative u) => ((Identity :. u) := a) -> (u :. Identity) := a

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Identity) := a) -> (a -> u b) -> (u :. (v :. Identity)) := b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Identity)) := a) -> (a -> u b) -> (u :. (w :. (v :. Identity))) := b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Identity))) := a) -> (a -> u b) -> (u :. (j :. (w :. (v :. Identity)))) := b

Adjoint Identity Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

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

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

eta :: a -> (Identity :. Identity) := a

epsilon :: ((Identity :. Identity) := a) -> a

(-|$) :: Covariant v => v a -> (Identity a -> b) -> v (Identity b)

($|-) :: Covariant v => v (Identity a) -> (a -> Identity b) -> v b

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

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

($$$$|-) :: (Covariant v, Covariant w, Covariant x, Covariant y) => ((v :. (w :. (x :. (y :. Identity)))) := a) -> (a -> Identity b) -> (v :. (w :. (x :. y))) := b

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

Defined in Pandora.Paradigm.Structure.Some.Stream

Methods

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

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

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

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

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

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

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

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

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)) := (:*:))

type Zipper Stream

Defined in Pandora.Paradigm.Structure.Some.Stream

type Zipper Stream = Tap ((Stream <:.:> Stream) := (:*:))

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)) := (:*:))