Pandora.Paradigm.Schemes.T_U

Documentation

newtype T_U ct cu p t u a

Constructors

T_U (p (t a) (u a))

Instances

Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (-->) (:*:) (:*:) ((Identity <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) <-- ((Identity <:.:> t) := (:*:)) a

Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap ((t <:.:> t) := (:*:)) :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

mult :: forall (a :: k) (b :: k). (Tap ((t <:.:> t) := (:*:)) a :*: Tap ((t <:.:> t) := (:*:)) b) --> Tap ((t <:.:> t) := (:*:)) (a :*: b)

(Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) ((t <:.:> u) := (:*:) :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Algebraic.Product

Methods

mult :: forall (a :: k) (b :: k). (((t <:.:> u) := (:*:)) a :*: ((t <:.:> u) := (:*:)) b) --> ((t <:.:> u) := (:*:)) (a :*: b)

(Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) ((t <:.:> u) := (:*:) :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Algebraic.Product

Methods

mult :: forall (a :: k) (b :: k). (((t <:.:> u) := (:*:)) a :*: ((t <:.:> u) := (:*:)) b) <-- ((t <:.:> u) := (:*:)) (a :*: b)

Semimonoidal (<--) (:*:) (:*:) t => Semimonoidal (<--) (:*:) (:*:) ((Identity <:.:> t) := (:*:) :: Type -> Type)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Methods

mult :: forall (a :: k) (b :: k). (((Identity <:.:> t) := (:*:)) a :*: ((Identity <:.:> t) := (:*:)) b) <-- ((Identity <:.:> t) := (:*:)) (a :*: b)

Morphable ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) List :: Type -> Type

Methods

morphing :: (Tagged ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) <:.> List) ~> Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) List

Morphable ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) <:.> Construction Maybe) ~> Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) (Construction Maybe)

Morphable ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ~> Morphing ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Morphable ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ~> Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Morphable ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

Associated Types

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into Wye) <:.> ((Maybe <:.:> Maybe) := (:*:))) ~> Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Morphable ('Into (Construction Maybe)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Construction Maybe)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Construction Maybe)) <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ~> Morphing ('Into (Construction Maybe)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Morphable ('Into (Comprehension Maybe)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Comprehension Maybe)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Comprehension Maybe)) <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ~> Morphing ('Into (Comprehension Maybe)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Morphable ('Into List) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ~> Morphing ('Into List) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Morphable ('Into List) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ~> Morphing ('Into List) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

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

Methods

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

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

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

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

Methods

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

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ~> Morphing ('Rotate 'Right) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ~> Morphing ('Rotate 'Left) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ~> Morphing ('Rotate 'Right) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ~> Morphing ('Rotate 'Left) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

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

Methods

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

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

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

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

Methods

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

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

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

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

Methods

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Right (Tape t) :: Type -> Type

type Substance 'Right (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Tape t) #=@ Substance 'Right (Tape t)) := Available 'Right (Tape t)

sub :: (Tape t #=@ Substance 'Right (Tape t)) := Available 'Right (Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Left (Tape t) :: Type -> Type

type Substance 'Left (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Tape t) #=@ Substance 'Left (Tape t)) := Available 'Left (Tape t)

sub :: (Tape t #=@ Substance 'Left (Tape t)) := Available 'Left (Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Root (Tape t) :: Type -> Type

type Substance 'Root (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Tape t) #=@ Substance 'Root (Tape t)) := Available 'Root (Tape t)

sub :: (Tape t #=@ Substance 'Root (Tape t)) := Available 'Root (Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Right (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Right (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Right (Tap ((t <:.:> t) := (:*:)))) := Available 'Right (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Right (Tap ((t <:.:> t) := (:*:)))) := Available 'Right (Tap ((t <:.:> t) := (:*:)))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Left (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Left (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Left (Tap ((t <:.:> t) := (:*:)))) := Available 'Left (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Left (Tap ((t <:.:> t) := (:*:)))) := Available 'Left (Tap ((t <:.:> t) := (:*:)))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Root (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Root (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Root (Tap ((t <:.:> t) := (:*:)))) := Available 'Root (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Root (Tap ((t <:.:> t) := (:*:)))) := Available 'Root (Tap ((t <:.:> t) := (:*:)))

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure ('Right :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Right (Tape t <:.> Tape t) :: Type -> Type

type Substance 'Right (Tape t <:.> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> (Tape t <:.> Tape t)) #=@ Substance 'Right (Tape t <:.> Tape t)) := Available 'Right (Tape t <:.> Tape t)

sub :: ((Tape t <:.> Tape t) #=@ Substance 'Right (Tape t <:.> Tape t)) := Available 'Right (Tape t <:.> Tape t)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure ('Left :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Left (Tape t <:.> Tape t) :: Type -> Type

type Substance 'Left (Tape t <:.> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> (Tape t <:.> Tape t)) #=@ Substance 'Left (Tape t <:.> Tape t)) := Available 'Left (Tape t <:.> Tape t)

sub :: ((Tape t <:.> Tape t) #=@ Substance 'Left (Tape t <:.> Tape t)) := Available 'Left (Tape t <:.> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Down :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Down (Tape t <:.> Tape t) :: Type -> Type

type Substance 'Down (Tape t <:.> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Down <:.> (Tape t <:.> Tape t)) #=@ Substance 'Down (Tape t <:.> Tape t)) := Available 'Down (Tape t <:.> Tape t)

sub :: ((Tape t <:.> Tape t) #=@ Substance 'Down (Tape t <:.> Tape t)) := Available 'Down (Tape t <:.> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Up :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Up (Tape t <:.> Tape t) :: Type -> Type

type Substance 'Up (Tape t <:.> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Up <:.> (Tape t <:.> Tape t)) #=@ Substance 'Up (Tape t <:.> Tape t)) := Available 'Up (Tape t <:.> Tape t)

sub :: ((Tape t <:.> Tape t) #=@ Substance 'Up (Tape t <:.> Tape t)) := Available 'Up (Tape t <:.> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

Associated Types

type Available 'Right ((t <:.:> t) := (:*:)) :: Type -> Type

type Substance 'Right ((t <:.:> t) := (:*:)) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> ((t <:.:> t) := (:*:))) #=@ Substance 'Right ((t <:.:> t) := (:*:))) := Available 'Right ((t <:.:> t) := (:*:))

sub :: (((t <:.:> t) := (:*:)) #=@ Substance 'Right ((t <:.:> t) := (:*:))) := Available 'Right ((t <:.:> t) := (:*:))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

Associated Types

type Available 'Left ((t <:.:> t) := (:*:)) :: Type -> Type

type Substance 'Left ((t <:.:> t) := (:*:)) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> ((t <:.:> t) := (:*:))) #=@ Substance 'Left ((t <:.:> t) := (:*:))) := Available 'Left ((t <:.:> t) := (:*:))

sub :: (((t <:.:> t) := (:*:)) #=@ Substance 'Left ((t <:.:> t) := (:*:))) := Available 'Left ((t <:.:> t) := (:*:))

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Tap ((t <:.:> t) := (:*:)) a -> u (Tap ((t <:.:> t) := (:*:)) b)

(Divariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) p, Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t >:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

(<-|-) :: (a -> b) -> ((t >:.:> u) := p) a -> ((t >:.:> u) := p) b

(forall i. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (p i), Bivariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) p, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t <:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

(<-|-) :: (a -> b) -> ((t <:.:> u) := p) a -> ((t <:.:> u) := p) b

(forall i. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (p i), Bivariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) p, Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t >:.:< u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

(>-|-) :: (a -> b) -> ((t >:.:< u) := p) b -> ((t >:.:< u) := p) a

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) a -> u (((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) b)

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

Defined in Pandora.Paradigm.Structure.Some.Stream

Methods

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

Extendable ((->) :: Type -> Type -> Type) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

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

Interpreted ((->) :: Type -> Type -> Type) (T_U ct cu p t u)

Defined in Pandora.Paradigm.Schemes.T_U

Associated Types

type Primary (T_U ct cu p t u) a

Methods

run :: T_U ct cu p t u a -> Primary (T_U ct cu p t u) a

unite :: Primary (T_U ct cu p t u) a -> T_U ct cu p t u a

(!) :: T_U ct cu p t u a -> Primary (T_U ct cu p t u) a

(||=) :: (Semigroupoid (->), Interpreted (->) u0) => (Primary (T_U ct cu p t u) a -> Primary u0 b) -> T_U ct cu p t u a -> u0 b

(=||) :: (Semigroupoid (->), Interpreted (->) u0) => (T_U ct cu p t u a -> u0 b) -> Primary (T_U ct cu p t u) a -> Primary u0 b

(<$||=) :: (Semigroupoid (->), Covariant (->) (->) j, Interpreted (->) u0) => (Primary (T_U ct cu p t u) a -> Primary u0 b) -> (j := T_U ct cu p t u a) -> (j := u0 b)

(=||$>) :: (Covariant (->) (->) j, Interpreted (->) u0) => (T_U ct cu p t u a -> u0 b) -> (j := Primary (T_U ct cu p t u) a) -> (j := Primary u0 b)

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) List = Maybe <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) (Construction Maybe) = (Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)

type Morphing ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) = Maybe <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) = (Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) = Wye

type Morphing ('Into (Construction Maybe)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Construction Maybe)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) = Construction Maybe

type Morphing ('Into (Comprehension Maybe)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Comprehension Maybe)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) = Comprehension Maybe

type Morphing ('Into List) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) = List

type Morphing ('Into List) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) = List

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

Defined in Pandora.Paradigm.Structure.Some.Stream

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

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

Defined in Pandora.Paradigm.Structure.Some.Stream

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

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) = Maybe <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:)) = Maybe <:.> ((Identity <:.:> ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) = Maybe <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) = Maybe <:.> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

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

Defined in Pandora.Paradigm.Structure.Some.Binary

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

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

Defined in Pandora.Paradigm.Structure.Some.Binary

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

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

Defined in Pandora.Paradigm.Structure.Some.Binary

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

type Available ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Right :: a -> Wye a) (Tape t) = Identity

type Available ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Left :: a -> Wye a) (Tape t) = Identity

type Available ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Root :: a -> Segment a) (Tape t) = Identity

type Available ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Substance ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Right :: a -> Wye a) (Tape t) = t

type Substance ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Left :: a -> Wye a) (Tape t) = t

type Substance ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Root :: a -> Segment a) (Tape t) = Identity

type Substance ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = t

type Substance ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = t

type Substance ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Right :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Right :: a -> Wye a) (Tape t <:.> Tape t) = Identity

type Available ('Left :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Left :: a -> Wye a) (Tape t <:.> Tape t) = Identity

type Available ('Down :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Down :: a -> Vertical a) (Tape t <:.> Tape t) = Identity

type Available ('Up :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Up :: a -> Vertical a) (Tape t <:.> Tape t) = Identity

type Available ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Available ('Right :: a -> Wye a) ((t <:.:> t) := (:*:)) = Identity

type Available ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Available ('Left :: a -> Wye a) ((t <:.:> t) := (:*:)) = Identity

type Substance ('Right :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Right :: a -> Wye a) (Tape t <:.> Tape t) = Tape t <:.> t

type Substance ('Left :: a -> Wye a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Left :: a -> Wye a) (Tape t <:.> Tape t) = Tape t <:.> t

type Substance ('Down :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Down :: a -> Vertical a) (Tape t <:.> Tape t) = t <:.> Tape t

type Substance ('Up :: a -> Vertical a) (Tape t <:.> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Up :: a -> Vertical a) (Tape t <:.> Tape t) = t <:.> Tape t

type Substance ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Substance ('Right :: a -> Wye a) ((t <:.:> t) := (:*:)) = t

type Substance ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Substance ('Left :: a -> Wye a) ((t <:.:> t) := (:*:)) = t

type Primary (T_U ct cu p t u) a

Defined in Pandora.Paradigm.Schemes.T_U

type Primary (T_U ct cu p t u) a = p (t a) (u a)

type (<:.:>) t u p = T_U Covariant Covariant p t u infixr 2

type (>:.:>) t u p = T_U Contravariant Covariant p t u infixr 2

type (<:.:<) t u p = T_U Covariant Contravariant p t u infixr 2

type (>:.:<) t u p = T_U Contravariant Contravariant p t u infixr 2